X axis stock price see 15 14 how european option

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Unformatted text preview: − qT + K e − rT = (1 − N (d 2 )) K e − rT − Se − qT (1 − N (d1 )) = K e − rT N (− d 2 ) − Se − qT N (− d1 ) 15-12 BS model in excel (with dividends) • See “BS div” • See “BS div VBA” • See “BS general” 15-13 How European call option prices react to input changes: stock price - See “BS chart” tab. X-axis = stock price See 15-14 How European option prices react to input changes: volatility - Exercise 3 15-15 Greeks in BS model - In the previous two slides, we observed that the In call option price changes with stock price and volatility volatility - So, we are interested in knowing how the call/put So, option changes with all inputs (i.e., the sensitivity of the option price to market conditions) of - Such sensitivity is usually labeled “Greeks” in Such option pricing option - Derivation details are available from Prof. Garven’s Derivation website (“Derivation and Comparative Statics of the Black-Scholes Call and Put Option Pricing Equations,”) http://www.garven.com/research.htm 16 Equations,”) 15- Delta (Δ) - Delta: represents the sensitivity of option price to Delta: stock price changes stock ∆call = ∂c / ∂S = ∂[ S e − qT N (d1 ) − K e − rT N ( d 2 ) ]/∂S = e −qT N (d1 ) > 0 ∆put = ∂p / ∂S = ∂[ K e −rT N (−d 2 ) − S e −qT N (−d1 ) ]/∂S = − e −qT N (−d1 ) < 0 The price change of a call option is positively related to The the price of its underlying asset (sto...
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