Option Pricing for Weighted Average of Asset Prices

Average options are path-dependent and have payoffs which depend on the average price over a fixed period leading up to the maturity date. This option is of interest and important for thinly-traded assets since price manipulation is prohibited, and both the investor and issuer may enjoy a certain degree of protection from the caprice of the market. There are several nice results for the average options with different approaches. In this paper, we consider to propose a more general weight instead of usual simple average, for which it may be possible to control the weights in the light of unexpected situation incurred. An analytical form of option pricing along with Monte Carlo simulations is obtained, and a numerical example is presented. In particular, our methodologies are based on Kemna & Vorst, Vorst and Levy, so that some comparisons for their results are made.