英文标题：
《Numerical analysis for Spread option pricing model in illiquid
underlying asset market: full feedback model》
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作者：
Ahmad Reza Yazdanian, T A Pirvu
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最新提交年份：
2014
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英文摘要：
This paper performs the numerical analysis and the computation of a Spread option in a market with imperfect liquidity. The number of shares traded in the stock market has a direct impact on the stock\'s price. Thus, we consider a full-feedback model in which price impact is fully incorporated into the model. The price of a Spread option is characterize by a nonlinear partial differential equation. This is reduced to linear equations by asymptotic expansions. The Peaceman-Rachford scheme as an alternating direction implicit method is employed to solve the linear equations numerically. We discuss the stability and the convergence of the numerical scheme. Illustrative examples are included to demonstrate the validity and applicability of the presented method. Finally we provide a numerical analysis of the illiquidity effect in replicating an European Spread option; compared to the Black-Scholes case, a trader generally buys more stock to replicate this option.
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中文摘要：
本文对不完全流动性市场中的差价期权进行了数值分析和计算。股票市场上交易的股票数量对股票价格有直接影响。因此，我们考虑一个完全反馈模型，其中价格影响完全纳入模型。价差期权的价格由一个非线性偏微分方程描述。通过渐近展开将其简化为线性方程组。采用Peaceman-Rachford格式作为交替方向隐式方法数值求解线性方程组。我们讨论了数值格式的稳定性和收敛性。举例说明了该方法的有效性和适用性。最后，我们对复制欧洲价差期权的非流动性效应进行了数值分析；与Black-Scholes案例相比，交易者通常会购买更多股票来复制该期权。
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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：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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