CapVol Method
Mémoire soutenu en 2010 par Frédéric Sabbah (ISFA)
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CapVol Method
Contents
2

Introduction

How does CapVol method work?

Choice of Volatility Calculation

Comparison of a Static and a CapVol basket

Further studies and conclusion
CapVol Method
CapVol Method
Introduction
 What

is CapVol Method?
It is a method used to decrease its exposition to volatility level changes.
 Using
capped volatility funds allow to:
 Calculate the guarantee price based on a constant volatility
 Eliminate the need to re-price the guarantees due to change in volatility levels
 Significantly reduce losses due to mismatch between effective volatility and
hedging assumption by fixing the hedging assumption to a level that remains
always higher than the realized volatility of the Cap Vol fund
 Capped volatility funds also allow optimizing product profitability when fund
management fees are lower than the cost of vega hedging. They also improve
product attractiveness and invested amount performance via rider charge
decrease. Indeed, when capped volatility funds are used, there is no need for a
volatility risk premium.
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CapVol Method
CapVol Method
How does CapVol method work?

CapVol: A simple principle
Risky basket
volatility
Risky basket (equity)
Safe
Basket(Bonds/Cash)
Volatility close to
volatility target
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CapVol Method
CapVol Method
How does CapVol method work?
 But this simple principle raises many questions?


Which returns step must we choose?

Which volatility must we select?

What about reallocation frequency? And threshold?
How to measure the effectiveness ?
Perfect situation: Realized volatility always below a certain value
Max of 1 year volatility
But the policyholders want to have a high volatility (dynamic portfolio)
Volatility of 1 year volatility
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CapVol Method
Choice of volatility calculation
Historic
volatility
Formula
1 m
 
 (uni  u)
m  1 i1
Exponential
volatility
2
2
n
  
2
n
2
n1
 (1  )un1 ²
Garch(1,1)
  Vl u
2
n
2
n1
 
Implied/realize
d 20 days
2
n1
 n _ im plied
1 N 1  n  k _ im plied
N
Parametri
zation


6
m = 20 Days
λ = 0.94
γ=0
α = 0.06
β = 0.94
 realized _ vol
k 0
N = 35 Days
Garch = Exponential
Implied volatility has two problems:

Overestimate realized volatility (Average implied vol on Sx5e on 10
years = 26% and 22% for historic vol)

Very few implied volatility indexes exist
CapVol Method
nk
CapVol Method
Choice of volatility calculation

Historic/Exponential
Vol target = 10%, Reallocation frequency = 1 Day, SPTR Index, FEDL01 Index, from Feb 90 to september 09
Comparison of realized volatility
Comparison of Max 1 Yr Vol and Vovol for SPTR
10.00%
9.80%
10.1%
1.80%
10.0%
1.60%
9.9%
9.8%
9.60%
9.7%
12.5%
1.40%
1.20%
9.40%
9.6%
1.00%
9.20%
9.5%
0.80%
9.4%
0.60%
9.00%
9.3%
9.2%
8.80%
8.60%
1%
3%
5%
7%
9%
11%
13%
15%
17%
19%
13.0%
12.0%
11.5%
11.0%
0.40%
10.5%
9.1%
0.20%
9.0%
0.00%
10.0%
1%
3%
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CapVol Method
7%
9%
11%
13%
15%
17%
19%
Threshold
Threshold
Realized Vol histo
5%
Realized Vol expo
Vovol 1 Yr histo
Vovol 1 Yr expo
Max 1 Yr Vol expo
Max 1 Yr Vol histo
CapVol Method
Comparison of a Static and a CapVol basket
US case, threshold = 5%, cap vol frequency = 1,over 20 years
Eur case, threshold = 5%, cap vol frequency = 1, over 10 years
Swiss case, threshold = 5%, cap vol frequency = 1 Days, over 9.5 years
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CapVol Method
CapVol Method
Comparison of a Static and a CapVol basket
Periods
Static basket 50/50 ,
realized vol = 7.7%
SPTR Index/FEDL01
Index
CapVol Basket expo: vol
target = 8%, realized vol
=8.1%, threshold = 5%
CapVol Basket implied: vol
target = 8%, realized vol
=8.2%, threshold = 5%
High volatility bull
market:period Oct
98/Feb 00
+28.0%
+18.8%
+17.6%
Low volatility bull
market: period Apr 03/
Jul 07
+43.0%
+54.4%
+54.0%
-17.6%
-17.6%
-17.3%
-28.9%
-16.9%
-18.9%
Mid volatility: bear
market Jan00 – Mar03
High volatility: bear
market Jul 07 – feb 09
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CapVol Method
CapVol Method
Comparison of a Static and a CapVol basket
IRR
SX5E/EUR1DR1T from May 99
to May 09
Static basket 50/50
Expo vol target = 10%
Effect of
Reallocation frequency 5
Days
Threshold 5%
Min cash portion 30%
Min equity exposure 30%
Mean
Worst
1 Year Volatility
Best
Mean
Min
Max
Vol
Reallocation
Total
Number
leverage
per year
change
per year
0
0
240
4,02
0,4%
0,8%
-26,9%
-22,9%
25,8%
27,4%
10,9%
10,4%
5,3%
9,2%
20,2%
11,9%
4,40%
0,48%
0,7%
-22,8%
27,1%
10,5%
9,1%
13,0%
0,70%
48
0,8%
-22,6%
26,6%
10,2%
8,9%
11,7%
0,50%
9,7%
7,3%
11,9%
10,9%
9,4%
14,1%
Exposure
Mean
Max
50%
56,8%
50%
100%
2,03
56,8%
100%
14%
46
2,37
55,8%
100%
12%
0,3%
0,8%
-22,9%
-25,3%
25,2%
1,05%
177
2,39
51,7%
70%
13,50%
27,4%
1,10%
201
3,74
57,8%
100%
30%
Threshold: Do not move the Max 1 yr Volatility and reduce the number of reallocation
It’s better to monitor the reallocation number by moving the threshold than the reallocation frequency
Min Cash portion: Reduce the Mean exposure without reducing the Max 1 yr Volatility
Min Equity Exposure: Increase the Max 1 yr Volatility
CapVol Method
50%
13,50%
,
Reallocation frequency: Increase the Max 1 yr Volatility but reduce the number of reallocation
10
Min
CapVol Method
Further studies and conclusion

To go further
 Adapt CapVol reallocation frequency to hedging requirement
 Compare Capvol method with options vega hedging (variance swap)
 Test CapVol method with stochastic volatility scenarios

Conclusion
 Easy principle but a lot of parameters
 Good method to keep volatility in a reasonnable range
 Is being studied in many insurance companies
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CapVol Method
Questions?
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CapVol Method