Estimating Deposit Insurance Premiums with
Stochastic Interest Rates: The Case of Taiwan
Hwei-Lin Chuang, Shih-Cheng Lee, and Min-Teh Yu *
April 28, 2006
Abstract
This study measures the deposit insurance premium under stochastic interest
rates for Taiwan’s banks by applying the two-step maximum likelihood
estimation method. The estimation results suggest that the current premiums charging 5, 5.5, and 6 basis points per dollar of insured deposits - are too low
and are not proportional to the risks of the insured banks. Moreover, a
comparison of the results estimated from different methods implies that the
under-estimation issue of the deposit insurance premium due to the problems
of statistical inconsistency and efficiency is more serious than that caused by
the exclusion of the interest rate risk. An examination of the size effect
indicates that large banks are more likely to have lower values of credit risk,
asset volatility, and deposit insurance premiums.
1*
Chuang: Department of Economics, National Tsing Hua University, Hsinchu 30013, Taiwan. Fax:
886-3-5722476, Email: hlchuang@mx.nthu.edu.tw. Lee : Department of Accounting, Yuan Ze University,
Jung-Li 32003, Taiwan. Email: sclee@saturn.yzu.edu.tw. Yu: Department of Finance, Providence
University, Taichung 43301, Taiwan. Tel.: 886-4-36320631, Fax: 886-4-26311170, Email:
mtyu@pu.edu.tw. The authors acknowledge the support provided by the National Science Council,
Taiwan. Corresponding author: Yu.
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Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
1. Introduction
Ever since the pioneer work of Merton (1977) showing that deposit insurance
can be modeled as a put option on the assets of insured institution, a lot of literature
on pricing deposit insurance has been accumulated using this option framework.
Progress has been seen in both the theoretical development in the estimation method
and the empirical applications. As to the estimation method, the market-value-based
approach developed by Ronn and Verma (1986) is extensively applied in the literature.
Their method set up a two-equation system - one for the relation between the equity
value and the bank’s asset value, and the other for the relation of the equity volatility
and the asset volatility - to estimate the two unobserved variables in Merton’s pricing
model - namely, the market value and volatility of assets. However, as shown in Duan
(1994), the estimators of the Ronn-Verma method are statistically inconsistent,
because their assumption of a constant equity volatility is incompatible with the
nature of stochastic equity volatilities implied in Merton’s pricing model. Duan (1994)
therefore introduces a maximum likelihood estimation (MLE) approach to deal with
this problem by fully utilizing the distributional assumption in the specification of the
theoretical model.
The empirical estimation of the deposit insurance premiums for banks in Taiwan
did not appear in the literature until the early 1990s.2 The fair pricing of the deposit
insurance premium has been investigated by Yu and Hsu (1993) and Duan and Yu
(1994). Yu and Hsu (1993) compute the premiums directly using the Ronn-Verma
method. Duan and Yu (1994) estimate the deposit insurance value for a group of
Taiwanese banks from 1985 to 1992 and find significant differences in the deposit
2
The Central Deposit Insurance Corporation (CDIC) of Taiwan was established in 1985. It was a
voluntary plan at first, but became compulsory for all depository institutions in 1999. The CDIC
charged a flat premium rate of 5 basis points (bps) in 1985 and 1986, 4 bps in 1987, and 1.5 bps in
1988 through 2000. A risk-based premium has been established since January 1, 2000, and the premium
rates can be 5, 5.5, or 6 bps.
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Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
insurance values estimated from the Ronn-Verma and MLE methods. Both studies
conclude that Taiwan’s premium policy provides subsidies to financial institutions.
In the deposit insurance literature, a typical way to model the dynamics of the
bank asset value is as a lognormal diffusion process. This modeling approach fails to
explicitly take into account the impact of stochastic interest rates on the asset value.
This shortcoming is particularly important for modeling a bank’s asset value, because
it is common for banks to hold a large portion of interest-rate-sensitive assets. Duan,
Moreau, and Sealey (DMS) (1995) are the first to incorporate the dimension of the
stochastic interest rate into the pricing of deposit insurance. However, the DMS
method suffers the same inconsistent problem embedded in the Ronn-Verma method.
To solve the inconsistent problem, Duan and Simonato (2002) apply the two-step
MLE approach to the DMS model. According to their empirical results for a group of
U.S. banks, the deposit insurance premiums using a maximum likelihood estimation
are much higher than those using the modified Ronn-Verma method. Moreover, their
Monte Carlo simulation supports the performance of the MLE method.
In order to measure the effect of the interest rate risk on valuing deposit
insurance in Taiwan, we intend to adopt the DMS deposit-insurance model and
estimate the premiums using the two-step MLE procedure to measure the deposit
insurance premiums with stochastic interest rates. We then compare our estimates
with alternative methods and previous results.
The structure of the paper is as follows. Section 2 reviews the DMS (1995)
model for our empirical framework. The two-step MLE procedure and the description
of the data are presented in Section 3. Section 4 presents the empirical findings and
the discussion of the results. The final section concludes this study by a brief
summary of our major findings.
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Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
2. Model
As the purpose of this study is to reexamine the deposit insurance premium with
the consideration of the interest rate risk for Taiwanese banks, our model is based on
the framework developed in DMS (1995). DMS extend Merton (1977) and Ronn and
Verma (1986) to incorporate stochastic interest rates into the deposit insurance pricing
model by generalizing Ronn and Verma’s two-equation system into a three-equation
structure via dividing the second equation into two separate equations in order to
capture interest rate risk.
The instantaneous interest rate is assumed to follow the mean-reverting
stochastic process as in Vasicek (1977) and can be expressed as:
drt  q (m  rt )dt  dZ rt ,
(1)
where rt is the instantaneous spot rate at time t, m is the long-run mean of the
instantaneous spot rate,  is the volatility of the instantaneous spot rate, q is a
positive constant measuring the magnitude of the mean-reverting force, and Z rt is a
Wiener process.
As to the bank’s assets, they are assumed to be characterized by a log-normal
process as the following:
dVt
 dt   V dZ Vt ,
Vt
(2)
where Vt represents the value of bank assets at time t,  and  V respectively
denote the instantaneous expected return and the volatility of the return on bank assets,
and Z Vt is a Wiener process.
The volatility of the assets of a depository institution,  V , is decomposed into
two parts - the interest rate risk and the credit risk as the following:
 V  V2 2  2 ,
(3)
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Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
where V is the instantaneous interest rate elasticity of the assets, and V   V  /  .
We define  to be the volatility of assets that is orthogonal to the interest rate and
1
   V (1   2 ) 2 . In addition,  is a correlation coefficient between the Wiener
processes Z Vt and Z rt , i.e.,   corr (dZVt , dZ rt ) / dt .
Because the parameter  V cannot be observed directly, DMS (1995) derive the
following two equations for the observable variable: bank’s equity return, denoted
by Qt as the substitutes.
Q   t [V  B(t , T )]  B(t , T ) ,
(4)
 Q  Q2  2   t2 2 ,
(5)
t
and
t
where  Qt
t
is the volatility of return on equity,
 t  N (ht )Vt / Qt , and
B(t , T )  [1  e  q (t ,T ) ] / q , which denotes the negative of the instantaneous interest rate
elasticity of the default-free zero-coupon bond. As shown in Vasicek (1977), given the
assumption of a constant risk premium , the price of a zero-coupon bond with $1
face value and T-t periods of maturity, P(rt , t , T ) , is equal to:
P(rt , t , T )  A(t , T )e  B (t ,T ) rt ,
(6)
where

