Abstract
We consider the pricing of exotic options when the price dynamics of the underlying risky asset are governed by a discrete-time Markovian regime-switching process driven by an observable, high-order Markov model (HOMM). We assume that the market interest rate, the drift, and the volatility of the underlying risky asset's return switch over time according to the states of the HOMM, which are interpreted as the states of an economy. We will then employ the well-known tool in actuarial science, namely, the Esscher transform to determine an equivalent martingale measure for option valuation. Moreover, we will also investigate the impact of the high-order effect of the states of the economy on the prices of some path-dependent exotic options, such as Asian options, lookback options, and barrier options.
Highlights
Regime switching models are important models in econometrics and finance
We consider the pricing of exotic options when the price dynamics of the underlying risky asset are governed by a discrete-time Markovian regime-switching process driven by an observable, high-order Markov model (HOMM)
We investigated the pricing of exotic options under a discrete-time Markovian regimeswitching process driven by an observable HOMM, which can incorporate the high-order effect in the states of the economy
Summary
Regime switching models are important models in econometrics and finance. They have received much attention among academic researchers and practitioners in modeling economic and financial time series. The advantage of a discrete-time framework is its flexibility to incorporate more features in the model, such as the high-order effect in the underlying Markov chain for the model parameters. Incorporating the high-order effect in the underlying Markov chain provides more flexibility in modeling the temporal behavior of the states of an economy and its impact on asset price dynamics. The impact of such a high-order effect on the behavior of option prices is not well explored in the literature. We consider the pricing of exotic options when the price dynamics of the underlying risky asset are governed by a discrete-time Markovian regime-switching process driven by an observable, high-order Markov model (HOMM).
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