Pricing of the Quanto Game Option with Asian Feature

The game option, which is also known as Israel option, is a new type of American option to give the option writer the right to cancel the contract before the maturity. This article studies the pricing behaviors of the quanto game option with Asian features based on partial differential equation and the stochastic analysis. The Asian feature in an option model refers to the payoff of the option depends on both the average asset price over the life of the option. The quanto options (currency-translated foreign equity options) are contingent claims where the payoff depends on exchange rate level at the option exercise time. The Asian quanto game options can be regarded as double-barrier European options for the features that both the holder and the writer can exercises the options contract at any time over the life of the option. We derive the pricing equation and provide the integral expression of pricing formula for the option. The option price is decomposed into the corresponding European option price and the penalty paid by the option writer for an early callable and the penalty paid by the option holder for early exercise of the option. In addition, we discuss optimal exercise strategies and continuation regions of the option.