吴述金, 王诗宇, 梁珊珊, 任艳科. 风险厌恶市场中基于在险价值风险测度的欧式期权定价[J]. 应用概率统计. DOI: 10.12460/j.issn.1001-4268.aps.2024.2022141
引用本文: 吴述金, 王诗宇, 梁珊珊, 任艳科. 风险厌恶市场中基于在险价值风险测度的欧式期权定价[J]. 应用概率统计. DOI: 10.12460/j.issn.1001-4268.aps.2024.2022141
WU Shujin, WANG Shiyu, LIANG Shanshan, REN Yanke. European Option Pricing Formula in Risk-Aversive Markets Based on the Risk Measure of VaR[J]. Chinese Journal of Applied Probability and Statistics. DOI: 10.12460/j.issn.1001-4268.aps.2024.2022141
Citation: WU Shujin, WANG Shiyu, LIANG Shanshan, REN Yanke. European Option Pricing Formula in Risk-Aversive Markets Based on the Risk Measure of VaR[J]. Chinese Journal of Applied Probability and Statistics. DOI: 10.12460/j.issn.1001-4268.aps.2024.2022141

风险厌恶市场中基于在险价值风险测度的欧式期权定价

European Option Pricing Formula in Risk-Aversive Markets Based on the Risk Measure of VaR

  • 摘要: 在风险厌恶市场中, 基于在险价值风险测度, 本文对标的资产服从几何布朗运动的欧式期权通过终值贴现的方式建立了期权定价模型. 特别地, 当期权交易者是风险中性时, 不需要风险补偿, 此时本文获得的定价模型退化为经典的Black-Scholes期权定价模型, 而且本文定价模型放宽了经典Black-Scholes期权定价模型的假设条件, 本文结果在不均衡、不完备的有套利市场下依然适用. 结果表明, 欧式期权的价值取决于标的资产的漂移系数μ, 其在经典的Black-Scholes模型中是无风险利率r的原因在于, 根据无套利原理, 在风险中性假设下风险资产的漂移系数μ必须等于无风险收益率r. 最后, 以上证50ETF期权为实证研究对象, 对风险厌恶市场中的欧式期权定价模型与已有模型进行误差分析, 结果表明, 本文模型的定价效果优于已有模型, 表现出更高的定价准确性.

     

    Abstract: Under the assumption of risk-aversive market, based on the risk measure of value at risk (VaR), this paper establishes an option pricing model for European options whose underlying assets are subject to geometric Brownian motion by means of terminal discount. Specifically, when the option traders are risk-neutral, they do not need risk compensation. At this time, the pricing model obtained in this paper degenerates into the Black-Scholes option pricing model, and the pricing model in this paper relaxes the assumptions of the Black-Scholes option pricing model, which is still applicable in the unbalanced and incomplete arbitrage market. The results show that the value of European option depends on the drift coefficient of the underlying asset μ, which is the risk-free interest rate r in the Black-Scholes model, because under the risk neutral assumption, the drift coefficient of the risk asset μ must be equal to the risk-free return rate r according to the no-arbitrage principle. Finally, taking the 50ETF option of Shanghai Stock Exchange as the empirical research object, the European option pricing model under the risk-aversive market and the existing model are analyzed by error indicators. The results demonstrate that the pricing effect of the model in this paper is better than the existing models, offering higher pricing accuracy.

     

/

返回文章
返回