Weak Convergence of Equity Derivatives Pricing with Default Risk

TL;DR

This paper develops a discrete-time model for pricing equity derivatives with default risk, demonstrating its convergence to continuous-time results and providing explicit formulas within a no-arbitrage framework.

Contribution

It introduces a novel discrete-time equity derivatives pricing model incorporating default risk, with proven weak convergence to continuous-time models and explicit pricing formulas.

Findings

Discrete-time model with default risk is stable and converges to continuous-time results.

Explicit pricing formulas derived within a no-arbitrage framework.

Model depends on default intensity linked to equity value.

Abstract

This paper presents a discrete--time equity derivatives pricing model with default risk in a no--arbitrage framework. Using the equity--credit reduced form approach where default intensity mainly depends on the firm's equity value, we deduce the Arrow--Debreu state prices and the explicit pricing result in discrete time after embedding default risk in the pricing model. We prove that the discrete--time defaultable equity derivatives pricing has convergence stability, and it converges weakly to the continuous--time pricing results.