Monte Carlo simulation

Abstract

This chapter discusses another major numerical method, namely simulation. It has proven extremely flexible and useful for addressing uncertainty in the price of assets and portfolios of assets. This notwithstanding, it is relatively inefficient when the number of state variables is low. Improved sampling methods are one attempt to making convergence faster. Regarding the valuation of derivative assets, simulation was initially confined to European-type options and path-dependent options given its forward-looking nature. Nonetheless, significant advances have taken place during the last decade or so. As a consequence, simulation has also extended to the valuation of American-type options, which require backward induction. Here we show how to generate random paths for a single stochastic process (be it either non-stationary or stationary) and for several (correlated or independent) processes. We then show how to apply Monte Carlo simulation to the valuation of investment options. We can also follow this approach for assessing the risk profile of a number of energy projects.