Short-Time Behavior in Arithmetic Asian Option Price Under a Stochastic Volatility Model with Jumps

In this paper, we study the short-time behavior of the arithmetic average of Asian option price (AOP) derived from a general class of the stochastic volatility model with jumps. The AOP that rarely has explicit expression can reduce the volatility in the option price because of the average of the underlying asset price over the time interval. We consider the future average process in the model which is a non-adapted process. By using the Malliavin calculus operators, we get a non-adapted Ito formula, and also a decomposition formula of the option price in the model. We apply the decomposition formula to find the short-time limit of the arithmetic AOP and the implied volatility.