Abstract: In recent years, the outbreak of COVID-19, fluctuations in energy market prices, and other global events have led to increasingly frequent occurrences of risk contagion across international financial markets. Understanding how international financial risks impact the Chinese market has become a prominent topic in academia. Most existing literature focuses on the stock market, using models such as risk spillover networks to study the mechanism and impact of international financial risks on China’s stock market. However, there has been relatively less focus in the literature on the risk spillover effects from international stock markets to China’s options market.
Building on existing empirical findings, we select the price fluctuations of the S&P 500 ETF from the US market as an exogenous risk source for China’s options market. Specifically, the initial outbreak of COVID-19 from February to April 2020 serves as the sample period to better examine the extreme financial risks from international markets on China’s options market. Inspired by the emerging field of economic physics, we employ an underdamped second-order system’s step response function to capture the turbulent patterns of the S&P 500ETF during the pandemic. This function is then embedded into the return process of the SSE 50ETF prices, constructing a BS model that incorporates international financial risks, referred to as the IFR_BS model.
However, financial physics models like the IFR_BS model typically pose challenges in deriving analytical expressions for options. Traditionally, numerical methods such as Monte Carlo simulations or finite difference methods are used for option pricing, but these approaches are limited by low computational efficiency and the inability to calibrate parameters in real-time, thus constraining practical applications. In recent years, Fourier transform-based analytical pricing algorithms, particularly the Fourier-Cosine method, have garnered wide attention due to their efficiency and precision. Nevertheless, this method heavily relies on the availability of characteristic functions. In this paper, we apply a perturbation method to derive a second-order asymptotic expression for the characteristic function of the asset price. We then use the Fourier-Cosine method to obtain an approximate analytical pricing formula for European options.
The numerical experiments demonstrate that the IFR_BS model can effectively characterize the trend and oscillation characteristics of stock prices, and produce statistical features such as peaks, fat tails, and skewness in asset returns. The option prices generated by the IFR_BS model exceed those of the traditional BS model, with larger perturbation parameters leading to higher option prices. The numerical error of the Fourier-Cosine method based on the second-order perturbation of the characteristic function is within 10%, and its efficiency of computing the option price is 40 times higher than that of the Monte Carlo method. The empirical analysis based on SSE 50ETF option data from February to April 2020 shows that the S&P 500-induced volatility in the SSE 50ETF exhibits time-varying characteristics, with a positive feedback relationship. The option pricing formula under the IFR_BS model, which considers international financial risk premiums, achieves higher overall pricing accuracy than the BS model. Moreover, it addresses the shortcoming of the BS model in valuing short-maturity options, especially the deep out-of-the-money options close to expiry. Given that short-maturity options generally exhibit high trading volumes in practical market transactions, the IFR_BS model has the greater practical value.

Key words: option pricing, international financial risks, underdamped function, characteristic function perturbation method, Fourier-Cosine method

摘要： 近年来如何刻画国际金融风险对中国市场的影响,成为学术界的热门热点之一。已有文献大多集中于研究国际股票市场之间的风险溢出效应,较少关注国际股票市场对中国期权市场的风险外溢效应。本文将标普500ETF走势嵌入上证50ETF的收益率过程,构建IFR_BS模型(BS Model with the Impact of International Financial Risk);然后应用特征函数微扰法和Fourier-Cosine定价方法,推导出该模型下欧式期权的近似解析定价公式。数值实验和实证结果表明:(1)IFR_BS模型可以较好地刻画上证50ETF收益率分布的“尖峰”、“肥尾”和“有偏”等统计特征。(2)考虑国际金融风险溢价的IFR_BS模型下的期权定价公式,可以解决BS模型对短到期期权尤其是短到期深度OTM期权估值不足的问题。

关键词: 期权定价, 国际金融风险, 欠阻尼函数, 特征函数微扰法, Fourier-Cosine方法