American option pricing under financial crisis

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  • Author: Xuemei Luo, Kaili Xiang and Chuan Ding
  • Date: 08 March 2019
  • Copyright: Image copyright of Patrick Rhodes

In a paper published in Applied Stochastic Models in Business and Industry, the authors 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, the authors 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, they introduce the penalty method for solving the nonlinear PDE. Numerical results suggest that the option value will be affected by the crash.

The paper is available here and the authors explain their findings in further detail below:

American option pricing under financial crisis

Xuemei Luo, Kaili Xiang and Chuan Ding

Applied Stochastic Models in Business and Industry, Volume 34, Issue 5,

Special Issue: Stochastic Models, Statistics and Their Applications

September/October 2018

Pages 597-606

thumbnail image: American option pricing under financial crisis

Initially motivated by work with Black and Scholes, option pricing has generated enormous interest. The original assumptions have been broadened, every kinds of options with their pricing model have arisen. The interest rate change from constant to
stochastic, stock price are not successive but interrupted by a series of jumps, option can be exercised at any time or at some specified time, taking transaction cost into consideration and so on.

This paper consider American option pricing under financial meltdown, different from European option, American option can be exercised at any time rather than at the expiry date. Penalty method has been introduced to solve the free-boundary problem when is the optimal exercise moment. This work has important influence on American option pricing, since in the real financial market, major events will have an impact on stock price, which make stock price is subject to the distribution with oscillatory term, this model depicts the realistic stock price dynamics vividly.

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