摘要翻译:
本文在有限状态空间上考虑了一个参数由连续时间平稳马尔可夫链驱动的跳扩散动力学模型,作为欧式未定权益的基础模型。对于这类过程,我们首先概述了Fourier变换方法在对数价格和对数罢工中有效地计算各种类型期权的价值,并作为一个具体的应用实例,给出了Merton跳扩散模型的两种状态切换形式下的一些数值结果。然后,我们给出了远期启动期权定价问题的一个闭式解,并利用这个结果在一般随机波动率框架下逼近了此类衍生品的价值。
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英文标题:
《Fourier Transform Methods for Regime-Switching Jump-Diffusions and the
Pricing of Forward Starting Options》
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作者:
Alessandro Ramponi
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最新提交年份:
2011
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分类信息:
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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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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英文摘要:
In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strike to efficiently calculate the value of various types of options and as a concrete example of application, we present some numerical results within a two-state regime switching version of the Merton jump-diffusion model. Then we develop a closed-form solution to the problem of pricing a Forward Starting Option and use this result to approximate the value of such a derivative in a general stochastic volatility framework.
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PDF链接:
https://arxiv.org/pdf/1105.4567