英文标题:
《Pricing Derivatives in a Regime Switching Market with Time Inhomogeneous
Volatility》
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作者:
Milan Kumar Das, Anindya Goswami and Tanmay S. Patankar
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最新提交年份:
2016
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英文摘要:
This paper studies pricing derivatives in an age-dependent semi-Markov modulated market. We consider a financial market where the asset price dynamics follow a regime switching geometric Brownian motion model in which the coefficients depend on finitely many age-dependent semi-Markov processes. We further allow the volatility coefficient to depend on time explicitly. Under these market assumptions, we study locally risk minimizing pricing of a class of European options. It is shown that the price function can be obtained by solving a non-local B-S-M type PDE. We establish existence and uniqueness of a classical solution of the Cauchy problem. We also find another characterization of price function via a system of Volterra integral equation of second kind. This alternative representation leads to computationally efficient methods for finding price and hedging. Finally, we analyze the PDE to establish continuous dependence of the solution on the instantaneous transition rates of semi-Markov processes. An explicit expression of quadratic residual risk is also obtained.
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中文摘要:
本文研究了年龄相关的半马尔可夫调制市场中衍生产品的定价问题。我们考虑一个金融市场,其中资产价格动态遵循一个制度转换几何布朗运动模型,其中系数依赖于有限多个年龄相关的半马尔可夫过程。我们进一步允许波动系数明确地依赖于时间。在这些市场假设下,我们研究了一类欧式期权的局部风险最小化定价。结果表明,通过求解非局部B-S-M型偏微分方程可以得到价格函数。我们建立了柯西问题经典解的存在唯一性。通过第二类Volterra积分方程组,我们还发现了价格函数的另一个特征。这种替代的表示方法导致了寻找价格和对冲的计算效率高的方法。最后,我们分析了偏微分方程,以建立解对半马尔可夫过程瞬时转移率的连续依赖关系。得到了二次剩余风险的显式表达式。
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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:Mathematics 数学
二级分类:Probability 概率
分类描述:Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用:例如中心极限定理,大偏差,随机微分方程,统计力学模型,排队论
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一级分类:Quantitative Finance 数量金融学
二级分类:Mathematical Finance 数学金融学
分类描述:Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法,包括随机、概率和泛函分析、代数、几何和其他方法
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