Pricing power exchange options with default risk, stochastic volatility and stochastic interest rate

This paper investigates the pricing issue of power exchange options with default risk, in which the dynamics of the underlying assets and the counterparty asset follow three correlated stochastic volatility models with stochastic interest rate. We assume that the volatility risk is decomposed into short-term and long-term volatility. The stochastic interest rate is driven by the CIR (Cox-Ingersoll-Ross) process. Based on the proposed model, we derive a closed-form solution for the price of power exchange option with default risk by means of Fourier transform. Besides, the price of power exchange option with default risk can be quickly computed by employing the fast Fourier transform (FFT) algorithm. The results of Monte Carlo simulations demonstrate that the FFT is fast and accurate. More importantly, the pricing model also shows that: (i) a higher long-run mean of the underlying asset price's instantaneous variance induces a higher value of power exchange option with default risk; (ii) the long-run mean of instantaneous variance in counterparty's asset value has a negative impact on the price of power exchange option with default risk; and (iii) the higher the long-run mean of stochastic interest rate, the higher the power exchange option price.