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American option pricing under financial crisis
Author(s) -
Luo Xuemei,
Xiang Kaili,
Ding Chuan
Publication year - 2018
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2310
Subject(s) - partial differential equation , valuation of options , arbitrage , crash , jump diffusion , black–scholes model , jump , finite difference methods for option pricing , mathematical economics , financial crisis , economics , index (typography) , mathematics , econometrics , financial economics , computer science , volatility (finance) , mathematical analysis , physics , keynesian economics , quantum mechanics , world wide web , programming language
In this paper, we take financial crisis into consideration for American call options and put options pricing problems by using a jump diffusion model. Under no‐arbitrage pricing principle, we obtain a PDE (partial differential equation), which is different from the PDE derived from the classical Black‐Scholes model, it adds a postcrash market index to the primary equation. Then, we introduce the penalty method for solving the nonlinear PDE. Numerical results suggest that the option value will be affected by the crash.