Repository :: Browsing by Author "Olengeile, Lilian"

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Price of risk under regime-switching exponential levy process using normal inverse Gaussian(nig)
(University of Dar es Salaam, 2013) Olengeile, Lilian
There has been a lot on attention on modelling dynamics of prices by Regime-switching model. In fact, regime-switching model capture exogeneous macroeconomic cycles against which asset prices evolves. In this dissertation, we study option pricing when the dynamics of the underlying risk asset is governed by regime-switching exponential Levy process. The market parame¬ters, i.e., interest rates, appreciation rate and volatility of the underlying asset are time independent and are governed by a continuous time, finite state hidden Markov chain. Based on the information that the trader has, we derive two pricing kernels and there¬fore, two different prices of the derivative. The first price is computed under the as¬sumption that, we do not take into consideration the risk induced by the Markov chain. The second is computed assuming that the price of risk is taken into consideration. As application, we study four particular cases: Regime-switching Black-Scholes model, regime-switching Merton-Jump diffusion model, regime-switching Variance-Gamma model and regime-switching Normal Inverse Gaussian. The latter being the novelty of this study. We then perform different numerical experiments on these models and find out that, the prices are significantly different when we price the risk than when we do not price the risk.