Abstract
Power exchange option is an exotic option which combines power option and exchange option. In this paper, we consider the pricing of the power exchange option under exchange rate volatility risk and issuing company bankruptcy risk. Meanwhile, considering the major events between the two countries, we add the Poisson jump process to the option model in order to reflect the impact of sudden factors on the price of transnational derivatives in the international market. According to the no-arbitrage principle, a mathematical model for pricing such problems is established, and explicit solutions are obtained. The numerical examples show that the model established in this paper is effective.
Highlights
As the influence of fierce market competition and homogenization of financial products, the traditional European option or American option can no longer meet the needs of investors
Power exchange option is an exotic option which is derived from exchange option and power option; both of them are powerful financial instruments for hedging nonlinear risks or incentive design of the executive stock option [1, 2], which are mainly traded in the OTC market
Gao and Wang [17], under the dual-currency model, used the method of measure transformation to give the European option pricing formula of asset price with jump process. Huang and He [18] studied the pricing theory of dual-currency European option and reset option under jump risk related to floating exchange rate
Summary
As the influence of fierce market competition and homogenization of financial products, the traditional European option or American option can no longer meet the needs of investors. The correlation between two kinds of risky assets was included in both the continuous part and the discontinuous part, while the correlation between the discontinuous part was linked through a common jump process, which improved the pricing framework of the power exchange option of Blenman and Clark [5] and obtained a clear pricing formula of the power exchange option. Gao and Wang [17], under the dual-currency model, used the method of measure transformation to give the European option pricing formula of asset price with jump process. Huang and He [18] studied the pricing theory of dual-currency European option and reset option under jump risk related to floating exchange rate. The Poisson jump process is added into the option to analyze the pricing of the power exchange options with dual currency with jump process
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