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Lecture6_BSmodel

# Table data see exercise4 for a practice for array

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Unformatted text preview: ck) – higher stock price means better profits from call option price The price change of a put option is negatively related The to the price of its underlying asset (stock) – lower stock price means better profits from put option price 15-17 Delta in excel • See “BS delta” • See “SuperBS” that computes both prices and delta • See “BS array” that outputs both prices and delta • See “BS table” that outputs both prices and delta in See Data Table Data • See “Exercise4” for a practice for array output 15-18 Gamma (Γ) - Gamma: represents how delta changes with Gamma: respect to stock prices (2nd order effect) (2 Γ call = ∂ 2 c / ∂S 2 = ∂[e − qT N (d1 )] /∂S = N ′(d1 ) e − qT /Sσ T Γ put = ∂ 2 p / ∂S 2 = ∂[− e − qT N (− d1 )]/∂S = N ′(d1 ) e − qT /Sσ T N ′(d1 ) = e − d12 / 2 / 2π The gammas of call and put are the same The See “Greeks” tab See 15-19 Vega - Vega: represents the sensitivity of option price to Vega: stock volatility stock Vega(call ) = ∂c / ∂σ = ∂[ S e − qT N (d1 ) − K e − rT N (d 2 ) ]/∂σ = Se −qT N ′(d1 ) T > 0 Vega( put ) = ∂p / ∂σ = ∂[ K e −rT N (−d 2 ) − S e −qT N (−d1 ) ]/∂σ...
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