The Preliminary Research of Stock Option Incentive and Good Power Price to
Senior Executives of the listed Companies in China
Hao Zhou
Management Institute of Zhejiang Gongshang University; the city of Hangzhou, P.R.China;
(zhoulihaochao@163.com)
Abstract - At present, the high development of
Knowledge economy is promoting industries of our
country unceasingly, and knowledge plays more and more
a vital role in the economic development process. Too
relied on the capital the industry originally, because of
high energy consumption and high pollution, many
companies do not meet the needs of the low-carbon
economy to eliminate now; or carrying on the industrial
upgrading to enhance the technique of production and the
product technique content, increased to the knowledge and
the technical request. The stock option incentive involves
the question of price formulation. Many foreign scholars
have proposed some models to study question, and we can
attain profits from the significance but too complex. This
article also studies the question of the stock option price.
According to the HU theory, this article establishes a
mathematics price model, causing the stimulators of the
driving plan to be possible to participate fully. And
simultaneously it avoids the inappropriate arbitrage
behaviors. This article has also carried on mathematics
proof to this model, confirming its superiority.
Key words price
Incentive; Stock option; Good power
I.THE INCENTIVE TO SENIOR MANAGER
According to the Request - Proxy theory,
professional managers, because they have specialized
superiority and so on knowledge and experience, have
the management authority of the listed company ;
Correspondingly company's owners are one of the most
important shareholders ,enjoying the property rights but
not need to participate in company's current
management directly. As senior managers create value
for company for their hard working, they have
demanded to share the massive surplus values. In order
to spur Senior managers create more values, some
powerful incentive measures need to be carried on. We
can know that senior managers of the listed company
own company's management authority. In order to
obtain more benefits, different people may be reduced
as far as possible because of the possible high cost.
As we all know, public companies should pay wide
attention to the benefits of both minority shareholder
and other benefit counterparts which include these
High-level superintendents. It is known that core staff
such as executives is playing a vital role in the routine
operation, so sharing part of surplus values with them is
not only costs but also revenue in the long run. We need
to realize that only taking the benefits of senior
managers into account, will they feel a sense of
belonging to the company; and only will they feel a
sense of belonging to the company ,will they do their
best for the company. It is also should be realized that
short-term incentive is not sufficient and the obsession
with short-term benefits can lead huge losses to the
listed company. So it is needed to carry on effective
measures to spur the core staff of the listed companies.
II. STOCK OPTION INCENTIVE
In recent decades, more and more people have realized
that the stock option driving plan is one method feasible
design, which may have a good driving restraint
functions for the listed company high pipe fitting.
First of all, we want to introduce the stock option
.The so-called stock option is that the public company
awards certain core staff including High-level
superintendent, core technologies personnel and other
core staff of some rights that they could purchase
certain amount stock, in the future. Because of the stock
option, it may urge the shareholders to create the value
diligently to realize the company value maximization,
as benefits of owners and core staffs such as executives
are common in some degree. What is more, the stock
option materially is one kind of stronger tendency
option. High-level superintendent are driven that the
object may endeavor by them in certain time, creating
certain value for the company, and enable the listed
company values to obtain the increment, manifesting in
the company share rise. Still so long as stock option's
good power price after including the good power spends
and so on expenses is lower than the line of temporary
company's stock price, High-level superintendents are
driven that the object will consider the good power, in
which price difference is the income that High-level
superintendents may obtain. And stock option may have
one kind of latent huge driving function, which will
promote them to work hard for better achievement
diligently, then creating greater value for the company.
Although after implementing stock option good
power spurring plan, stock rights of the listed enterprise
may be diluted, the company values created by stock
spurring would be greater than not carrying on the stock
option. Because of some reasonable system design,
even if the stimulator leaves someday, most of them
might choose to sell off the company share, then
original shareholders enjoy the first purchase power; we
may also stipulate that certain special stockholder's
rights drive in the plan in stock certain time limiting the
circulation, which serves the purpose on controlling the
listed High-level superintendent changing job at will. At
the same time, it is no needs to use the cash to carry on
the drive, which is advantageous in the guarantee to
good cash flow.
Although implementing one good stock option plan
at the appropriate opportunity might be able to produce
good driving results, at the same time we should also
consider some limitations and possible existing
questions of the stock option spurring. Only
understanding the merits and the shortcomings of the
stock option driving plan comprehensively, we will
make use of it to be better.
