Analytical valuation of vulnerable options under a stochastic volatility model with a stochastic long-term mean

So-Yoon Cho; Geonwoo Kim; So-Yoon Cho; Geonwoo Kim

doi:10.3934/math.2025903

AIMS Mathematics

2025, Volume 10, Issue 9: 20219-20234. doi: 10.3934/math.2025903

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Analytical valuation of vulnerable options under a stochastic volatility model with a stochastic long-term mean

So-Yoon Cho ¹,
Geonwoo Kim ^{2
,
,}

1.
Department of Statistics, Sungkyunkwan University, Seoul 03063, Republic of Korea
2.
School of Natural Sciences, Seoul National University of Science and Technology, Seoul 01811, Republic of Korea

Received: 13 June 2025 Revised: 25 August 2025 Accepted: 29 August 2025 Published: 04 September 2025
MSC : 91G20

We derive the explicit pricing formulas for vulnerable options under a stochastic volatility model with stochastic long-term mean. We extend the He and Chen model to incorporate counterparty default risk and derive explicit solutions for option prices using the characteristic function of the underlying asset's log-price. The option writer defaults when their asset value falls below a predetermined boundary, reducing the option payoff. Our numerical examples show that option prices are highly sensitive to default boundaries and exhibit asymmetric responses to volatility parameters.
- vulnerable option,
- stochastic volatility,
- characteristic function,
- stochastic long-term mean
Citation: So-Yoon Cho, Geonwoo Kim. Analytical valuation of vulnerable options under a stochastic volatility model with a stochastic long-term mean[J]. AIMS Mathematics, 2025, 10(9): 20219-20234. doi: 10.3934/math.2025903

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Abstract

We derive the explicit pricing formulas for vulnerable options under a stochastic volatility model with stochastic long-term mean. We extend the He and Chen model to incorporate counterparty default risk and derive explicit solutions for option prices using the characteristic function of the underlying asset's log-price. The option writer defaults when their asset value falls below a predetermined boundary, reducing the option payoff. Our numerical examples show that option prices are highly sensitive to default boundaries and exhibit asymmetric responses to volatility parameters.

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