v 2 B 2 (t , T ) 
A(t , T )  exp  ( B(T  t )  (T  t )) 
,
4q


v v 2
  m  2 .
q 2q
Let the face value of insured deposits be F. Since the deposits are insured, the
full obligation to the depositors at time T is X  Fe RT , where R is the fixed and
continuously compounded rate of return on these deposits. We can relate the equity
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Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
value, Qt , and the asset value, Vt , of a depository institution as the following:
Qt  Vt N (ht )  XP(rt , t , T ) N (ht   t ) ,
(7)
where
ht 

 t
Vt
ln 
 ,
 t  P(rt , t , T ) X  2
1
 (T ) 1 q (T )

 2 e
1 
q
 q

 t2  (V2 v 2   2 )(T  t )  2V v 2 

 (T ) 2
 1  e 2 q (T )
 v 2  2  3 e  q (T )  1  
3
q
 2q
q




 .

Based on the stochastic process specification for the instantaneous interest rate
(equation (1)) and for the bank’s assets (equation (2)), it can be shown that the market
value of deposit insurance premium per dollar of insured deposits at time t, I t , is
given by:
I t  XP(rt , t , T )[1  N (ht   t )]  Vt [1  N (ht )] .
(8)
By solving the simultaneous system of Equations (4), (5), and (7), we can obtain
the values of V ,  , and Vt . We then can solve for the premium of deposit
insurance by plugging the values of Vt , V , and  into Equation (8).
3. Estimation Procedure and Data
3.1 MLE for Vasicek’s Term Structure Model
The log-likelihood function of the instantaneous spot rate of Vasicek (1977) as
shown in equation (1) is developed in Duan (1994) as follows:
Lr (rt , t  1,..., n; q, m, v) 

n
n 1
n 1
1
ln( 2 ) 
ln V (v, q ) 
[rt  m  (rt 1  m)e q ]2 ,

2
2
2V (v, q) t 2
(9)
where V (v, q ) is the conditional variance of rt . However, rt is unobservable and
therefore the likelihood function shown in equation (9) cannot be applied. Given that
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Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
the price of a zero-coupon bond with $1 face value and a maturity of T-t period is
specified as equation (6), at a certain period of time t, the continuously compounded
interest rate on the zero-coupon bond with maturity T-t, Rt (T  t ) , can be written as:
Rt (T  t )  
B(T  t; r )
1
1
ln Pt (T  t; r )  
ln A(T  t; r ) 
rt ,
T t
T t
T t
(10)
where  r denotes the set of interest rate parameters q , m ,  , and  . As
Rt (T  t ) is observable, equation (10) is the key for transformation.
The transformation from unobservable rt to the observable Rt (T  t ) through
equation (10) leads to the following log-likelihood function.
L( Rt (T  t ), t  1,..., n; r )  (n  1) ln( T  t )  (n  1) ln B(T  t; r )
^
where
r t ( r ) 

n 1
n 1
ln( 2 ) 
ln V (v, q )
2
2

n
^
^
1
[r t ( r )  m  (r t 1 ( r )  m)e  q ] 2 ,

2V (v, q ) t  2
1
[(T  t ) Rt (T  t )  ln A(T  t ; r )] .
B(T  t ; r )
This
(11)
likelihood
function based on the observable Rt (T  t ) can then be used to estimate the interest
rate parameters  r .
3.2 Two-Step MLE for the Deposit Insurance Premiums
D&S (2002) develops a MLE procedure to estimate the three-equation system of
DMS (1995) in order to avoid the inconsistency problem due to confusing the
parameters with random variables. This MLE procedure is briefly described as below.
Let wt be a 2×1 vector of unobserved variables at time t and wt  [rt , ln Vt ]' ,
and yt is a 2×1 vector of observed variables at time t and yt  [ P(rt , t , T ), Qt ]' . Let
 be a parameter vector, in which elements are related to the two unobserved
variables and   [q, m, v,  ,  , V ,]' . The mapping relation between the observable
and the unobservable variables is Y  M (W ; ) , where Y  [ y1' ,..., y n' ]' and
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Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
W  [ w1' ,..., wn' ]' . Given this mapping relation, it can be shown that the density
function of W is a multivariate normal distribution (D&S (2002), p. 115), and
therefore we can derive an expression for the likelihood function of W .

 V 
Define ut  rt , ln  t 
 Vt 1 




 Vˆt ( ) 
 . Applying the
and uˆ t ( )  rˆt ( ), ln 
 Vˆ ( ) 

 t 1

above mapping relation, the logarithm of the full-information likelihood function for
the DMS (1995) model is then given by:
L( ; P(), Qt , t  1,, n)