We must pay attention to the Macro-economic
environment, when the whole national economy moves
overheated, like certain time 2007 ago, several of
professions economies mostly were on the departure
date in the second half of the year, and the stock market
was the bull market. At that time, implementing the
stock option spurring plan was not proper, even if Highlevel superintendent were driven that the object did not
take. Relying on the good economic situation, even if
they did not work hard, it still was possible to obtain
good salary. So we may obtain such conclusion that
implementing
the stock option plan is more cost
payout at that time, but the income created from Highlevel superintendent in the value obtained was
insufficient. So that was not best time. Similarly, when
our national economy and even the global economic are
worn out, various professions economy are when the
departure date or just experiencing the big risk crisis,
the stock price unceasingly falls, like the second half of
the year to present's situation in 2007. Even if Highlevel superintendent is quite diligent, facing the falling
stock price, under certain good power price terms,
regarding them is disadvantageous. Therefore, the
spurring plan could not achieve the anticipated driving
affection. Then it is still not the best time to carry on the
stock option driving plan. Similarly it may be the
profession difference, even if
the big economic
environment is the same, some professions are in the
rise time, occupies the rise time profession to be listed
company to carry on the stock option to drive, must pay
a higher cost, but obtaining the relatively insufficient
income; Otherwise, the companies in the decline
profession, also will meet the phenomenon, because the
stock value may decline unceasingly, High-level
superintendent will not expect too greatly about the
future, therefore, the option drive that also will have the
problem. In other words, when the national economy is
moving well, the difference, either a profession is when
the obvious rise time or the winter is not the best time to
carry on the stock option drive.
Therefore, this article supposes that our national
economy will move normally, namely in certain time
(implements in stock option actuation duration), and the
Macroeconomic is not under heating or not overheated
circumstance, will not fluctuate greatly.
III. PRELIMINARY STUDY OF GOOD POWER
PRICE
Generally speaking, stock option driving plan of the
listed company involves some essential factors, such as
the stock option awarding object; originate of the stock,
good power price, the awarding quantity and good
power condition. What is more, the good power price is
one core question of stock option driving plan, and the
hypothesis of good power price may have something to
do with the driving affects in the very great degree, also
having direct relation with the listed company and
stimulators, the benefit of two sides. In order to study
the problem of good power price, this article is under
the supposition condition that we have mentioned in
front, then studying stock option good power price
formulation as well as other correlated questions.
We have to say that the formulation of good power
price must observe the related legal rules of our country.
As we all know, Securities Supervisory Association has
issued " Stockholder's rights of the listed Company
Driving Policing method (Implementation)”, which was
implemented on December 31, 2005, saying that the
stipulation of the listed company when awarding the
driven object with stock option, they must determine the
good power price or the good power price definite
method beforehand, and the good power price should
not be lower than the following price that is high:
(a) The company sign stock closing price --stockholder's rights drive that the draft plan abstract
announces on the preceding trading day;
(b) The company sign stock average closing price --stockholder's rights drive that the draft plan abstract
announces in the first 30 trading days.
We may see that this stipulation was only the
limited to the stock good power price lower, leaving big
space for the good power price's formulation.
Stock option's good power price may be calculated
through Blake - Scholes Model, which was proposed by
Fischer Black and Myron Schole, who was Nobel
economic prize winner, and it is suitable in the stronger
tendency western-style option estimate value. Also we
can see that this model basis “the non-arbitrage
principle” (Arbitrage-free Principle) proposed, and the
formula expression is that the stock option value f is
equal to the result of the stock current price Ps
multiplying the standardized normal distribution N(d1)
then subtract the option good power price X multiplying
the standardized normal distribution N (d2) multiplying
one changing number , namely
And f
is the stock option value, Ps is the stock current price, X
for the option good power price,
t is the option due time, which is under the stock
continual compound interest the year returns ratio
standard deviation, N (di) is the standardized normal
distribution and it is smaller than di probability (i =1,
2); r is the non-risk interest rate 1. [1-6]
However, Blake – Scholes Model had not
considered the situation in which the stock option was
carried out, and the time of implementing the spurring
plan was before the due date. Therefore, this model
seems only to be suitable for good power price making
of the western-style stock option usually. If it is carried
on in good power price making of American stock
option, then one big deviation may present. Moreover,
if we choose this formula to calculate the good power
price, something will seem to be more complex.
