基于CEV模型的上证50股指期权定价研究

Research on the Pricing of SSE 50 Index Options Based on the CEV Model

摘要: 股指期权作为中国市场中较新的金融产品，能够有效对冲市场波动。传统期权评估方法基于波动率恒定假设具有局限性，无法解释尖峰厚尾、波动率微笑等反市场现象；而方差常弹性(Constant elasticity of variance, CEV)模型将假定推广到波动率变化的情况，更符合实际市场。本研究探讨CEV模型在上证50股指期权价值评估中的应用及有效性，并对不同参数组合下的CEV期权定价结果进行多层次分析。通过单因素及多因素敏感性分析，得到期权在误差最小时的不确定因素取值及期权理论价值。CEV期权定价结果非常贴近市场价格，具有更准确的预测效果，可以作为投资者期权定价及风险管理决策的理论依据。

Abstract: As a relatively new financial product in the Chinese market, index options can effectively hedge against market volatility. Traditional option evaluation methods, based on the assumption of constant volatility, have limitations and cannot explain market anomalies such as leptokurtosis and volatility smiles. The Constant Elasticity of Variance (CEV) model extends this assumption to accommodate changing volatility, making it more aligned with actual market conditions. This paper uses the SSE 50 as an example to explore the application and effectiveness of the CEV model in evaluating the value of SSE 50 index options. It conducts a multi-level analysis of CEV option pricing results under different parameter combinations. Through single-factor and multi-factor sensitivity analyses, the study identifies the values of uncertain factors and theoretical option values that minimize errors. The CEV option pricing results closely align with market prices, offering more accurate predictive capabilities. This can serve as a theoretical basis for investors in option pricing and risk management decisions.