The Variance of Standard Options

Speaker
Adi Ben Meir, Department of Mathematics, Bar-Ilan
Date
01/04/2012 - 10:30Add to Calendar 2012-04-01 10:30:00 2012-04-01 10:30:00 The Variance of Standard Options The most commonly used theory of option pricing is the Black-Scholes PDE model, which is used to obtain the expectation (first moment) of an option's current value. We show that modified Black-Scholes PDEs can be used to obtain the n-th moment of an option's current value. We demonstrate how to find the second moment and the zeroth order moment for  different standard options (European options, barrier options, American options), and use this to find the variances of the option values, and the probabilities to  expire worthless.These latter two quantities give us a perspective of the option's risk, which is important in investment decisions and in pricing theories. אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Abstract

The most commonly used theory of option pricing is the Black-Scholes PDE model, which is used to obtain the expectation (first moment) of an option's current value. We show that modified Black-Scholes PDEs can be used to obtain the n-th moment of an option's current value. We demonstrate how to find the second moment and the zeroth order moment for  different standard options (European options, barrier options, American options), and use this to find the variances of the option values, and the probabilities to  expire worthless.These latter two quantities give us a perspective of the option's risk, which is important in investment decisions and in pricing theories.

Last Updated Date : 20/03/2012