Derivation of Black - Scholes Formula by Change of Time

Method

Anatoliy SwishchukMathematical and Computational Finance Laboratory,

Department of Mathematics and Statistics,University of Calgary

“Lunch at the Lab” TalkApril 14, 2005

Geometric Brownian Motion

Option Pricing

European Call Option Pricing(Pay-Off Function)

European Call Option Pricing

Black-Scholes Formula

Change of Time Method

Solution for GBM EquationUsing Change of Time

Properties of the Process

Properties of the Solution of GBMUsing Change of Time Method

Risk-Neutral Stock Price

Explicit Expression for

European Call Option Through

Derivation of Black - Scholes Formula I

Derivation of Black-Scholes Formula II (continuation)

Derivation of Black - Scholes Formula III (continuation)

Derivation of Black - Scholes Formula IV (continuation and the end)

Thank You for Your Attention!