1. Derivation of Black - Scholes Formula by Change of Time Method Anatoliy Swishchuk Mathematical and Computational Finance Laboratory, Department of Mathematics and Statistics, University of Calgary “Lunch at the Lab” Talk April 14, 2005

2. Geometric Brownian Motion

3. Option Pricing

4. European Call Option Pricing (Pay-Off Function)

5. European Call Option Pricing

6. Black-Scholes Formula

7. Change of Time Method

8. Solution for GBM Equation Using Change of Time

9. Properties of the Process

10. Properties of the Solution of GBM Using Change of Time Method

11. Risk-Neutral Stock Price

12. Explicit Expression for

13. European Call Option Through

14. Derivation of Black - Scholes Formula I

15. Derivation of Black-Scholes Formula II (continuation)

16. Derivation of Black - Scholes Formula III (continuation)

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

18. Thank You for Your Attention!