Options Pricing and Hedging in a RegimeSwitching Volatility Model
 Publication Year:
 2014

 Bepress 925

 Bepress 127
 Repository URL:
 https://ir.lib.uwo.ca/etd/2160; https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=3581&context=etd
 Author(s):
 Tags:
 Analytic Approximation; Coupled Partial Differential Equations; European Option; Hedging; Implied Volatility; Option Pricing; Quantitative Finance; RegimeSwitching; Risk Premia; Applied Mathematics; Finance; Numerical Analysis and Computation; Other Applied Mathematics; Partial Differential Equations
article description
Both deterministic and stochastic volatility models have been used to price and hedge options. Observation of real market data suggests that volatility, while stochastic, is well modelled as alternating between two states. Under this twostate regimeswitching framework, we derive coupled pricing partial differential equations (PDEs) with the inclusion of a statedependent market price of volatility risk (MPVR) term.Since there is no closedform solution for this pricing problem, we apply and compare two approaches to solving the coupled PDEs, assuming constant Poisson intensities. First we solve the problem using numerical solution techniques, through the application of the CrankNicolson numerical scheme. We also obtain approximate solutions in terms of known BlackScholes formulae by reformulating our problem and applying the CauchyKowalevski PDE theorem. Both our pricing equations and our approximate solutions give way to the analysis of the impact of our statedependent MPVR on theoretical option prices. Using financially intuitive constraints on our option prices and Deltas, we prove the necessity of a negative MPVR. An exploration of the regimeswitching option prices and their implied volatilities is given, as well as numerical results and intuition supporting our mathematical proofs.Given our regimeswitching framework, there are several different hedging strategies to investigate. We consider using an option to hedge against a potential regime shift. Some practical problems arise with this approach, which lead us to set up portfolios containing a basket of two hedging options. To be more precise, we consider the effects of an option going too far in and outofthemoney on our hedging strategy, and introduce limits on the magnitude of such hedging option positions. A complementary approach, where constant volatility is assumed and investor's risk preferences are taken into account, is also analysed.Analysis of empirical data supports the hypothesis that volatility levels are affected by upcoming financial events. Finally, we present an extension of our regimeswitching framework with deterministic Poisson intensities. In particular, we investigate the impact of time and stock varying Poisson intensities on option prices and their corresponding implied volatilities, using numerical solution techniques. A discussion of some eventdriven hedging strategies is given.