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 Black & Scholes : A Standard Option Pricing Model ( Part 1 )
Issued on July 10 2011 par Calendarspread
Black & Scholes option pricing model is the most known amongst traders. Here is how one could derive it.
Black & Scholes model is the most known amongst traders. It may be one of the most famous formula known over the world.
This option pricing model is in fact a pure extension of the Louis Bachelier Option Pricing Model, written in 1900. Here is how one could derive it. (Widely inspired by P.W.). I - A Basic Equation We know from Time And Volatility Equivalence that if S follows a geometric brownian motion, If r <> 0 V(S,t) = Δ . S + (1/r) . (0.5 . Γ . S² . σ² + Θ) Where, V Option Value Δ Option Delta r continuously compound Interest Rate Γ Option gamma σ annualized volatility Θ annualized theta T yearly maturity t present date It's sometimes written as rV(S,t) - rΔ . S + 0.5 . Γ . S² . σ² + Θ = 0 ps : if r = 0 (0.5 . Γ . S² . σ² + Θ) = 0 II - General Solution The principle widely used changes of variables.     As far as Black Scholes assumptions hold, it provides a way to price a lot of derivative products. Next : Black & Scholes : A Standard Option Pricing Model ( Part 2 ) Previous : Black & Scholes : A First Attempt Pdf connexes : - Understanding N(d1) and N(d2) : Risk-Adjusted Probabilities in the Black-Scholes Model - Black-Scholes Option Pricing Model - On the Black-Scholes Equation: Various Derivations OPTIONS PRICING MODEL - INDEX OPTIONS PRICING MODEL - INDEX OPTIONS PRICING MODEL - CHAPTER I OPTIONS PRICING MODEL - CHAPTER II OPTIONS PRICING MODEL - CHAPTER III Calendarspread |
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