A Jump-Diffusion Process for Asset Price with Non-Independent Jumps

A market recovery model, defined as a jump-diffusion model for the asset price where the jumps and the diffusion are not independent, is proposed. In this model a jump will be triggered when there is an unusually large downward movement over a certain time interval, and the jump size is correlated to this downward drop. We show that the market data supports such a model and parameter estimates based on market data is discussed. An explicit formula for the risk-neutral drift will be presented so that the option prices based on this model can be computed through Monte-Carlo simulation of the asset price. The characteristic function for the asset price is derived, through which the option prices can be computed by numerical integration. The volatility of asset classes in this model, defined by the variance swap (VIX) equation, is analyzed. A sensitivity study of the volatility with respect to jump parameters is performed. Results are compared to other well-known jump models.