看涨期权价格的无套利插值

IF 1.3 Q2 STATISTICS & PROBABILITY

Statistics & Risk Modeling Pub Date : 2020-01-01 DOI:10.1515/strm-2018-0026

Christian Bender, Matthias Thiel

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引用次数: 0

摘要

摘要本文提出了一种新的看涨期权价格和隐含波动率相对于行权的插值方法，该方法首先生成了一条固定期限的平滑且不存在静态套利的隐含波动率曲线。我们的插值方法是基于一个无套利的金融“参考”模型的看涨价格函数的扭曲。如果市场数据与参考模型相容，则再现参考模型的认购价格。给定一组不同行权和期限的看涨期权价格，我们可以利用这种一维插值方法在每个输入期限上构造看涨期权价格曲面，并将生成的曲线插值到期限维上。我们以Black-Scholes模型为参考模型，得到了N. kahal [a arbitrage-free interpolation of volatility, Risk 17 2004, 5,102 - 106]作为特例的算法。

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Arbitrage-free interpolation of call option prices

Abstract In this paper, we introduce a new interpolation method for call option prices and implied volatilities with respect to the strike, which first generates, for fixed maturity, an implied volatility curve that is smooth and free of static arbitrage. Our interpolation method is based on a distortion of the call price function of an arbitrage-free financial “reference” model of one’s choice. It reproduces the call prices of the reference model if the market data is compatible with the model. Given a set of call prices for different strikes and maturities, we can construct a call price surface by using this one-dimensional interpolation method on every input maturity and interpolating the generated curves in the maturity dimension. We obtain the algorithm of N. Kahalé [An arbitrage-free interpolation of volatilities, Risk 17 2004, 5, 102–106] as a special case, when applying the Black–Scholes model as reference model.

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来源期刊

Statistics & Risk Modeling STATISTICS & PROBABILITY-

CiteScore

1.80

自引率

6.70%

发文量

期刊介绍： Statistics & Risk Modeling (STRM) aims at covering modern methods of statistics and probabilistic modeling, and their applications to risk management in finance, insurance and related areas. The journal also welcomes articles related to nonparametric statistical methods and stochastic processes. Papers on innovative applications of statistical modeling and inference in risk management are also encouraged. Topics Statistical analysis for models in finance and insurance Credit-, market- and operational risk models Models for systemic risk Risk management Nonparametric statistical inference Statistical analysis of stochastic processes Stochastics in finance and insurance Decision making under uncertainty.