Pricing vulnerable options with variable default boundary under jump-diffusion processes

Abstract

For the pricing of vulnerable options, we improve the results of Klein and Inglis [Journal of Banking and Finance] and Tian et al. [The Journal of Futures and Markets], considering the circumstances in which the writers of options face financial crisis. Our pricing model faces the risks of default and the occasional impact experienced by the underlying assets and counterparty's assets. The correlation between the option's underlying assets and the option writer's assets is clearly modeled. Asset prices are driven by the jump-diffusion processes of two related assets. Furthermore, we consider a variable default boundary (VDB) based on the option's potential debt and the option writer's other liabilities. In case financial distress happens, the payout rate is connected to the option writer's assets. Through the Taylor expansion, we derive an approximate explicit valuation for vulnerable options.MSC: 60H10; 60J75; 60H30; 90G20; 90G40

Pricing European Vulnerable Options with Jumps and Stochastic Default Obstacles Barrier under Regime Switching

“…Since the dynamics of risky asset values are not continuous, some literature introduces jumping processes, compound Poisson processes, or self-exciting Hawkes processes to better describe their value models. These studies discuss the pricing formula for European vulnerable options (see XU [6], TIAN [7], Ma [8], and Zhou [9]). Wang [10] proposed decomposing the underlying asset risk and counterparty assets into systemic and nonsystemic risks and used the obtained pricing formula to discuss the difference between vulnerable option prices.…”

Closed-form pricing formula for foreign equity option with credit risk

“…In fact, two types models have been studied for the improved asset dynamics: the jump-diffusion models and the stochastic volatility models. In [7][8][9][10], the jump-diffusion models of underlying assets were considered for valuing of the vulnerable options. In [11][12][13][14], the stochastic volatility models, which describe the volatility smile in the real market, were used for the improvement of the vulnerable option pricing.…”

“…Comparison between Monte-Carlo simulation result and the closed-form formula. Note that C MC implies the Monte-Carlo results based on the stochastic dynamics presented in (7)-(10) …”

Power Exchange Option with a Hybrid Credit Risk under Jump-Diffusion Model

“…With these results, there have been many studies on the improvement of the pricing model for the vulnerable option under the structural model. Models such as the stochastic interest rate model [4], early counterparty risk model [5,6], stochastic volatility model [7][8][9][10] and jump-diffusion model [11][12][13][14] have been used to extend the pricing models of vulnerable options under the structural model. In addition, the pricing models of vulnerable options under the reduced-form model have been studied in recent years.…”