We propose a novel Monte Carlo simulation method for two-dimensional stochastic differential equation (SDE) systems based on approximation through continuous-time Markov chains (CTMCs). Specifically, we propose an efficient simulation framework for asset prices under general stochastic local...

In this paper, we propose a general approximation framework for the valuation of (path-dependent) options under time-changed Markov processes. The underlying background process is assumed to be a general Markov process, and we consider the case when the stochastic time change is constructed from...

The Chicago Board of Options Exchange (CBOE) advocates linking variable annuity (VA) fees to its trademark VIX index in a white paper (CBOE, 2013a, b). It claims that the VIX-linked fee structure has several advantages over the traditional fixed percentage fee structure. However, the evidence...

We propose a novel Monte Carlo simulation method for two-dimensional stochastic differential equation (SDE) systems based on approximation through continuous-time Markov chains (CTMCs). Specifically, we propose an efficient simulation framework for asset prices under general stochastic local...

In this paper we derive exact closed-form density functions of the generalized Verhulst process (see Mackevicius (2015), Jakubowski and Wisniewolski (2015)), and the Bessel process with a constant drift (see Coman et al (1998), Linetsky (2004)), which have applications in mathematical biology...

We study the first hitting time of integral functionals of time-homogeneous diffusions, and characterize their Laplace transforms through a stochastic time change. We obtain explicit expressions of the Laplace transforms for the geometric Brownian motion (GBM) and the mean-reverting GBM process....