n 1
1 n

ln    uˆt ( )  Et 1 (ut ) 1 uˆt ( )  Et 1 (ut )
2
2 t 2
n
  ln[ P(rt , t , T ) B(t , T )Vt N (ht )] ,
(12)
t 2
where Et 1 (ut ) is the expected value and  is the covariance matrix of u t .
Given this likelihood function it seems straight forward to estimate the parameter
values in  and then substitute these estimates into equation (8) to solve for the
deposit insurance premium It. However, there are two issues for directly applying the
likelihood function of equation (12) to obtain the parameter estimates. First, Equation
(12) is specified for a single bank only. If there is more than one bank, then this
likelihood function should be expanded for joint estimation. This will become inpractically complex as the number of banks grows. Second, the time structure effect
of the interest rate is a long-run phenomenon, as Vasicek’s mean-reverting process for
the interest rate suggests that it usually takes a long time for the interest rate to return
to its mean level. On the contrary, the movement of asset value (and the movement of
equity value) changes rapidly, or in other words, it is a short-run phenomenon and
should be captured in a short period of time. Therefore, it is inappropriate to set the
same time horizon for estimating parameters of the bond pricing model to capture the
mean reversion in the interest rate and for estimating the equity valuation function to
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Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
yield the volatility parameters.
D&S (2002) proposes a two-step estimation procedure to deal with these
problems. The first step is to estimate the interest rate parameters only, which is
similar to the approach in Duan (1994). The second step is to estimate the equity
valuation parameters in Equation (12) taking the interest rate parameters obtained in
the first step as given. This two-step estimation procedure not only produces
consistent estimators, but also allows for setting different time horizons in the
estimation of the interest rate parameters and the parameters of the bank’s equity
value function.
In sum, our estimation procedure can be described as a two-step maximum
likelihood approach. The first step estimates the interest rate parameters for each year
using daily commercial paper observations during the ten-year preceding period. A set
of ten-year interest rate data is used in order to capture the long-run mean-reverting
characteristics. For example, the daily observations of 1982 to 1991 are taken to
obtain the interest rate parameters of 1991. The same procedure is run to yield interest
rate parameters for each year from 1991 through 2002. Hence, we have twelve sets of
interest rate parameter estimates.
The second step estimates equity valuation parameters of the objective year with
the interest rate parameters treated as given - that is, in the second step the interest rate
parameters are set at the values calculated from the first step, and then the equity
valuation parameters are obtained based on the data of daily equity and quarterly
updated debt observations for each bank at each available year. This procedure is
repeated twelve times for each bank at the available years in our sample period.
3.3 Data
The sample in this study includes twenty-eight banks chosen from domestic
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Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
CDIC-insured financial institutions in Taiwan. These sample banks are all listed in the
TSE and therefore their daily stock return data are available. Their listed codes in the
TSE are 2801, 2802, 2803, 2806, 2807, 2808, 2809, 2811, 2812, 2815, 2824, 2826,
2828, 2829, 2830, 2831, 2834, 2836, 2837, 2838, 2839, 2840, 2842, 2843, 2844, 2845,
2847, and 2849.
The daily stock return and the quarterly equity and debt data of balance sheets
are from the TEJ database. These observations span from 1991 to 2002. The
dividend-adjusted market value of equity is measured by multiplying the daily price
with the common shares outstanding. The debt is updated quarterly according to the
quarterly balance sheet.
Because the purpose of this study is to examine the deposit insurance premium, it
would be better to construct a debt series including the deposits only. However, the
TEJ database did not record the detailed data of deposits until recent years, and as
such it is impossible to construct a complete debt series for total deposits for our
entire sample period. Therefore, the debt variable is defined to be total debt from the
balance sheets in our debt series. One advantage of using the total debt information is
that historically all debts, insured and uninsured, are treated the same when banks fail.
The interest rate data used in this study are drawn from the three-month
commercial paper collected from the TEJ database. The daily observations of the
primary 90-day commercial paper are drawn for years from 1982 to 2002 to estimate
the interest rate parameters.
4. Results and Discussion
4.1 Interest Rate
The estimation results of the interest rate parameters from the first step are
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Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
reported in Table 1. The estimates of the long-run mean m based on a 10-year
sample period are all significant for the years from 1991 to 2002. This estimate
increases gradually from 0.686 in 1991 to the maximum of 0.808 in 1997. It then
reduces at a faster rate from 0.808 to the minimum of 0.0498 in 2002. This inverse U
shape of a first increasing pattern and then a decreasing pattern is also shown in the
estimated values for the volatility parameter  . The maximum value of estimates for
 is 0.0513 for the year 1997 and the minimum value occurs at 0.0282 for the year
2002.
The estimates of the mean-reverting force parameter q vary a great deal from
the minimum of 0.4597 in 1991 to the maximum of 1.8930 in 2000. This greater
variation in the estimation results for q is similar to those found in D&S (2002).
Moreover, there is no clear pattern for the changes in the estimated values of q .
Finally, the estimates of risk premium  are all insignificant with an undetermined
