The price of risk under regime switching exponential levy model using regime switching Meixner model

In this work, option valuation problems are investigated when the price dynamics of the underlying asset is governed by a regime switching Meixner model. In the model, parameters such as interest rate, appreciation rate and volatility are assumed to be time-dependent. Since the regime switching model leads to aan incomplete market characterized by infinitely many equivalent martingale measures, the regime switching Esscher transform introduced by Elliot et al., (2005) is used to select one set from many equivalent martingale measures. Then, pricing kernels are developed leading to two conceeptually different derivative pricing rules which are pricing or not pricing a regime switching risk associated with the Markov chain. These pricing rules are used to determine the Esscher parameters under two kernels. Finally, numerical experiments are conducted to assess the impact of pricing versus not pricing a regime switching risk on the prices of exotic call options such as fixed-strike Lookback option, up and in Barrier option and fixed-strike Asian option. The results obtained are compared with the results for Black-Scholes model to assess the impact of jumps on the prices of exotic call options mentioned earlier. In the analysis, the results show that, regime switching Meixner model which takes into account the effect of jumps gives higher prices than Black-Scholes model which do not take into account the effect of jumps.