Advances in Risk Management

362 MODEL SELECTION AND HEDGING OF FINANCIAL DERIVATIVES

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5

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45

20% 
15% 
10% 
5% 0% 5% 10% 15% 20%

Gamma error

Volga error

Vanna error

Total error

Figure 18.2The hedging error probability density function obtained by

assuming that the additional claim has the same expiry (1 year) as the

option to hedge but different strike (K=1). The trader uses a

stochastic volatility model. All errors are expressed as a percentage

of the initial cost of the option

5.00

5.00

10.00

15.00

20.00

25.00

30.00

40% 
30% 
20% 
10% 0% 10% 20%

Gamma error

Volga error

Vanna error

Total error

Figure 18.3The hedging error probability density function obtained by

assuming that the additional claim has the same strike (K=0.975) as the

option to hedge but different expiry (2 years). The trader uses a

stochastic volatility model. All errors are expressed as percentage

of the initial cost of the option

We study two different cases. First we assume that we choose forDa liq-
uid at-the-money option that has the same expiry as the option to hedge (i.e.
a one-year call). In Figure 18.2 we show the hedging error coming from the
Gamma, the Volga and the Vanna terms separately, as well as the total error.