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摘要翻译：
本文研究了具有相关布朗噪声的一般线性随机波动率模型。在这类模型中，资产价格满足线性SDE，线性系数为波动过程。该类包括Black-Scholes模型、对数正态随机波动率模型和Heston随机波动率模型。对于线性随机波动率模型，我们导出了金融资产套利价格和欧式看涨期权和看跌期权价格的概率密度函数表示。在对数正态随机波动率模型下，给出了欧式看涨期权和看跌期权的密度函数和价格的闭式公式。对于Heston和推广的Heston随机波动率模型，我们也得到了一些新的结果。
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英文标题：
《Linear stochastic volatility models》
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作者：
Jacek Jakubowski and Maciej Wisniewolski
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最新提交年份：
2013
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains among others Black-Scholes model, a log-normal stochastic volatility model and Heston stochastic volatility model. For a linear stochastic volatility model we derive representations for the probability density function of the arbitrage price of a financial asset and the prices of European call and put options. A closed-form formulae for the density function and the prices of European call and put options are given for log-normal stochastic volatility model. We also obtain present some new results for Heston and extended Heston stochastic volatility models.
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PDF链接：
https://arxiv.org/pdf/0909.4765
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