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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

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Geometric Brownian Motion

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Option Pricing

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European Call Option Pricing (Pay-Off Function)

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European Call Option Pricing

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Black-Scholes Formula

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Change of Time Method

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Solution for GBM Equation Using Change of Time

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Properties of the Process

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Properties of the Solution of GBM Using Change of Time Method

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Risk-Neutral Stock Price

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Explicit Expression for

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European Call Option Through

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Derivation of Black - Scholes Formula I

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Derivation of Black-Scholes Formula II (continuation)

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Derivation of Black - Scholes Formula III (continuation)

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

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Thank You for Your Attention!

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