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While calculating european call option prices, using the variance-gamma model formula provided by Madan, Carr & Chang (1998), I noticed that, holding all other things constant, the value of an ITM call option in the VG-model seems to decline with $\sigma$ when the skewness parameter $\theta < 0$.

Below is depicted, for ATM, ITM and OTM-options respectively, the call price reduced by the mean price of its category (by parameters and moneyness category) versus $\sigma$. My concern regards figures 2 and 5.

I understand the argument, as is also presented in answers to many other questions about the vega of ITM-options, that due to the limited downside of call-options, an increase in volatility will also mean a higher expected payoff and therefore value.

My question is, whether this is also true for ITM options when the underlying distribution of returns is negatively skewed?

It is possible that the reason for this pattern in the figures is incorrect calculations on my behalf.

The option prices are for $S_0 =1000$, $r_f = 0.002$, $(T-t)=0.3$,

$K_{ATM}=1000$, $K_{ITM}=900$ and $K_{OTM}=1100$, and the VG-parameters shown in the graphs.

(The titles of the figures use "," instead of "." as decimal points)

enter image description here

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