Pricing Of Geometric Average Asian Futures Options In The Dual Currency Model

This thesis mainly studies the pricing of geometric average Asian options. Theunderlying asset of above Asian option is assumed to be a futures contract, i.e.futures option, for more practical application value.Two methods are adopted to solve the pricing of geometric average Asian op-tions:1) Partial Differential Equation (PDE). This method trys to find the PDEwhich satisfies the price of financial derivative instrument in the single currencymarket model through Δ hedging, simplifying the complex equation into Cauchyproblem for heat conduction equation through reasonable variable substitution. Fur-thermore, we obtain the pricing formula of financial derivative instrument. Thismethod is cited from Lishang Jiang[1], but with a different result.2) MartingaleMeasure Analysis. When this method is adopted, it is necessary to take the pricingof geometric average Asian options into consideration in different market models,i.e. single currency market and dual currency market. The key to the method isto find an equivalent martingale measure through Girsanov theorem, making thediscount process of underlying asset price a martingale process under this measure.And in this measure, we get the return expectation discount of the tradable assetswith the application of the Fundamental Theorem of Asset Pricing.