Analysis of pricing financial derivatives under regime-switching economy
thesisposted on 28.03.2022, 16:38 authored by Farzad Alavi Fard
In this thesis we argue that regime-switching models can significantly improve the pricing models for financial derivatives. We use three examples to analyse the valuation of derivative contracts under the Markovian regime-switching framework, namely, 1) a European call option, 2) a Ruin Contingent Life Annuity, and 3) a participating product. Such a regime-switching framework unveils a potent class of models. Throughout the modulation of the model parameters by a Markov chain, they can simultaneously explain the asymmetic leptokurtic features of the returns' distribution, as well as the volatility smile and the volatility clustering effect. The intuition behind regime-switching models is to capture the appealing idea that the macro-economy is subjected to regular, yet unpredictable in time, states, which in turn affects the prices of financial securities. The market considered in this thesis is incomplete in general due to additional sources of uncertainty, particularly the regime-switching risk. Under these market conditions, a perfectly replicating trading strategy does not exist and there is more than one equivalent martingale measure. As a result, a perfect hedge for derivative contracts is impossible and the holder of the financial derivative needs to impose some testable restrictions to price the residual risk. In this study, we argue that a condition that minimizes the elative entropy between the risk-neutral and the historical probability measures is very suitable. Such condition, determines a price for the derivative contract that maximizes an exponential utility function for the holder. For doing so, we either use the Minimum Entropy Martingale Measure or Esscher Transform to choose the equivalent martingale measure. Due to the complexity of the pricing models, stemmed from either the modeling assumptions or the path-dependency of the payoff of the derivatives products, there is no known analytical solution to our problems. We employ different numerical methods in each chapter, depending on the respective modeling framework, to approximate the solutions. We also examine numerically the performance of simple hedging strategies by investigating the terminal distribution of hedging errors and 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 are also discussed.