Abstract
We present a study of the short maturity asymptotics for Asian options in a jump-diffusion model with a local volatility component, where the jumps are modeled as a compound Poisson process. The analysis for out-of-the-money Asian options is extended to models with Lévy jumps, including the exponential Lévy model as a special case. Both fixed and floating strike Asian options are considered. Explicit results are obtained for the first-order asymptotics of the Asian options prices for a few popular models in the literature: the Merton jump-diffusion model, the double-exponential jump model, and the Variance Gamma model. We propose an analytical approximation for Asian option prices which satisfies the constraints from the short-maturity asymptotics, and test it against Monte Carlo simulations. The asymptotic results are in good agreement with numerical simulations for sufficiently small maturity.
Acknowledgments
The authors are grateful to the Associate Editor and two anonymous referees whose comments and suggestions have greatly helped improve the quality of the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 The Lévy density is said to be completely monotone if and only if, for all , one has for x>0, and the same condition holds for x<0 with .