摘要翻译:
近年来,在随机波动率模型(如Heston模型)下,人们对股票期权的定价越来越感兴趣。由于标准的有限差分格式可能导致模拟结果的显著偏差,Heston模型的模拟往往是困难的。将偏差降低到一个可接受的水平不仅具有挑战性,而且计算要求很高。在本文中,我们通过提供一种替代的模拟策略来解决这个问题--一种系统地减少模拟中的偏差的策略。此外,我们的方法是自适应的,并实现了减少偏差“接近”最小的计算努力。我们用一个数值例子来说明这一特征。
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英文标题:
《Adaptive Simulation of the Heston Model》
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作者:
Ian Iscoe and Asif Lakhany
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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:Mathematics 数学
二级分类:Classical Analysis and ODEs 经典分析与颂歌
分类描述:Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics
特殊函数、正交多项式、调和分析、Ode、微分关系、变分法、逼近、展开、渐近
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一级分类:Mathematics 数学
二级分类:Numerical Analysis 数值分析
分类描述:Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法,科学计算
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英文摘要:
Recent years have seen an increased level of interest in pricing equity options under a stochastic volatility model such as the Heston model. Often, simulating a Heston model is difficult, as a standard finite difference scheme may lead to significant bias in the simulation result. Reducing the bias to an acceptable level is not only challenging but computationally demanding. In this paper we address this issue by providing an alternative simulation strategy -- one that systematically decreases the bias in the simulation. Additionally, our methodology is adaptive and achieves the reduction in bias with "near" minimum computational effort. We illustrate this feature with a numerical example.
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PDF链接:
https://arxiv.org/pdf/1111.6067