This work aims to provide an efficient method to evaluate the Credit Value Adjustment (CVA) for a vulnerable European option, which is an option subject to some default event concerning the issuer solvability. Financial options traded in OTC markets are of this type. In particular, we compute the CVA in some popular stochastic volatility models such as SABR, Hull et al., which have proven to fit quite well market derivatives prices, admitting correlation with the default event. This choice covers the relevant case of Wrong Way Risk (WWR) when a credit deterioration determines an increase in the claim value. Contrary to the structural modeling adopted in [G. Wang, X. Wang & K. Zhu (2017) Pricing vulnerable options with stochastic volatility, Physica A 485, 91–103; C. Ma, S. Yue & Y. Ma (2020) Pricing vulnerable options with Stochastic volatility and Stochastic interest rate, Computational Economics 56, 391–429], we use the reduced-form intensity-based approach to provide an explicit representation formula for the vulnerable option price and related CVA. Later, we specialize the evaluation formula and construct its approximation for the three models mentioned above. Assuming a CIR model for the default intensity process, we run a numerical study to test our approximation, comparing it with Monte Carlo simulations. The results show that for moderate values of the correlation and maturities not exceeding one year, the approximation is very satisfactory as of accuracy and computational time.

中文翻译：

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随机波动率模型中的 CVA 和脆弱期权

这项工作旨在提供一种有效的方法来评估易受攻击的欧洲期权的信用价值调整 (CVA)，该期权是一种受一些与发行人可解决性有关的违约事件影响的期权。在场外交易市场交易的金融期权属于这种类型。特别是，我们在一些流行的随机波动率模型中计算 CVA，例如 SABR、Hull等。，这已被证明非常适合市场衍生品价格，承认与默认事件的相关性。当信用恶化决定索赔价值增加时，此选择涵盖了错误方式风险 (WWR) 的相关案例。与 [G. Wang, X. Wang & K. Zhu (2017) 为具有随机波动性的脆弱期权定价，物理学甲 485, 91–103; C. Ma, S. Yue & Y. Ma (2020) 为具有随机波动率和随机利率的脆弱期权定价，计算经济学 56, 391–429]，我们使用简化形式的基于强度的方法为易受攻击的期权价格和相关 CVA 提供明确的表示公式。之后，我们对评估公式进行了专门化，并为上述三个模型构建了它的近似值。假设默认强度过程的 CIR 模型，我们进行数值研究以测试我们的近似值，并将其与蒙特卡洛模拟进行比较。结果表明，对于中等值的相关性和不超过一年的期限，该近似值在准确性和计算时间方面非常令人满意。