Abstract:
We derive closed formulas for the prices of European options andtheir sensitivities when the underlying asset follows a double-exponentialjump diffusion model, as considered by S. Kou in 2002. This author hasderived the option price by making use of double series where each termrequires the computation of a sequence of special functions, such thatthe implementation remains difficult for a large part of financial users. Ourpresent result provides an alternative to the Kou's formula easily toimplement, even for the Excel/VBA environment.
Machine summary:
com Abstract We derive closed formulas for the prices of European options and their sensitivities when the underlying asset follows a double-exponential jump diffusion model, as considered by S.
This author has derived the option price by making use of double series where each term requires the computation of a sequence of special functions, such that the implementation remains difficult for a large part of financial users.
Then we present, in Section 3, our main results about the option price and sensitivities in the case of a double exponential jump-diffusion mo del as considered by Kou. It appears here that our formulas are easy to perform in comparison of the other existing results [Me; 1976], [Ko; 2002], [Qu-Ra; 2007] and [Di; 2007].
Therefore we can also assume the existence of some regular two- variables function C such that C(S,)=Price_Call_KJD(T, S, K, , r, q, ) Recall that the sensitivities of the call-price with respect to these variables S and are given by the following expressions: Vol. 1 / No. 1 / winter 2011 In this section, we consider the Kou's framework Jump diffusion and provide the alternative pricing and sensitivities formulas for the results obtained in [Ko; 2002], [Qu-Ra; 2007] and [Di; 2007].
The closed formulas, either for the option price or its sensitivities, found in this work would be a new impetus on the use of double exponential jump diffusion model as an interesting alternative to the (limited) Black and Scholes pricing used by a large part of academics and practitioners in finance since the seventies.