We solve two optimal stopping problems whose payoff functions are the maximum and the minimum of two state variables driven by the Ornstein-Uhlenbeck processes. We consider a class of problems where we obtain analytical solutions. Furthermore, by making use of the analytical results we study...

We propose a method for constructing an arbitrage-free multi-asset pricing model which is consistent with a set of observed single- and multi-asset derivative prices. The pricing model is constructed as a random mixture of N reference models, where the distribution of mixture weights is obtained...

A State Price Density (SPD) is the density function of a risk neutral equivalent martingale measure for option pricing, and is indispensible for exotic option pricing and portfolio risk management. Many approaches have been proposed in the last two decades to calibrate a SPD using financial...

This paper investigates time-changed infinite activity derivatives pricing models from the sequential Bayesian perspective. It proposes a sequential Monte Carlo method with the proposal density generated by the unscented Kalman filter. This approach overcomes to a large extent the particle...

Catastrophe (CAT) bond markets are incomplete and hence carry uncertainty in instrument pricing. As such various pricing approaches have been proposed, but none treat the uncertainty in catastrophe occurrences and interest rates in a sufficiently flexible and statistically reliable way within a...

In this paper we consider option pricing using multivariate models for asset returns. Specifically, we demonstrate the existence of an equivalent martingale measure, we characterize the risk neutral dynamics, and we provide a feasible way for pricing options in this framework. Our application...

This paper presents a tailor-made discrete-time simulation model for valuing path-dependent options, such as lookback option, barrier option and Asian option. In the context of a real-life application that is interest to many students, we illustrate the option pricing by using Quasi Monte Carlo...

Fast and accurate sampling of conditional time-integrated variance in the Heston model is an important and challenging problem. We proved that this very complicated distribution converges to the moment-matched Inverse Gaussian distribution as the time interval goes to infinity. Leveraging on...

Recently, simulation methods combined with regression techniques have gained importance when it comes to American option pricing. In this paper we consider such methods and we examine numerically their convergence properties. We first consider the Least Squares Monte-Carlo (LSM) method of...

The implied volatility surface (IVS) is a fundamental building block in computational finance. We provide a survey of methodologies for constructing such surfaces. We also discuss various topics which can influence the successful construction of IVS in practice: arbitrage-free conditions in both...