Contagion and Default Risks in Derivative Pricing: A Hawkes-Based Model

Modern financial systems do not exist in isolation but form part of a complex global network of interconnected financial systems. This globalization of financial systems significantly increases the risk of contagion in financial markets, impacting asset prices and other important economic factors, including interest rates and market volatility. This phenomenon informs not only investors’ investment strategies but also the prices of contingent claims. In this article, we present a derivative pricing model in an incomplete and globalized financial market. To appreciate the dynamics and impact of some important market factors, particularly default risks due to contagion, we consider two different financial markets with defaultable assets: in one market, we consider a stock whose price process follows a Heston stochastic volatility model, and in the other, a stock that follows a Hawkes-type jump diffusion model whose intensity is subjected to external systemic shocks. In both markets, we derive an indifference price for a contingent claim that is subject to the risk of default and show the impacts the investor’s risk aversion and external shocks on the price of the contingent claim.