Prices of asian options under stochastic interest rates

Asian options are the popular second generation derivative products and embedded in many structured notes to enhance upside performance. The embedded options, as a result, usually have a long duration. The movement of interest rates becomes more important in pricing such long-dated options. In this paper, the pricing of Asian options under stochastic interest rates is studied. Assuming Hull and White model for the interest rates, a closed-form formula for geometric-average options is derived. As a by-product, pricing formula is also given for plan-vanilla options under stochastic interest rates.