Extracting risk-neutral densities from option prices using mixture binomial trees
Extracting risk-neutral densities from option prices using mixture binomial trees
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使用混合二项式树从期权价格中提取风险中性密度
DOI：
10.1109/cifer.1999.771112
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
H. Zimmermann
中科院分区：
文献类型：
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作者：
Christian D. Pirkner;A. Weigend;H. Zimmermann
自1987年10月股市崩盘以来，指数期权的价格明显偏离布莱克-斯科尔斯理论。这一事实在文献中被重点记录为波动性微笑（M. Rubinstein 1994）。定价误差表明模型的假设没有捕获期权价格中嵌入的所有相关信息。作为对这个问题的回应，之前的研究放宽了一些基本假设，以便得出更现实的价格。例如，底层安全性的数据生成过程中的变化，例如跳跃扩散或方差模型的恒定弹性。我们扭转这个思路：我们将记录的期权价格作为给定的，并估计与当前市场估值一致的隐含定价内核。为了使风险中性密度的形状灵活并允许概率为非高斯分布，我们使用混合分布的概念。我们将我们的方法应用于最近在芝加哥商品交易所交易的标准普尔 500 指数期货期权数据集。该数据跨越 1998 年，包含 22497 个美式期货期权的结算价格。
Since the stock market crash in October of 1987, prices of index options deviate significantly from Black-Scholes theory. This fact is prominently documented in the literature as the volatility smile (M. Rubinstein 1994). The pricing error is a sign that the assumptions of the model do not capture all relevant information embedded in option prices. As response to this problem, previous research has relaxed some of the underlying assumptions in order to arrive at more realistic prices. Examples are changes in the data generating process of the underlying security, e.g., jump diffusion or constant elasticity of variance models. We reverse this direction of thought: we take recorded option prices as given and estimate the implied pricing kernel that is consistent with current market valuations. To be flexible in the shape of the risk-neutral density and to allow probabilities to be non-Gaussian, we use the concept of mixture distributions. We apply our methodology to a recent dataset of options on the S&P 500 index future traded on the Chicago Mercantile Exchange. The data spans the year 1998 and contains settlement prices for 22497 American-style futures options.