Choi Sun-Yong, Veng Sotheara, Kim Jeong-Hoon, Yoon Ji-Hun
Department of Financial Mathematics, Gachon University, Gyeonggi, 13120 Republic of Korea.
Graduate School of Science, Royal University of Phnom Penh, Phnom Penh, 12156 Kingdom of Cambodia.
Comput Econ. 2022;59(3):1113-1134. doi: 10.1007/s10614-021-10121-w. Epub 2021 Apr 26.
The stochastic elasticity of variance model introduced by Kim et al. (Appl Stoch Models Bus Ind 30(6):753-765, 2014) is a useful model for forecasting extraordinary volatility behavior which would take place in a financial crisis and high volatility of a market could be linked to default risk of option contracts. So, it is natural to study the pricing of options with default risk under the stochastic elasticity of variance. Based on a framework with two separate scales that could minimize the number of necessary parameters for calibration but reflect the essential characteristics of the underlying asset and the firm value of the option writer, we obtain a closed form approximation formula for the option price via double Mellin transform with singular perturbation. Our formula is explicitly expressed as the Black-Scholes formula plus correction terms. The correction terms are given by the simple derivatives of the Black-Scholes solution so that the model calibration can be done very fast and effectively.
Kim等人（《应用随机模型与商业工业》，30(6):753 - 765，2014年）提出的随机方差弹性模型是预测金融危机中可能出现的异常波动行为的有用模型，市场的高波动性可能与期权合约的违约风险相关。因此，研究随机方差弹性下具有违约风险的期权定价是很自然的。基于一个具有两个独立尺度的框架，该框架可以最小化校准所需参数的数量，但能反映基础资产和期权卖方公司价值的基本特征，我们通过带奇异摄动的双重梅林变换得到了期权价格的封闭形式近似公式。我们的公式明确表示为布莱克 - 斯科尔斯公式加上修正项。修正项由布莱克 - 斯科尔斯解的简单导数给出，这样模型校准可以非常快速有效地完成。
