Pricing variance swaps under a stochastic interest rate and volatility model with regime-switching

In this paper, we investigate the pricing of variance swaps under a Markovian regime-switching extension of the Schöbel-Zhu-Hull-White hybrid model. The parameters of this model, including the mean-reversion levels and the volatility rates of both stochastic interest rate and volatility, switch over time according to a continuous-time, finite-state, observable Markov chain. By utilizing techniques of measure changes, we separate the interest rate risk from the volatility risk. The prices of variance swaps and related fair strike values are represented in integral forms. We illustrate the practical implementation of the model by providing a numerical analysis in a two-state Markov chain case, which shows that the effect of both stochastic interest rate and regime-switching is significant in the pricing of variance swaps.8 page(s

Asset pricing and portfolio optimization under regime switching models

Theoretical thesis.Bibliography: pages 145-155.1. Introduction -- 2. Option valuation under a double regime-switching model -- 3. Pricing variance swaps under a stochastic interest rate and volatility model with regime switching -- 4. Mean-variance portfolio selection with uncertain investment horizon under a regime-switching jump-diffusion model -- 5. Stochastic differential game, Esscher transform and general equilibrium under a Markovian regime-switching Lévy model -- 6. Conclusion.Recently, there has been a considerable interest in applications of regime-switching models in various aspects of finance and insurance. One of the main features of these models is that some model parameters are modulated by a finite-state Markov chain. This makes regime-switching models very useful to describe structural changes in macro-economic conditions, periodical fluctuations in business cycles and sudden transitions in market modes.In this thesis, a continuous-time, finite-state, observable Markov chain is adopted to model the regime switches. Our regime-switching models are a set of diffusion models, jump-diffusion models or Levy models coupled by the underlying Markov chain. Under this modeling set up, the financial market is incomplete. So asset pricing and portfolio optimization problems are more involved.Roughly speaking, this thesis can be divided into two parts. The first part is devoted to asset pricing problems under regime-switching models. Due to the market incompleteness, the equivalent martingale measure is not unique. Therefore, we either choose a particular equivalent martingale measure using the Esscher transform or start directly from a risk-neutral measure. We present analytical pricing formulae for European options and variance swaps in Chapters 2 and 3, respectively. Numerical and empirical implementations of these formulae show that the regime-switching effect is material for asset pricing problems.In the second part of this thesis, we apply the stochastic optimal control theory to discuss portfolio optimization problems under regime-switching models. In Chapter 4, we use the dynamic programming principle approach to solve a mean-variance portfolio selection problem with uncertain investment horizon. Explicit expressions of the efficient portfolio and the efficient frontier are obtained. In Chapter 5, the stochastic optimal control theory for portfolio optimization problems is borrowed to investigate an fundamental issue in asset pricing problems, i.e. the selection of equivalent martingale measures. We derive and compare equivalent martingale measures selected by three different approaches, that is, the stochastic differential game approach, the Esscher transformation approach and the general equilibrium approach.Mode of access: World wide web1 online resource (ix, 157 pages) colour illustration