Because there is a series of limitations, it is difficult to
operate in reality. [7-19]Then the following is the
introduction of the stock option good power price
formulation application from the HU theory which was
established by Professor Zuguang Hu, in April, 2010.
And some implications of HU theory have advantages
that can avoid the situation in which executives may
operate the good power price at will .What is more, the
using of implications of HU theory relatively. It is said
that some companies that believe the theory have attain
great achievement.[20] So we try to study HU theory and
its implication totally, including its model, implications
and the proof.
IV. THE APPLICATION OF HU THEORY IN GOOD
POWER PRICE
In front of this article, we have mentioned, because
the present's marketing
system is not only the
consummation, these stimulators own management
authority of public company, with suitable resources.
As information is not symmetry sometimes, through the
property operation as well as the information disclosed
and other methods may fry the stock price high in a
short time. As a result, the self-interest goal is possible.
However some applications of HU theory may reduce
the loss from self-interest behavior through methods
designed.
The HU theory establishment's stock option
driving model is:
a. Firstly , the board of directors permit the
stimulators proposing a good power date (we suppose
that the stock is to be carried in the time of 3 years later)
that may be achieved, anticipated company share price
P0;
b. Line of power price Pe is decided by equation
below, then good power price Pe is equal to the result of
the company current stock price P C plus W *（ P0 - PC ）
,namely
Pe = PC + W * (P0 - PC)
c. If stock option price expectation P 0 of
stimulators is smaller than future stock actual price Pr
from newspaper future, he will receive penalty, and the
penalty quantity D is unders-report subjects to a penalty
the coefficient v and future stock actual price Pr and by
the stimulator from newspaper difference of future
stock price expectation P0 product
D = v * (Pr - P0)
There are factors needed to introduce, and they are in
the following:
Pe is for good power price;
PC is the company current stock price;
P0 is the company share price when the good
power date which High-level superintendent proposes,
is also drove they must realize the goal , P 0 is bigger
than PC ; Pr is the stock good power date actual price .
W is the weighting factor, and its value is from 0 to
1. When w is 0, the good power price is the current
stock price, which is unable to form the restraint to
stimulators; When W is 1, the good power price will be
the future stock price expectation; if w is closer to 0,
then the driving function to stimulator may be bigger;
on the contrary, if w is closer to 1, the restraint function
to be more obvious. Therefore the value w may be
regarded as one kind of adjustment variable. Moreover,
this article supposes that our economy will not change
greatly in future. However, even if the national
economy presents some changes, it is still possible to
carry on the adjustment through the value w, so
economy fluctuation would not bring too much negative
influence. Namely, the suitable accent small w may
revise the overheated economy to bring exceeds the
quota the driving, w moves in a big way, the question
which worn out may alleviate the economy to bring the
driving which is insufficient. As W is the adjustment
variable value, may act according to the achievement of
the listed company achievement, stimulator's
performance, the profession characteristic which the
Macro economic situation as well as locates is carried
on the nimble hypothesis. Simultaneously something
need to be considered are different stimulators to
company's historical contribution, present's achievement
as well as the future the value which will be created for
the company.
Differently, V can be seen as a penalty coefficient,
is 0 to 100% between values. When v is close to 100%,
then the punishing dynamics is bigger. In order to
reduce the punishment, High-level superintendent will
enhance the future stock price anticipated; which serves
to be public company's benefit. Even if High-level
superintendent fries stock price high through property
operation as well as the information asymmetrical
superiority in a short time, also will receive suitable
penalty, then avoid the large quantity arbitrage loss.
That is, when High-level superintendent the self-interest
arbitrage motive is bigger, may suitably raise v value. V
value should also not be oversized, oversized, which
means that the serious punishment. We also note that
the too serious restraint will not favor spurring Highlevel superintendent to create more values positively for
the company.
At last, what we need to stress is that the penalty
coefficient value V must certainly be bigger than
weighting factor w.
