An Accurate Lattice Mode for Pricing Catastrophe Equity Put Under the lump-Diffusion Process

Abstract

A catastrophe equity put (CatEPut) is constructed to recapitalize an insurance company that suffers huge compensation payouts due to catastrophic events (CEs). The company can exercise its CatEPut to sell its stock to the counterparty at a predetermined price when its accumulated loss due to CEs exceeds a predetermined threshold and its own stock price falls below the strike price. Much literature considers the evaluations of a CatEPut that can only be exercised at maturity; however, most CatEPuts can be exercised early so the company can receive timely funding. This paper adopts lattice approaches to evaluate CatEPuts with early exercise features. To solve the combinatorial exposition problem due to the trigger of CatEPuts' accumulated loss, our method reduces the possible number of accumulated losses by taking advantage of the closeness of integral additions. We also identify and alleviate a new type of nonlincarity error that yields unstable numerical pricing results by adjusting the lattice structure. We provide a rigorous mathematical proof to show how the proposed lattice can be constructed under a mild condition. Comprehensive numerical experiments are also given to demonstrate the robustness and efficiency of our lattice.