Pricing reset options with multiple reset features under stochastic interest rate and jump diffusion model

The price for the reset option with multiple strike resets and reset dates when the risky asset follows a jump-diffusion model and interest rate satisfies Vasicek term structure framework is considered. We first obtain closed-form solution for the reset option by applying the change of numeraires. Second, we investigate the results of numerical evaluations of the reset option prices and show how they vary with both jump risks and the numbers of reset dates through numerical examples. The results show that the jumps risks can significantly affect the reset option values, and ignoring the jump risks may lead to serious biases in pricing option.