sign.
4.2 Deposit Insurance Premium
The second step maximum likelihood estimation results of the deposit insurance
premium are presented in Tables 2 and 3. Table 2 reports the results for one specific
bank - the First Commercial Bank. We also estimate the deposit insurance premium
without the consideration of the interest rate risk as in Duan and Yu (1994) and the
results are presented in the lower panel of Table 2. The estimated values of the deposit
insurance premium for this specific bank vary from the minimum of 0.0397 for 1996
to the maximum of 120.7303 for the year 2000. The two-step maximum likelihood
estimated deposit insurance premium for each year is higher than the premiums
estimated in Duan and Yu (1994). This result is intuitively plausible as the two-step
MLE approach include the interest rate risk while Duan and Yu do not consider the
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Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
interest rate risk in their model.
In order to have a general idea about the results of all the banks in our sample,
the value-weighted averages of the estimation results for the 28 banks in our study are
reported in Table 3. We also estimate the deposit insurance premium based on DMS’s
(1995) method and Duan and Yu’s (1994) approach for comparison. These estimation
results are all reported in Table 3. The value-weighted average of the two-step
maximum likelihood estimates of the deposit insurance premium, denoted by IPPmle
in Table 3, ranges from 5.0125 to 396.9562. It is plausible to have such a big variation
in the estimated values of the deposit insurance premium given the volatile market
risk. These value-weighted average estimates are all much higher than the flat-rate
assessments at 1.5 basis points from 1997 to 1999 and the three-level flat-rate
premiums (5, 5.5, and 6 basis points) charged by CDID from 2000 onwards.
Table 3 also reports the year-end market value of equity (denoted by Equity), the
year-end book value of debt (denoted by Debt) and the ratio of Equity and Debt
(denoted by E/D). According to Table 3, the E/D ratio and the value of assets have a
positive relationship. Since the equity is viewed as a call option on the value of assets
in which the strike price is its debt value, the inputs of equity and debt value through a
proper transformation can yield the estimates of the asset values and volatility, and
then can be used to calculate the deposit insurance premiums. In addition, the E/D
ratio and the insurance premium are negatively related since the asset values and
volatility are the inputs of the deposit insurance premium through their put-option
relationship. As the equity is calculated by multiplying the stock price with the
outstanding common shares, the denominator of the E/D ratio is highly positively
related to the weighted stock market index and the weighted bank stock index.
The result of the two-step MLE approach shows that the maximum likelihood
estimates of instantaneous expected return on assets,  mle , are statistically
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Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
insignificant with un-determined signs. The estimates of credit risk,  mle , are
significant and positive. All the estimates of the interest rate elasticity of a bank’s
assets,  mle , are negative. This finding is consistent with the negative relationship
between the interest rate and the asset value. The estimates of the bank asset value,
Vmle , and the value of insurance premium per dollar of insured deposits, IPPmle , are
significant. A larger estimate of Vmle is not necessary to predict a smaller estimate of
IPPmle as shown in Table 3. This is because the determinants of IPPmle include not
only Vmle , but also the estimates of volatility,  mle and  mle .
The estimates of the bank asset value, Vmle , are higher than the book value of
debts. However, they are smaller than the sum of the book value of debts and the
market value of equity. Their differences are 20169, 17170, 16990, 17503, 18221,
15990, 17555, 19537, 20568, 31238, 28196, and 42857 million dollars (NT$) from
1991 through 2002 respectively.
From the results of the modified Ronn-Verma method, the estimates of credit risk
of the non-MLE method,  mrv , are smaller than those of the two-step MLE method,
 mle , which explains for the vast difference between their estimated deposit insurance
premiums. The deposit insurance premiums of the modified Ronn-Verma method are
highly under-estimated. This finding is similar to that of D&S (2002) for ten U.S.
banks. Both the empirical studies of Duan and Yu (1994) for Taiwanese banks and
D&S (2002) for the U.S. banks point out that the modified Ronn-Verma method
seriously underestimates the insurance premium, because of the problems of
inconsistency and asymptotic inefficiency. In other words, our findings provide
further evidence to support the arguments in Duan and Yu (1994) and D&S (2002).
According to the results estimated based on the MLE of the Ronn-Verma method,
the maximum likelihood estimates of instantaneous expected return on assets without
considering the stochastic interest rate,  DY , are not significant, and neither are those
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Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
of  mle . The Ronn-Verma method takes the volatility as a whole, whereas the
modified Ronn-Verma method decomposes the volatility into two parts. Hence, the
estimates of asset value differ between these two methods. The estimates of asset
value based on the Ronn-Verma method are higher than those estimated from the
modified Ronn-Verma.
Comparing the results of the two-step MLE for the deposit insurance premium
with those obtained from the modified Ronn-Verma method (denoted by IPPmrv) and
Duan and Yu’s approach (denoted by IPPDY), it is found that the two-step MLE yields
much higher deposit insurance premium estimates than IPPmrv, while the two-step
MLE and Duan and Yu’s approach have much closer estimation results. These results
imply that the under-estimation issue due to the problem of statistical inconsistency
