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Fard, Farzad Alavi and Siu, Dr. Tak (Ken) Kuen

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  • Paper Title: Pricing and Managing Risks of European-Style Options in a Markovian Regime-Switching Binomial Model
  • Department Affiliation: Applied Finance and Actuarial Studies
  • Supervisor's Names:
    • Doctor Tak Kuen Siu
    • Doctor Ryle Perera

Purpose:

We price regime switching risk, when pricing contingent claims in discrete time nance. In addition, we analyse the risk of market incompleteness under Markovian regime switching framework.

Originality:

This is the first paper in the literature that prices regime switching risk, when pricing contingent claims in discrete time finance.

Abstract:

We discuss the pricing and risk management problems of standard European-style options ina Markovian regime-switching CRR binomial model. The market in the model is incomplete, so the no-arbitrage condition is not enough to x a unique pricing kernel, hence, a unique option price. Using the minimal entropy martingale measure, we determine a pricing kernel and derive the corresponding delta hedging strategy. We examine numerically the performance of the hedging strategy by investigating the terminal distribution of hedging errorsand the associated risk measures such as Value at Risk and Expected Shortfall. The impacts of the frequency of re-balancing the hedging portfolio and the transition probabilities of the modulating Markov chain on the quality of hedging will also be discussed.

Design/methodology/approach:

Using the minimal entropy martingale measure, we determine a pricing kernel and derive the corresponding delta hedging strategy. We examine numerically the performance of the hedging strategy by investigating the terminal distribution of hedging errors and the associated risk measures such as Value at Risk and Expected Shortfall.

Keywords:

Binomial Tree, Markov Chain, Regime Switching, Hedging Error, Value at Risk, Expected Shortfall, Non-parametric Distribution