In this work, we consider the issue of pricing exchange options and spread options with stochastic interest rates. We provide the closed form solution for the exchange option price when interest rate is stochastic. Our result holds when interest rate is modeled with a stochastic term structure of general form, which includes Vasicek model, CIR term structure, and other well-known term structure...

In this paper, we present global nonlinear gyrokinetic simulations including finite βe effects and collisions in tokamak geometry. Global electromagnetic simulations using conventional δf particle in cell methods are very demanding, with respect to numerical resources, in order to correctly describe the evolution of the non-adiabatic part of the electron distribution function. This difficulty h...

For general volatility structures for forward rates, the evolution of interest rates may not be Markovian and the entire path may be necessary to capture the dynamics of the term structure. This chapter identifies conditions on the volatility structure of forward rates that permit the dynamics of the term structure to be represented by a two-dimensional state variable Markov process. The permis...

Fully sequential selection procedures have been developed in the field of stochastic simulation to find the simulated system with the best expected performance when the number of alternatives is finite. Kim and Nelson proposed the KN procedure to allow for unknown and unequal variances and the use of common random numbers. KN approximates the raw sum of differences between observations from two...

We present an unbiased numerical integration algorithm that handles both low-frequency regions and high-frequency details of multidimensional integrals. It combines quadrature Monte Carlo by using a quadrature-based approximation as control variate the signal. adaptively build constructed piecewise polynomial, which can be analytically integrated, accurately reconstructs integrand. then recover...

The standard method for generating multi-t vectors is simple and convenient but it has the disadvantage that the generated multi-normal and multi-t vectors are not similar. For t-copula models this destroys much of the variance reduction when using the result of the multinormal model as external control variate. Therefore we develop a new generation method for multi-t vectors. It is based on th...

An efficient Monte-Carlo simulation for the pricing of barrier options in a Markov-switching model is presented. Compared to a brute-force approach, relying on the simulation of discretized trajectories, the presented algorithm simulates the underlying stock-price process only at state changes and at maturity. Given these pieces of information, option prices are evaluated using the probability ...

Monte-Carlo Tree Search (MCTS) has proven to be a powerful, generic planning technique for decision-making in single-agent and adversarial environments. The stochastic nature of the Monte-Carlo simulations introduces errors in the value estimates, both in terms of bias and variance. Whilst reducing bias (typically through the addition of domain knowledge) has been studied in the MCTS literature...