不同于传统的思路, 本文以奈特不确定的视角处理带有随机波动率的期权定价问题. 首先, 证明随机波动率模型本质上是一个奈特不确定问题; 并且用折现相对熵来度量奈特不确定大小. 然后, 通过一个效用函数来权衡奈特不确定和奈特溢价, 求得个体在奈特不确定下最优概率测度, 导出了含奈特厌恶度γ 的欧式看涨期权定价公式. 通过Monto Carlo模拟发现个体奈特厌恶度γ 和期权的到期日对期权的价格有重要影响, 并使用沪市权证实例给出奈特厌恶度γ 的具体估算方法.
Abstract
This paper deals with the stochastic volatility option pricing model in the viewpoint of Knightian uncertainty. First, we prove that the stochastic volatility model is in fact a Knightian uncertainty model; and we use the discounted relative entropy to measure the Knighitan uncertainty. Then, having balanced the Knightian uncertainty and Knightian premium through a utility function, we get the optimum probability measure, and we get the price formula of European call option with Knightian aversion degree γ. We find that γ and expiration date have important effect on the price of option by Monte Carlo simulation, and we give an example to show how to estimate the values of γ.
关键词
随机波动率 /
奈特不确定 /
奈特溢价 /
相对熵 /
期权定价
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Key words
stochastic volatility /
Knightian uncertainty /
Knightian premium /
relative entropy /
option pricing
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中图分类号：
F830.9
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参考文献
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脚注
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基金
国家自然科学基金(70671005, 70831001)
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