Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility
Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility
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多尺度随机波动下欧式期权渐进性的数值研究
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
S. Silvestrov
中科院分区：
文献类型：
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作者：
Betuel Canhanga;A. Malyarenko;Jean;Ying Ni;S. Silvestrov
多尺度随机波动率模型放宽了Black-Scholes期权定价模型中的恒定波动率假设。这样的模型可以捕捉波动的微笑和倾斜，从而更准确地描述交易价格的走势。Christoffersen等人。管理科学55(2):1914-1932（2009）提出了一个基础价格由两个波动分量控制的模型，一个变化快，另一个变化慢。Chiarella和Ziveyi在《苹果数学计算》224:283-310（2013）中对Christoffersen的模型进行了改造，计算出了美国期权定价的近似公式。他们利用Duhamel原理推导出与期权价格相关的边值问题的积分形式解。利用特征变换、傅里叶变换和拉普拉斯变换等方法，获得了较准确的美式期权价格。在作者（Canhanga et al. 2014）之前的研究中，以Chiarella和Ziveyi苹果数学计算224:283-310（2013）模型为例对欧式期权进行定价。这项早期工作的新颖之处在于提出了期权价格的渐近展开式。本文通过实验和数值研究，探讨了由该渐近展开式给出的近似公式的准确性。我们还提出了一种校准由一阶渐近近似公式产生的参数的方法。我们的近似期权价格将与Chiarella和Ziveyi的近似期权价格进行比较，苹果数学计算224:283-310（2013）。
Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. Manag Sci 55(2):1914–1932 (2009) presented a model where the underlying price is governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American option prices. In a previous research of the authors (Canhanga et al. 2014), a particular case of Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013).