Asian Options pricing under exponential Ornstein–Uhlenbeck dynamics

Asian options are quite popular in commodity derivative markets where mean–reversion is widely observed. In this paper we consider a jump-diffusion exponential Ornstein-Uhlenbeck dynamics. From a mathematical perspective,... [ view full abstract ]

Asian options are quite popular in commodity derivative markets where mean–reversion is widely observed. In this paper we consider a jump-diffusion exponential Ornstein-Uhlenbeck dynamics. From a mathematical perspective, the problem turns out to be related with the sum of correlated log-normal random variables, whose distribution in unknown. We propose 2 methods to overcome this issue and proceed with pricing:

• Moment Matching (MM)
• Lower Bound (LB)

In particular, in order to implement MM we calculate analytically the moments of the arithmetic average of prices and fit various distributions. MonteCarlo with various Control Variables is used as benchmark to evaluate numerical results.