Pricing options and equity-indexed annuities in a regime-switching model by trinomial tree method

In this paper we summarize the main idea and results of Yuen and Yang (2009, 2010a, 2010b). The Markov regime-switching model (MRSM) has recently become a popular model. The MRSM allows the parameters of the market model depending on a Markovian process, and the model can reflect the information of the market environment which cannot be modeled solely by linear Gaussian process. The Markovian process can ensure that the parameters change according to the market environment and at the same time preserves the simplicity of the model. It is also consistent with the efficient market hypothesis that all the effects of the information about the stock price would reflect on the stock price. However, when the parameters of the stock price model are not constant but governed by a Markovian process, the pricing of the options becomes complex. We present a fast and simple trinomial tree model to price options in MRSM. In recent years, the pricing of modern insurance products, such as Equity-Indexed annuity (EIA) and variable annuities (VAs), has become a popular topic. These products can be considered investment plans with associated life insurance benefits, a specified benchmark return, a guarantee of an annual minimum rate of return and a specified rule of the distribution of annual excess investment return above the guaranteed return. EIA usually has a long maturity time, hence it is not appropriate to assume that the interest rate and the volatility of the equity index are constants. One way to deal with this problem is to apply the regime switching model. However, the valuation of derivatives in such model is challenging when the number of states are large, especially for the strong path dependent options such as Asian options. Our trinomial tree model provides an efficient way to solve this problem.