The following content is the explanation of
formulation superiority in the stock option good power
price about the HU theory. We try to prove that if some
rules are designed properly, the spurring function of
stock option is very remarkable. What is more, we are
able to learn enough inspirations from the HU theory. In
order to explain the issues, it is needed to use some
examples.
Now the first thing we need to is making a
supposition that stock price PC of one public company
three years ago was each 100 Yuan, stipulates rear area
three years the feasible power, according to this
company's growth potential at that time, then the stock
price might amount to 120 Yuan three year later. In fact
now stock price Pr is truly 120 Yuan. And W is 0.5, V
is 0.8. According to the economic man supposition, the
human are the self-interest. For arbitrage as far as
possible, senior managers will have the following plan
alternative:
(a)The first situation is that executives may pull
down the anticipated stock price intentionally. For
example, they may decide the anticipated company
share price P0 is 110 Yuan, then good power price Pe is
equal to the result of the company current stock price
PC plus W *（ P0 - PC ）,namely
Pe = PC + W *（ P0 - PC ）= 100 + 0.5 * （ 110 - 100）= 105（
1）
punishment quantity is equal to the result of penalty
coefficient v multiply the difference of the stock good
power date actual price Pr and the company current
stock price P0, namely
D = v * （ Pr - P0 ） = 0.8 * （ 120 - 110 ） = 8
（2 ）
(b) The second situation is that executives may
report the stock expectation price P0 realistically. For
example, they may decide that the anticipated company
share price P0 is 120 Yuan, so the power price is Pe is
equal to the result of the company current stock price PC
plus W *（ P0 - PC ）,namely
Pe = PC + W *（P0 - PC）= 100 + 0.5 *（120 - 100）=
110
The power price is each 110 Yuan immediately,
because this time anticipated stock price P0 is equal to
actual price Pr, therefore does not need to receive the
punishment. Final each income R is equal to the result
of 120 subtract 110, so we can know the last revenue is
10 Yuan.
(c) The third situation is that the future stock price
expectation P0 is anticipated too high. According to the
economic general knowledge, we may know the
possibility is very small. If the price expectation is
higher than a line of temporary actual price obviously,
High-level superintendents of the listed company will
appear to be very incompetent, with one defeated
feeling. Moreover the good power price P e is equal to
the result of the company current stock price P C plus W *
（ P0 - PC ）, namely
Pe = PC + W *（ P0 - PC ）=（1 - w）* PC + W * P0
Because weighting factor w is bigger than 0, P e
and P0 are related, along with stock price expectation, s
rising, good power price also have a corresponding
enlargement. As a result, stimulator's arbitrage space is
also compressed correspondingly. Therefore, High-level
superintendent do not hope a high anticipation of the
future stock price.
In the ordinary circumstances, stimulators would
not expect the stock good power price to be too high,
even surpassing the actual price. The too high good
power price is disadvantageous for them; and setting the
stock price anticipated establishment in a high position
intentionally is impossible. However, because the HU
theory has the penalty factor, which will force Highlevel superintendent not to be possible the lowland to
reduce to future stock each price anticipated, which may
cause the final price expectation is as close to actual
price as possible. In the synthesis, reporting the stock
price expectation realistically conforms to High-level
superintendent as well as the listed company, s benefit;
if stimulators want stock price expectation to reduce the
good power price by more arbitrage through the low
newspaper. Likewise, High-level superintendent wants
then to carry on the stock option arbitrage through the
operation stock price the behavior also to be possible to
be similar limits, reducing adverse effect as far as
possible in reality. Now the following is mathematics to
the HU theory in the stock option good power price
formulation's application to prove:
First of all, we want to say that R stands for the last
revenue that executives may gain from the listed
company stock option incentive plan. As we all know,
the last revenue is the result of total revenues subtract
the number of punishment quantity and the good power
price. Furthermore, we get the following equality: R =
Pr –Pe– D
And we also know that D is equal to the result of v *
（Pr - P0）,then
R= Pr - PC – W *（P0 - PC）- v *（Pr - P0）
= （ 1 – v ） * Pr - (1 – w) * PC + （ v - w ） * P0
（3 ）
Because good power price Pe must be smaller than
actual price Pr, therefore Pe = PC + W *（P0 - PC） will
be smaller than Pr or equal to it.
So (1 –w) * PC + W * P0 is smaller than Pr or equal to it.
W* P0 is smaller than Pr - (1 - w)* PC or equal to it.
