Continuous Asian Options Research Articles

Sensitivity analysis for averaged asset price dynamics with gamma processes

The main purpose of this paper is to derive unbiased Monte Carlo estimators of various sensitivity indices for an averaged asset price dynamics governed by the gamma Lévy process. The key idea is to apply a scaling property of the gamma process with respect to the Esscher density transform parameter. Our framework covers not only the continuous Asian option, but also European, discrete Asian, average strike Asian, weighted average, spread options, and geometric average Asian options. Numerical results are provided to illustrate the effectiveness of our formulas in Monte Carlo simulations, relative to finite difference approximation.

Efficient solutions for discrete Asian options

While in the literature most studies on pricing focus on continuous Asian options, in this paper we provide efficient solutions for both European and American discrete average price Asian options. The method used for deriving the approximation formula for European Asian options is based on the idea of Bouaziz et al. (J Bank Finance 18:823–839, 1994) and Taso et al. (J Futures Mark 23:487–516, 2003) in which the Taylor expansion is used to obtain the approximation formula for continuous average strike Asian options. By using the Taylor expansion to the second order, a simple and accurate solution can be obtained. The approximation formula for the European Asian option can further be used to enhance the efficiency of the pricing of the American Asian options when using the numerical method.