and efficiency is more serious than the exclusion of the interest rate risk. Moreover,
IPPmle is somewhat larger than IPPDY in every year except for the years of 1991, 1996,
1997 and 1998. According to D&S (2002), the two-step MLE procedure yields higher
values of the deposit insurance premium, because of the larger estimates of the credit
risk and the lower estimated values for banks’ assets than the corresponding book
values of debts.
The volatility of assets is divided into two parts:
interest-rate risk and credit
risk - and their relation can be expressed as  V  V2 2   2 . The estimation
results in Table 3 suggest that neither the interest rate risk nor the credit risk
dominates in explaining the volatility of asset values. These two components jointly
affect the volatility of asset values.
4.3 Size Effect
In order to examine whether bank size has any implication in determining the
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Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
deposit insurance premium, we further classify our samples into three categories 3 and
conduct the second-step estimation procedure to investigate the size effect on the
deposit insurance premium.
Table 4 presents the estimation results of the subsamples for large, medium, and
small banks, respectively. Panel A presents the results based on Duan and Yu’s method
(1994) which treats the total asset risk as a whole, and Panel B reports the results
based on the two-step MLE method which includes the interest rate risk as well as the
asset risk. As shown in Panel A, the estimates of total risk,  DY , decease as the firm
size grows. The estimates of  DY are in general the largest for small banks and the
smallest for large banks.
The estimates of the deposit insurance premium for the large banks are smaller
than the estimates of medium banks for all sample periods except for the year 1992.
However, there is no consistent pattern of the difference in the estimates of the deposit
insurance premium between medium banks and small banks. Comparing the large
bank group with the small bank group, the estimates of insurance premium for large
banks are smaller than those of the small banks except for 1991. In other words, large
banks tend to have smaller estimates of the deposit insurance premium due to their
relatively smaller estimates of total risk.
According to Panel B, all the estimates of credit risk,  mle , are smaller for the
large banks than that for the small banks. However, there is no unanimous direction of
pattern both between the large and medium banks and between the medium and small
banks.
3
The criteria to classify the size of our sample banks are: A bank is classified as a large bank if its asset
value is higher than NT$700 billion and a small bank if its asset value is lower than NT$100 billion at the end
of 1991 and 1992. As for 1993, 1994, and 1995, a large bank is defined to have assets larger than NT$800
billion, and a small bank has assets lower than NT$150 billion. For the period of 1996-2002, a large bank has
assets larger than NT$1,000 billion. A small bank has assets lower than NT$150 billion for 1996, NT$200
billion for 1997, NT$300 billion for 1998, and NT$350 billion for the period of 1999-2002. If a bank is neither
a large nor a small one according to the above definition, then it will be classified as a medium bank.
- 15 -
Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
As for the estimates of interest rate elasticity of bank assets,  mle , the absolute
value of estimates is smaller for the large banks than that for the medium banks, and
the absolute value of estimates is smaller for the medium banks than that for the small
banks. The absolute value of the estimates for the interest rate elasticity of bank assets,
in general, decreases with banks. Larger banks have smaller interest rate responses.
Given that large banks tend to have smaller credit risk and smaller absolute value
of interest rate elasticity of bank assets, their estimated deposit insurance premium,
IPPmle, is smaller than that for the medium and small banks except for a few years.
However, there is no apparent clear-cut difference in the estimated deposit insurance
premium between medium and small banks. In sum, both Panel A and Panel B show
the risks are lower for large banks, and therefore the estimated deposit insurance
premiums are smaller for them.
Based on the estimation results of this study, the current risk-based premiums of
5, 5.5, and 6 basis points are too low and are not proportional to the risks of the
insured banks. These under-priced premiums as well as not being able to close down
undercapitalized banks promptly together may encourage insured banks to take
excessive risk, which destabilizes the deposit insurance scheme and the banking
system. The regulators should at least enhance the supervision to contain their risk
exposure and charge risk-based premiums according to their economic risk exposure
measured by market-based data.
5. Conclusion
This study applies the two-step maximum likelihood estimation approach
derived in D&S (2002) to estimate the interest rate and equity pricing parameters,
which are then used to measure the deposit insurance premiums for banks in Taiwan.
The first step of our empirical procedure is to estimate the interest rate parameters by
MLE based on the Vasicek term structure model. The interest rate parameters are
- 16 -
Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
brought into the full-information likelihood function as fixed in the second step to
estimate the equity pricing parameters. The deposit insurance premium is calculated
through the option relationship between the bank asset values and the deposit
insurance premium. This two-step MLE method can solve the inconsistent and
asymptotic inefficient problems of the DMS (1995) method
Our empirical results indicate that the present premiums set up by the CDIC - 5,
5.5, and 6 basis points - are too low and are not proportional to the risks of the insured
banks. The bank characteristic of market value of equity to book value of debts ratio
is positively related with the asset value and negatively related with the deposit
