This study presents an analytical exact solution for the price of VIX options under stochastic volatility model with simultaneous jumps in the asset price and volatility processes. We shall demonstrate that our new pricing formula can be used to efficiently compute the numerical values of a VIX...

In this paper, we introduce the concept of multi-stage compound options to the valuation of convertible bonds (CBs). Rather than evaluating a nested high-dimensional integral that has arisen from the valuation of multi-stage compound options, we found that adopting the finite difference method...

In this paper, we present a correction to Merton (1973)'s well-known classical case of pricing perpetual American put options by considering the same pricing problem under a stochastic volatility model with the assumption that the volatility is slowly varying. Two analytic formulae for the...