Market price of risk

Abstract

Most people find stochastic calculus intimidating and skip through complex equations. While there is no way of simplifying them, this work is an attempt to relate some of the widely used concepts in pricing financial derivatives to the practical market observations. Recent financial crisis has brought many adverse economic changes, but has also challenged the long-standing beliefs, such as that interest rates will always remain positive. Although the debate on its exact causes is unlikely to be settled, many blame complex derivatives and underlying models. Quantitative analysts that developed them, on the other hand, claim that the math was correct, but the complex products were mis-sold. Regardless of what side one wishes to take, the fact remains that the stochastic differential equations and integrals underlying most derivatives pricing models cannot be easily related to the actual market movements. Here, Markov and Wiener processes - the cornerstones of financial calculus - are explained in relation to return on investment, via market price of risk.

Keywords

• stochastic variables
• Markov process
• Wiener process
• Ito process
• market price of risk