Then P0 is smaller than [Pr - (1 - w) * PC] / w or P0
is equal to it.
Supposing [Pr - (1 - w) * PC] / w = Pr + n ,n is one
random real number, so we may obtain the following:
N
=
(1
w)*
(Pr
PC)
/
w
(4)
So P0 is smaller than [Pr - (1 - w) * PC] / w or
P0 is equal to it. And we also know that [Pr -
(1 - w) * PC] / w= Pr +n= Pr+ (1 - w) *(Pr PC) / w
= [Pr + (1- w)* PC] / w
(5)
Now we let Y is equal to [Pr + (1 - w) * PC] / w.
Then we may know that the result of (Y – Pr) is
equal to n .And n also is equal to the result of (1 - w)*
(Pr - PC) / w
We may know that the current price PC is smaller
than actual price Pr by the front supposition; therefore
Pr is smaller than Y. We may also know that present's
stock price PC is known, line of temporary stock price Pr
is also the constant which is regarded as to be unable to
affect, weighting factor w and the penalty coefficient V
one to pass through the hypothesis also to be possible to
be regarded as a constant. Now the only variable is
anticipated stock price P0, and P0 influence income R,
i.e. Because we suppose under-report subject to a
penalty the coefficient V to be bigger than weighting
factor w, simultaneously may see from the above
equality increases along with P0, income R increases.
Moreover, we may know by (c), stock option income R
and price expectation P0 is being related, when the
number of P0 is equal to Y ,namely [Pr+(1-w)* PC] /w
may obtain the greatest income. Therefore, according to
the HU theory, only High-level superintendent report
the stock option expectation price truthfully, will they
gain the biggest benefits. As a result, the number that
executives give is close to the actual stock price as far
as possible. Then when the number executives report is
equal to Y, which is the result of [Pr+ (1-w)* PC] /w,
they are able to obtain the greatest income. The number
of stock price expectation that is closest to actual stock
price may reduce the opportunity, because of which
High-level superintendent make a profit through the
operation of stock price, serving the listed company, s
benefit. At the same time, executives of the listed
company may also obtain the stock option income after
creating the massive values for company.
We may know that the current price P C is smaller
than actual price Pr by the front supposition; therefore
Pr is smaller than Y. We may also know that present's
stock price PC is known, line of temporary stock price Pr
is also the constant which is regarded as to be unable to
affect, weighting factor w and the penalty coefficient V
one to pass through the hypothesis also to be possible to
be regarded as a constant. Now the only variable is
anticipated stock price P0, and P0 influence income R,
i.e. Because we suppose under-report subject to a
penalty the coefficient V to be bigger than weighting
factor w, simultaneously may see from the above
equality increases along with P0, income R increases.
Moreover, we may know by (c), stock option income R
and price expectation P0 is being related, when the
number of P0 is equal to Y ,namely [Pr+(1-w)* PC] /w
may obtain the greatest income. Therefore, according to
the HU theory, only High-level superintendent report
the stock option expectation price truthfully, will they
gain the biggest benefits. As a result, the number that
executives give is close to the actual stock price as far
as possible. Then when the number executives report is
equal to Y, which is the result of [Pr+ (1-w)* PC] /w,
they are able to obtain the greatest income. The number
of stock price expectation that is closest to actual stock
price may reduce the opportunity, because of which
High-level superintendent make a profit through the
operation of stock price, serving the listed company, s
benefit. At the same time, executives of the listed
company may also obtain the stock option income after
creating the massive values for company.
V. CONCLUSION
In our life, the High-level superintendents always
have suitable understanding to all kinds of information
of this company as well as its competitors. It could be
said that they have enough information to affect the
stock price sometimes, which is not permitted in law,
but they have enough superiority to change something.
In the ordinary circumstances, they are able to make
very close forecast about this company's stock price in
future certain time. Relying on information as well as
enough resources, they may operate the stock price by
the arbitrage. Although having the related negotiable
securities law to supervise, the present law is not still
perfect, and some pessimistic regions exist. So it is
needed to design some rules to restrain reasonably, and
these executives may obtain the proper stock option
income after creating value for the company. At the
same time, they will not gain too much illegal benefit,
as rules that have been designed may compress the
space to gain extraneous income.
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