insurance premium. Moreover, the weighted stock market index and the weighted
bank stock index have a positive relation with the market value of equity to book
value of debts ratio.
The two-step maximum likelihood estimates of deposit insurance premiums are
much higher than those estimated from the modified Ronn-Verma method after
solving the simultaneous equations directly. This is due to higher values of credit risk
estimated from the former method. This finding coincides with that of Duan and Yu
(1994) and D&S (2002). A comparison of the results among the two-step MLE
approach, the modified Ronn-Verma method, and Duan and Yu’s (1994) procedure
further implies that the under-estimation issue of the deposit insurance premium due
to the problem of statistical inconsistency and inefficiency is more serious than that
caused by the exclusion of the interest rate risk.
After classifying the sample banks by their size to investigate the size effect on
the deposit insurance premium, it is found that small banks have higher estimates of
credit risk, asset volatility, and deposit insurance premiums. On the contrary, the large
banks have smaller estimates of credit risk, asset volatility, and deposit insurance
premiums. In sum, this study estimates deposit insurance premiums with
- 17 -
Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
incorporation of the interest rate risk and provides further evidence that there is a
serious underestimation of the deposit insurance premium due to the problems of
inconsistency and asymptotic inefficiency in the Ronn-Verma method.
References
Black, F. and M. Scholes, 1973, The pricing of options and corporate liabilities,
Journal of Political Economy 81, 637-659.
Cox, J. C., J. E. Ingersoll, and S. A. Ross, 1985, A theory of the term structure of
interest rates, Econometrica 53 (2), 385-402.
Duan, J. C., 1994, Maximum likelihood estimation using price data of the derivative
contract, Mathematical Finance 4 (2), 155-167.
Duan, J. C., A. Moreau and C. W. Sealey, 1995, Deposit insurance and bank interest
rate risk: Pricing and regulatory implications, Journal of Banking and Finance
19, 1091-1108.
Duan, J. C. and J. G. Simonato, 2002, Maximum likelihood estimation of deposit
insurance value with interest rate risk, Journal of Empirical Finance 9 (1),
109-132.
Duan, J. C. and M. T. Yu, 1994, Assessing the cost of Taiwan’s deposit insurance,
Pacific Basin Finance Journal 2, 73-90.
Hull, John C., 2000, Options, futures, and other derivatives, 4th edition, Prentice-Hall,
Inc..
Laeven, Luc, 2002, Bank risk and deposit insurance, The World Bank Economic
Review 16 (1), 109-137.
Laeven, Luc, 2002, Pricing of deposit insurance, World Bank Policy Research
Working Paper 2871.
Merton, R. C., 1977, An analytic derivation of the cost of deposit insurance and loan
guarantees, Journal of Banking and Finance 1, 3-11.
Ronn, E. I. and A. K. Verma, 1986, Pricing risk-adjusted deposit insurance: An
option-bases model, Journal of Finance 41, 871-895.
Vasicek, O., 1977, An equilibrium characterization of the term structure, Journal of
Financial Economics 5, 177-188.
Yu, M.-T and L.-L. Hsu, 1993, Regulatory Constraints and Deposit Insurance Pricing,
Taiwan Economic Review, Vol. 21, No. 1, pp. 45-59.
- 18 -
Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
Table 1. Estimation Results of the Interest Rate Parameters
Vasicek (1977) assumes the instantaneous spot rate follows a mean-reverting process: drt  q(m  rt )dt  dZ t , where rt is the instantaneous
risk-free rate of interest at time t, m is the long-run mean of the interest rate,  is the volatility of the interest rate, q is a positive constant
measuring the magnitude of the mean-reverting force, and Z t is a Wiener process.  denotes the risk premium.
Paramet 1982-199 1983-19 1984-19 1985-19 1986-19 1987-19 1988-19 1989-19 1990-19 1991-20 1992-20 1993-20 1982-20
ers
1
92
93
94
95
96
97
98
99
00
01
02
02
m
0.0686 0.0724 0.0706 0.0739 0.0749 0.0758 0.0808 0.0784 0.0715 0.0678 0.0608 0.0498 0.0603
(0.0327) (0.0236) (0.0239) (0.0235) (0.0216) (0.0179) (0.0123) (0.0112) (0.0120) (0.0078) (0.0140) (0.0252) (0.0187)
q
0.4597 0.6408 0.6409 0.6726 0.7602 0.9162 1.4440 1.6239 1.3557 1.8930 1.0678 0.6554 0.4625
(0.3227) (0.3431) (0.3449) (0.3699) (0.3841) (0.3877) (0.4394) (0.4634) (0.4526) (0.6946) (0.5822) (0.4952) (0.2068)
v
0.0429 0.0446 0.0448 0.0468 0.0481 0.0469 0.0513 0.0501 0.0428 0.0374 0.0328 0.0282 0.0348
(0.0018) (0.0019) (0.0019) (0.0022) (0.0023) (0.0022) (0.0027) (0.0028) (0.0023) (0.0030) (0.0023) (0.0017) (0.0009)
λ
0.0140 0.0060 -0.0109 -0.0467 -0.1004 0.0583 0.0860 0.3575 0.3361 0.4001 0.4380 0.3581 0.1834
(0.5486) (0.5360) (0.5407) (0.5357) (0.5448) (0.5512) (0.5522) (0.5589) (0.5523) (0.5500) (0.5419) (0.5410) (0.3811)
- 19 -
Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
Table 2. Estimation Results for the First Commercial Bank
Equity is the year-end market value of shareholders’ equity and Debt is the year-end total debt from the quarterly balance sheet obtained from
the TEJ database. Equity and debt are in million NT$. E/D is the ratio of Equity over Debt.  mle is the two-step MLE estimate of instantaneous
expected return on assets.  mle is the two-step MLE estimate of credit risk.  mle is the two-step MLE estimate of interest rate elasticity of assets.
Vmle is the two-step MLE estimate of year-end assets. IPPmle is the two-step MLE estimate of the insurance premium per dollar of insured deposits
in basis points.  mrv ,  mrv , Vmrv , and IPPmrv are the solutions of the modified Ronn-Verma method (with interest rate risk).  DY ,  DY , VDY , and
IPPDY are estimated from the MLE of the Ronn-Verma method as in Duan and Yu (1994). The standard errors are shown in parentheses.
Year end
1991
Equity
118973
Debt
E/D
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
84206
216530
263846
181535
302862
246303
141624
128036
75110
82547
87897
767118
719899
808414
811526
835293
888069
977003
1024201
1096443
1147297
1192000
1252581
0.1551
0.1170
0.2678
0.3251
0.2173
0.3410
0.2521
0.1383
0.1168
0.0655
0.0693
0.0702
Two-Step Maximum Likelihood Estimation Results
Year end
1991
1992
 mle
0.0048
-0.0706
