Computation of Greeks Using Malliavin Calculus: Malliavin Calculus for Both Continuous and Jump Processes and Greeks in Finance

An Important aspect of Mathematical Finance is the pricing of stocks and other assets. Mathematical techniques using stochastic differential equations were developed in the 1970's that led to a breakthrough in the field and enabled the provision of insurance against loss and the provision of a degree of certainty in financial transactions that was unavailable previously. The pricing of assets changes as initial prices, volatility, interest rates and time to maturity change, and there are important other quantities which have an influence on prices. To guard against loss it is essential to know precisely how prices change as these quantities vary. Unfortunately, stochastic and other complexities make this difficult to do. A method of calculation known as the Malliavin calculus has been used in many papers to provide methods for such calculations. This monograph provides a comprehensive outline of the relevant portions of the calculus and its applications to finance, as well as of several important extensions, and uses it to obtain new results which will assist in this much used analysis.