Hidden Markovian regime-switching models for pricing and investment in financial markets

Abstract

Option valuation and asset allocation are important and practically relevant problems to financial markets. Incorporation of the impact of regime shifts on asset prices is important from the practical perspective since structural changes in economic states may result in dramatic price fluctuations in the financial market.In practice, the underlying economic states may not be directly observable. Thisprovides a practical ground for works on option valuation and asset allocation under Markovian regime-switching models.Due to the unrealistic geometric Brownian motion assumption for the underlying security’s price imposed in the Black-Scholes option pricing model, we study an option pricing problem under a stochastic interest rate and volatility model with continuous-time hidden Markovian regime switches. By interpreting the states of the modulating Markov chain as hidden states of an economy, the models considered in this thesis are able to incorporate risks of interest rate, volatility and macroeconomic transitions. By means of the standard separation principle, filtering and option valuation problems are separated. Robust filters for the hidden states of the economy and their robust filtered estimates of unknown parameters from the Expectation Maximization (EM) algorithm are presented based on standard techniques in filtering theory. Then an explicit expression of a conditional characteristic function relevant to option pricing is presented and an efficient implementation is developed to value the options. Numerical experiments are given to illustrate the flexibility of filtering algorithms and the significance of regime-switching in option pricing.On account of the long-term memory of financial data, an optimal portfolio selection problem is considered under a discrete-time Higher-Order Hidden Markov-Modulated Autoregressive (HO-HMMAR) model for price dynamics. Estimation methods based on Expectation-Maximization (EM) algorithm are used to estimate the model parameters with a view to reducing numerical redundancy. The asset allocation problem is then discussed in a market with complete information using the standard Bellman's principle. Numerical results based on real financial data reveal that the HO-HMMAR model with order two has a better out-of-sample forecasting accuracy thanthe HMMAR model. The optimal portfolio strategies from the HO-HMMAR model outperform those from the HMMAR model without long-term memory.