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Derivation of Black - Scholes Formula by Change of Time Method

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. Geometric Brownian Motion. Option Pricing.

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Derivation of Black - Scholes Formula by Change of Time Method

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  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 EquationUsing Change of Time

  9. Properties of the Process

  10. Properties of the Solution of GBMUsing 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!

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