Valuing catastrophe equity put options with liquidity risk, default risk and jumps

The growing frequency of natural disasters and the impacts of climate change have caused many companies to face liquidity shortages. Consequently, how to hedge such risks has become an urgent issue for investors to consider. To construct an effective hedge tool, in this paper we mainly explore the pricing problem of catastrophe equity put options (CatEPuts) with liquidity risk. In the context of losses caused by catastrophic events, we use Markov modulated Poisson processes (MMPP) to depict its intensity. The default event of the option issuer occurring at any time before the expiration of the option and the correlation existing between the stock and the assets of the option issuer are also considered and involved in our model. Under this framework, we obtain a closed-form formula for CatEPuts with liquidity risk and default risk under MMPP by applying Escher transformation and multidimensional normality. Finally, we conduct numerical analysis. By comparing solutions with and without influencing factors, the significance of risk factors and jump diffusion processes are elucidated. It also includes sensitivity analysis to explore the impact of key parameters on the price of CatEPuts. In addition, as an application we explore some realistic cases, such as the measure of VaR. Through risk management analysis, it demonstrates that CatEPuts can effectively hedge catastrophic risks.