Chris Strickland

Monte Carlo Valuation of Interest Rate Derivatives Under Stochastic Volatility

CHRIS STRICKLAND is with the Financial Options Research Centre at the University of Warwick. 0th Longstaff and Schwartz [1992] (LS) and Fong and Vasicek [1992] (FV) have developed two-factor stochastic volatility models of the term strucB ture in whch the two factors are the short rate and the variance of the short rate. The motivation behind these models is recogrution that the assumption of perfect correlation between rates implicit in one-factor models is too restrictive and that the volatihty of interest rates changes randomly over time and is correlated with the level of interest rates. The Longstaff-Schwartz model is developed in a general equilibrium framework, and the processes for the interest rate and the volathty of the interest rate are endogenously determined. LS are able to derive closedform solutions to the prices of dxount bonds and also to price ducount bond options “analytically” within their framework.’ The model of Fong and Vasicek is perhaps more intuitive. They start by assuming plausible stochastic processes for the short rate and short rate volatility. In their article, however, FV describe pricing only discount bonds, and the solution they present requires complex (as opposed to real) algebra, posing potential problems for practical implementation. Since then, Selby and Strickland [1995] have detailed a series solution for the bond price that can be implemented easily and computationally efficiently in a programming language or spreadsheet, avoiding the need to deal with complex numbers. The contribution of this article to this literature is twofold. First, we extend the work of Fong and Vasicek and show how to price a wide variety of interest rate derivatives withm their framework. We begin by showing how to price hscount bond options, and

A Multi-factor Structural Model for Australian Electricity Market Risk

In this paper, we develop a general framework for the modelling of Australian electricity market risk based on the structural relationships in the market. The model framework is designed to be consistent with temperature and load mean forecasts, market forward price quotes, the dependence of load on temperature, and the dependence of price on load. The primary use of the model is for the accurate evaluation of the market risk of an electricity generation and retail company but it can also be used for the valuation of electricity market derivatives and assets. We demonstrate the application of our framework to the Australian National Electricity Market (NEM).