(0.1017)
 mle
 mle
mle
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
0.2113
0.0291
-0.0368
0.1489
0.0372
-0.0391
0.0309
0.0005
0.0331
0.0088
(0.1223)
(0.1363)
(0.1133)
(0.0731)
(0.0911)
(0.1293)
(0.0841)
(0.0830)
(0.0796)
(0.0610)
(0.0687)
0.0960
0.0741
0.0958
0.1024
0.0631
0.0755
0.1127
0.0689
0.0628
0.0595
0.0418
0.0468
(0.0037)
(0.0035)
(0.0036)
(0.0035)
(0.0020)
(0.0017)
(0.0041)
(0.0021)
(0.0027)
(0.0020)
(0.0015)
(0.0021)
-0.5409
-0.5379
-0.7004
-0.4023
-0.6237
-0.3885
-0.3194
-0.1680
-0.5214
-0.4951
-0.4724
-0.6991
(0.3057)
(0.1805)
(0.4162)
(0.3203)
(0.2377)
(0.1830)
(0.1664)
(0.3478)
(0.2930)
(0.3829)
(0.0967)
(0.2685)
- 20 -
Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
Vmle
IPPmle
860858
780860
1000523
1050957
991754
1164288
1193079
1134293
1190484
1182313
1237627
1300818
(400)
(385)
(74)
(25)
(7)
(0)
(226)
(142)
(254)
(460)
(222)
(493)
58.1601
55.0445
5.3707
2.2540
0.8850
0.0397
19.2049
23.1253
30.7240 120.7303
44.3697
59.7137
(8.1812)
(9.2860)
(1.9328)
(0.6786)
(0.3335)
(0.0137)
(3.9380)
(2.9650)
(4.9364)
(4.7320)
(8.3119)
(6.2641)
MLE of the Ronn-Verma Method, Duan & Yu (1994)
Year end
1991
1992
 DY
0.0001
-0.0803
(0.1119)
 DY
VDY
IPPDY
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
0.2211
0.0152
-0.0275
0.1569
0.0279
-0.0320
0.0479
0.0039
0.0608
0.0298
(0.0530)
(0.1579)
(0.0957)
(0.0699)
(0.0928)
(0.1359)
(0.0999)
(0.0845)
(0.1092)
(0.0879)
(0.0577)
0.1048
0.0498
0.1077
0.0944
0.0653
0.0800
0.1145
0.0755
0.0688
0.0742
0.0562
0.0444
(0.0030)
(0.0011)
(0.0013)
(0.0029)
(0.0016)
(0.0013)
(0.0019)
(0.0012)
(0.0018)
(0.0011)
(0.0011)
(0.0009)
882469
803928
1024464
1075336
1016806
1190928
1222109
1164310
1222552
1210362
1270060
1338793
(445)
(30)
(42)
(13)
(6)
(1)
(126)
(128)
(247)
(534)
(332)
(155)
47.2174
2.4675
5.9447
0.4433
0.2633
0.0273
12.2447
14.7955
17.5799 104.9920
37.6452
13.4592
(5.7990)
(0.4108)
(0.5203)
(0.1560)
(0.0744)
(0.0073)
(1.2893)
(1.2504)
(2.2502)
(2.7881)
(1.2401)
- 21 -
(4.6524)
Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
Table 3.
Estimation Results of the Deposit Insurance Pricing Model
Equity is the year-end market value of shareholders’ equity and Debt is the year-end total debt from the quarterly balance sheet obtained from
the TEJ database. Equity and debt are in million NT$. E/D is the ratio of Equity over Debt.  mle is the two-step MLE estimate of instantaneous
expected return on assets.  mle is the two-step MLE estimate of credit risk.  mle is the two-step MLE estimate of interest rate elasticity of assets.
Vmle is the two-step MLE estimate of year-end assets. IPPmle is the two-step MLE estimate of the insurance premium per dollar of insured deposits
in basis points.  mrv ,  mrv , Vmrv , and IPPmrv are the solutions of the modified Ronn-Verma method (with interest rate risk).  DY ,  DY , VDY , and
IPPDY are estimated from the MLE of the Ronn-Verma method as in Duan and Yu (1994). The standard errors are shown in parentheses.
Year end
1991
Equity
111133
Debt
E/D
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
68884
164753
208183
135684
167443
132923
72200
73069
47727
50051
50437
591577
530772
561230
578402
600364
530395
544026
581093
611020
648430
689040
731614
0.1879
0.1298
0.2936
0.3599
0.2260
0.3157
0.2443
0.1242
0.1196
0.0736
0.0726
0.0689
Two-Step Maximum Likelihood Estimation Results
Year end
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
 mle
0.0290
-0.0235
0.2132
0.1081
-0.0272
0.1447
0.0700
-0.0161
0.0520
-0.0110
0.0387
0.0130
(0.1482)
(0.1303)
(0.1446)
(0.1374)
(0.1122)
(0.1215)
(0.1807)
(0.1472)
(0.1417)
(0.1826)
(0.1909)
(0.2644)
0.1318
0.0864
0.1032
0.1177
0.0819
0.0882
0.1140
0.0780
0.0826
0.0947
0.0802
0.0972
(0.0049)
(0.0038)
(0.0038)
(0.0040)
(0.0027)
(0.0024)
(0.0040)
(0.0020)
(0.0033)
(0.0030)
(0.0038)
(0.0045)
-0.5942
-0.5437
-0.6710
-0.4600
-0.6860
-0.4706
-0.3900
-0.2535
-0.5074
-0.4631
-0.4817
-0.8213
(0.3504)
(0.2194)
(0.3749)
(0.2339)
(0.3017)
(0.2306)
(0.2026)
(0.4133)
(0.3600)
(0.4159)
(0.3416)
(0.9111)
 mle
 mle
mle
- 22 -
Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
Vmle
IPPmle
682541
582486
708993
769082
717827
681848
659394
633756
663521
664919
710895
739194
(353)
(283)
(56)
(43)
(47)
(10)
(190)
(204)
(340)
(718)
(808)
(2323)
70.9280
48.0653
5.0125
7.4044
16.3508
10.2450
65.0354
98.0546 120.7537 311.6521 245.1668 396.9562
(9.5399)
(8.1635)
(1.5731)
(1.7792)
(2.0295)
(1.0192)
(7.1751)
(6.6884) (11.9247) (16.9328) (20.2827) (37.5695)
The Modified Ronn-Verma Method, DMS (1995)
Year end
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
 mrv
 mrv
0.0595
0.0413
0.0955
0.1048
0.0476
0.0512
0.0817
0.0436
0.0416
0.0423
0.0366
0.0317
-0.6007
-0.7774
-0.9080
-0.4697
-0.9143
-0.4644
-0.5428
-0.5083
-0.3448
-0.4012
-0.7354
-0.7484
Vmrv
684968
583843
709149
769148
717595
681597
659115
634445
663532
674476
714572
758914
IPPmrv
0.4713
1.0717
2.0661
2.7767
0.0943
0.1873
5.3700
8.3037
8.7880
48.1875
40.8671
40.1631
MLE of the Ronn-Verma Method, Duan & Yu (1994)
Year end
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
 DY
0.0183
-0.0357
0.2204
0.0913
-0.0188
0.1552
0.0576
-0.0093
0.0660
-0.0063
0.0633
0.0399
(0.1667)
(0.1036)
(0.1504)
(0.1331)
(0.1072)
(0.1385)
(0.1947)
(0.1752)
(0.1542)
(0.1736)
(0.1830)
(0.1522)
0.1438
0.0799
0.1104
0.1178
0.0862
0.0965
0.1204
0.0892
0.0945
0.1028
0.0887
0.0870
(0.0032)
(0.0013)
(0.0017)
(0.0027)
(0.0016)
(0.0017)
(0.0023)
(0.0017)
(0.0017)
(0.0018)
(0.0019)
(0.0018)
698668
599897
726043
786550
735965
697847
675685
651739
687169
685866
734626
773161
(339)
(45)
(25)
(19)
(22)
(14)
(122)
(183)
(263)
(666)
(598)
(709)
72.3888
19.7417
4.3238
6.0281
14.4990
15.0560
67.3298
99.6722 109.0419 244.7238 189.7599 255.3895
(6.0486)
(1.3654)
(0.4248)
(0.4973)
(0.6971)
(1.0464)
(3.8054)
(5.7464)
 DY
VDY
IPPDY
- 23 -
(5.5437)
(9.9918)
(9.7099)
(9.7841)
Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
Table 4.
Size Effect on Deposit Insurance Premium
The sample banks are grouped into three categories by their size in order to examine the size effect on deposit insurance premium. Panel A
reports the results estimated from the MLE of the Ronn-Verma method and Panel B presents the two-step MLE results. The results reported are the
