跳扩散模型下国内外利率随机的双币种期权定价

Pricing Quanto Options in a Jump-Diffusion Model with Stochastic Domestic and Foreign Interest Rates

双币种期权是投资于国外风险资产的一种风险管理合约,其收益不仅依赖国外风险资产价格的变化,还受汇率及国内外利率的双重波动影响,在国际贸易及汇率风险对冲方面应用十分广泛。本文假设股价和汇率均服从Merton跳扩散模型,并考虑国内外利率满足Hull-White随机模型时四种双币种标准欧式看涨期权的定价。利用鞅方法和跳扩散过程的Girsanov测度变换法,给出了它们价格的显示式,通过数值实例比较了与Black-Scholes模型的相应结果,并分析利率参数和跳跃参数对期权价格的影响。

The quanto option is a contract which invests to foreign assets and whose payoff depends on not only the price of foreign stock, but also the effect of exchange rate and domestic and foreign interest rates. The quanto option is widely used in international trade and risk management. This paper considers the valuations for four types on quanto European call options under the assumption of foreign-stock price and exchange rate both satisfing a jump-diffusion model and domestic and foreign interest rates being random. The analytical price formulas for the quanto options are firstly obtained by applying martingale method and Girsanov measure transformation method with jump diffusion process. Secondly, these results in the proposed model are compared with those in the Black-Scholes model through numerical calculation. Finally, we analyze the interest rate and jumping parameters on option price effect.