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CapVol MethodMémoire soutenu en 2010 par Frédéric Sabbah (ISFA)

CapVol Method Contents

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Introduction

How does CapVol method work?

Choice of Volatility Calculation

Comparison of a Static and a CapVol basket

Further studies and conclusion

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 Introduction

Risky basket volatility

Risky basket (equity) Safe Basket(Bonds/Cash)

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CapVol: A simple principle

Volatility close to volatility target

CapVol Method

CapVol Method How does CapVol method work?

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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

CapVol Method How does CapVol method work?

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²)1( 121

2 nnn u

Historic volatility

Exponential volatility

Garch(1,1) Implied/realized 20

days

Formula

Parametrization m = 20 Days λ = 0.94

γ = 0α = 0.06β = 0.94

N = 35 Days

2

1

2 )(1

1

m

iinn uu

m 2

121

2 nnln uV

1

0 _

_1_

N

k kn

kn

n

volrealized

implied

N

implied

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

CapVol Method Choice of volatility calculation

Historic/ExponentialVol target = 10%, Reallocation frequency = 1 Day, SPTR Index, FEDL01 Index, from Feb 90 to september 09

Comparison of Max 1 Yr Vol and Vovol for SPTR

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

1.40%

1.60%

1.80%

1% 3% 5% 7% 9% 11% 13% 15% 17% 19%

Threshold

10.0%

10.5%

11.0%

11.5%

12.0%

12.5%

13.0%

Vovol 1 Yr histo Vovol 1 Yr expo Max 1 Yr Vol expo Max 1 Yr Vol histo

Comparison of realized volatility

8.60%

8.80%

9.00%

9.20%

9.40%

9.60%

9.80%

10.00%

1% 3% 5% 7% 9% 11% 13% 15% 17% 19%

Threshold

9.0%

9.1%

9.2%

9.3%

9.4%

9.5%

9.6%

9.7%

9.8%

9.9%

10.0%

10.1%

Realized Vol histo Realized Vol expo

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CapVol Method Choice of volatility calculation

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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 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%

Mid volatility: bear market Jan00 – Mar03 -17.6% -17.6% -17.3%

High volatility: bear market Jul 07 – feb 09 -28.9% -16.9% -18.9%

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CapVol Method Comparison of a Static and a CapVol basket

Reallocation frequency: Increase the Max 1 yr Volatility but reduce the number of reallocation

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

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CapVol Method Comparison of a Static and a CapVol basket

Mean Worst Best Mean Min Max VolNumber per year

Total leverage change per year

Mean Max Min

Static basket 50/50 0,4% -26,9% 25,8% 10,9% 5,3% 20,2% 4,40% 0 0 50% 50% 50%Expo vol target = 10% 0,8% -22,9% 27,4% 10,4% 9,2% 11,9% 0,48% 240 4,02 56,8% 100% 13,50%Effect of ,

0,7% -22,8% 27,1% 10,5% 9,1% 13,0% 0,70% 48 2,03 56,8% 100% 14%

0,8% -22,6% 26,6% 10,2% 8,9% 11,7% 0,50% 46 2,37 55,8% 100% 12%

9,7% 7,3% 11,9% 1,05% 177 2,39 51,7% 70% 13,50%

0,8% -25,3% 27,4% 10,9% 9,4% 14,1% 1,10% 201 3,74 57,8% 100% 30%

1 Year VolatilityIRR Reallocation Exposure

SX5E/EUR1DR1T from May 99 to May 09

Reallocation frequency 5 Days

Min cash portion 30%

Threshold 5%

Min equity exposure 30%

25,2%-22,9%0,3%

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 Further studies and conclusion

Questions?

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