value-weighted average of each subsample. The portfolios of each subsample change every year, according to their asset values. The standard errors
of estimates are in parentheses.
Panel A: MLE of the Ronn-Verma Method
Large Banks
Year end
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
 DY
0.0240
-0.0830
0.1819
0.0715
-0.0455
0.1482
0.0215
-0.0295
0.0491
-0.0099
0.0645
0.0330
(0.1453)
(0.0625)
(0.1407)
(0.1029)
(0.0774)
(0.0983)
(0.1357)
(0.1129)
(0.1060)
(0.1307)
(0.1382)
(0.0687)
0.1216
0.0567
0.1033
0.1011
0.0708
0.0834
0.1163
0.0831
0.0769
0.0818
0.0693
0.0477
(0.0026)
(0.0009)
(0.0014)
(0.0029)
(0.0015)
(0.0014)
(0.0022)
(0.0015)
(0.0015)
(0.0014)
(0.0014)
(0.0009)
854628
786256
964034
1047889
979022
1132566
1154029
1113205
1155216
1143538
1207731
1273303
(405)
(41)
(34)
(12)
(11)
(3)
(134)
(196)
(297)
(755)
(709)
(250)
71.0024
7.1945
4.8535
0.4899
0.7751
0.1978
12.6135
24.4135
37.3837 161.7324 119.4969
34.9320
(5.4228)
(0.5721)
(0.4322)
(0.1560)
(0.1400)
(0.0328)
(1.4643)
(2.0167)
(2.8563)
(2.1226)
 DY
VDY
IPPDY
(6.9176)
(6.2233)
Medium Banks
Year end
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
 DY
-0.0109
0.0497
0.2872
0.1231
0.0208
0.0737
0.0548
-0.0203
0.0953
-0.0055
0.0761
0.0210
(0.2350)
(0.1774)
(0.1654)
(0.1829)
(0.1422)
(0.1030)
(0.1486)
(0.1075)
(0.1560)
(0.2475)
(0.2308)
(0.2380)
0.2132
0.1224
0.1212
0.1457
0.1048
0.0832
0.0976
0.0735
0.1042
0.1406
0.1126
0.1336
 DY
- 24 -
Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
VDY
IPPDY
(0.0052)
(0.0020)
(0.0022)
(0.0024)
(0.0016)
(0.0016)
(0.0019)
(0.0010)
(0.0018)
(0.0023)
(0.0023)
(0.0027)
210398
225182
310485
369731
396949
461215
522415
635415
691400
709108
772932
784233
(136)
(55)
(10)
(34)
(40)
(12)
(91)
(130)
(319)
(1015)
(820)
(1512)
78.9295
39.6629
2.9116
16.3949
17.5113
3.5949
34.5983
46.2498
87.7126 362.2927 225.6542 506.4189
(8.1495)
(2.6072)
(0.3638)
(1.1125)
(1.0456)
(0.3158)
(1.8386)
(2.0696)
(4.6658) (13.8843) (11.5629) (17.0255)
Small Banks
Year end
1991
1992
1993
1994
1995
1996
 DY
0.1065
0.2051
0.3271
0.1408
0.0278
0.2583
(0.2443)
(0.3173)
(0.1967)
(0.1954)
(0.2440)
0.2363
0.1927
0.1442
0.1474
(0.0058)
(0.0035)
(0.0023)
53169
67786
(29)
 DY
VDY
IPPDY
1998
1999
2000
2001
2002
0.1179
0.0241
0.0481
-0.0038
0.0467
0.0718
(0.2542)
(0.3539)
(0.3174)
(0.2012)
(0.1284)
(0.1685)
(0.1301)
0.1516
0.1361
0.1602
0.1135
0.1007
0.0785
0.0786
0.0683
(0.0027)
(0.0022)
(0.0024)
(0.0029)
(0.0027)
(0.0019)
(0.0016)
(0.0018)
(0.0017)
98311
106236
117491
132526
154847
196361
205581
214440
228144
226550
(42)
(7)
(3)
(23)
(37)
(149)
(231)
(162)
(168)
(222)
(157)
56.2615 113.4706
7.8279
(7.2305)
(7.4842)
(0.8875)
5.7124 199.0056
(0.7057)
(6.0885)
1997
55.9473 200.2612 238.6419 207.5962 186.9166 214.5289 165.0040
(3.7792) (10.3196) (13.8209)
- 25 -
(9.3334)
(8.3947) (10.8516)
(8.5624)
Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
Panel B: Two-Step Maximum Likelihood Estimation Results
Large Banks
Year end
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
 mle
0.0315
-0.0737
0.1758
0.0860
-0.0550
0.1395
0.0309
-0.0373
0.0326
-0.0164
0.0384
0.0069
(0.1255)
(0.1232)
(0.1516)
(0.1116)
(0.0819)
(0.0952)
(0.1336)
(0.0936)
(0.0916)
(0.1113)
(0.0881)
(0.1015)
0.1086
0.0751
0.1028
0.1038
0.0693
0.0789
0.1160
0.0755
0.0666
0.0699
0.0490
0.0564
(0.0038)
(0.0035)
(0.0037)
(0.0036)
(0.0023)
(0.0017)
(0.0042)
(0.0021)
(0.0025)
(0.0024)
(0.0017)
(0.0025)
-0.6169
-0.5287
-0.6868
-0.4217
-0.6395
-0.4105
-0.2728
-0.2034
-0.5213
-0.4603
-0.4551
-0.6701
(0.2895)
(0.2044)
(0.4101)
(0.2314)
(0.2459)
(0.1933)
(0.1650)
(0.3566)
(0.2541)
(0.3554)
(0.1756)
(0.3483)
835125
763938
941547
1024633
954949
1106951
1126635
1084870
1125891
1117092
1181364
1233958
(408)
(390)
(84)
(17)
(22)
(2)
(224)
(194)
(322)
(812)
(440)
(1039)
68.8946
56.9835
7.1224
1.4823
2.2543
0.3140
21.0571
34.4036
47.2083 203.5687 114.4723 141.0544
(8.1048)
(9.5315)
(2.1983)
(0.4862)
(0.7499)
(0.0610)
(4.0746)
(3.7483)
(5.7756) (10.0301)
 mle
 mle
mle
Vmle
IPPmle
(6.5891) (13.2048)
Medium Banks
Year end
1991
1992
1993
1994
 mle
0.0095
0.0664
0.2777
0.1430
(0.2196)
(0.1370)
(0.1286)
0.2041
0.1050
(0.0085)
 mle
 mle
mle
1995
1996
1997
1998
1999
2000
2001
2002
0.0118
0.0614
0.0657
-0.0288
0.0856
-0.0106
0.0461
0.0003
(0.1799)
(0.1443)
(0.1057)
(0.1428)
(0.1303)
(0.1410)
(0.2608)
(0.2232)
(0.4325)
0.1020
0.1411
0.0962
0.0825
0.0935
0.0714
0.0908
0.1266
0.0985
0.1386
(0.0040)
(0.0038)
(0.0049)
(0.0032)
(0.0028)
(0.0031)
(0.0015)
(0.0041)
(0.0029)
(0.0042)
(0.0054)
-0.5090
-0.5726
-0.6346
-0.5048
-0.7903
-0.4964
-0.4561
-0.2117
-0.4290
-0.5568
-0.5557
-1.0625
(0.5466)
(0.2401)
(0.2998)
(0.2403)
(0.3694)
(0.2193)
(0.1803)
(0.3906)
(0.3985)
(0.5069)
(0.4078)
(1.4699)
- 26 -
Deposit Insurance Premium under Stochastic Interest Rate: An Empirical Study of Taiwan’s Banks
Vmle
IPPmle
206307
221001
303909
362026
387686
450542
510365
618002
677404
697148
755237
762009
(191)
(61)
(5)
(95)
(92)
(11)
(156)
(265)
(391)
(920)
(1356)
(4795)
79.3668
25.9871
0.9766
18.5905
21.2002
2.4264
33.4220
87.2828
73.8300 367.1022 246.9313 625.6219
(14.3258)
(4.5640)
(0.3514)
(4.2682)
(3.8316)
(0.5890)
(4.3235)
(5.4912)
(9.7988) (14.9990) (20.6099) (58.5161)
Small Banks
Year end
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
 mle
0.1334
0.2305
0.3205
0.1685
0.0401
0.2462
0.1371
0.0200
0.0322
-0.0063
0.0304
0.0346
(0.2386)
(0.2337)
(0.1622)
(0.1911)
(0.2823)
(0.1889)
(0.3086)
(0.2211)
(0.1914)
(0.1602)
(0.2494)
(0.2221)
0.2289
0.1612
0.1239
0.1420
0.1437
0.1119
0.1408
0.0879
0.0886
0.0816
0.0881
0.0874
(0.0099)
(0.0074)
(0.0061)
(0.0039)
(0.0026)
(0.0034)
(0.0051)
(0.0025)
(0.0032)
(0.0036)
(0.0052)
(0.0054)
-0.6406
-0.5991
-0.7170
-0.7161
-0.4395
-0.5563
-0.4754
-0.3523
-0.5841
-0.3590
-0.4204
-0.6777
(0.5428)
(0.3614)
(0.4202)
(0.2162)
(0.5361)
(0.3136)
(0.2931)
(0.4969)
(0.4186)
(0.3688)
(0.4195)
(0.7912)
52085
66573
96140
103785
114604
129681
151914
192794
198480
206354
220365
215490
(38)
(60)
(6)
(3)
(18)
(24)
(188)
(144)
(299)
(401)
(514)
(585)
58.5569
69.6343
3.0767
(12.4242) (13.7900)
(1.2581)
 mle
 mle
mle
Vmle
IPPmle
5.9846 188.9044
(1.0203)
(5.0945)
37.7015 179.1598 175.0916 246.1383 349.4127 365.0345 373.5168
(3.3115) (16.1267) (11.0448) (20.3413) (25.5736) (32.6762) (36.3473)
- 27 -