Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in regime-switching models. In this article, we reduce an...

This paper establishes the second-order convergence rates of the continuous-time Markov chain (CTMC) approximation method for pricing continuously monitored occupation time derivatives (step options, conditional Asian options) and arithmetic Asian options and their Greeks. We fill the gap in the...

We propose an explicit closed-form approximation formula for the price of discretely monitored single or double barrier options whose underlying asset evolves according to a generic one-dimensional Markov process. This set of stochastic processes includes, but is not limited to, diffusion and...

Recently, Cai et al. (2015) proposed closed-form double transform approxima- tion formulas for prices of both discretely and continuously monitored Asian options under the setting of a general continuous-time Markov chain. In this note, we analytically invert the Z−transform and the Laplace...

We consider two sequences of Markov chains inducing equivalent measures on the discrete path space. We establish conditions under which these two measures converge weakly to measures induced on the Wiener space by weak solutions of two SDEs, which are unique in the sense of probability law. We...

We study both theoretically and empirically option prices on firms undergoing a cash merger offer. To estimate the merger's success probability, we use a Markov Chain Monte Carlo (MCMC) method using a state space representation of our model. Our estimated probability measure has significant...

A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general formula for the martingale price of a European call option. A...

A discrete time model of financial markets is considered. It is assumed that the stock price evolution is described by a homogeneous Markov chain. In the focus of attention is the expected value of the guaranteed profit of the investor that arises when the jumps of the stock price are bounded....

We consider a semi-Markov modulated market consisting of a riskless asset or bond, B, and a risky asset or stock, S, whose dynamics depend on a semi-Markov process x. Using the martingale characterization of semi-Markov processes, we note the incompleteness of semi-Markov modulated markets and...

This paper establishes the precise second order convergence rates of the continuous-time Markov chain (CTMC) approximation method for pricing options and calculating its Greeks under the general framework of stochastic local volatility models, which include the Heston and SABR models as special...