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BlackScholes

# BlackScholes - The Black-Scholes Formula By Dr Fernando Diz...

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The Black-Scholes Formula By Dr. Fernando Diz

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The Black Scholes Formula C = S N(d1) - E e -rT  N(d2) where: d1 = (ln(S/E) + (r+sigma 2 /2)T)/sigma*sqrt(T) d2 = d1 - sigma*sqrt(T) N(d1), N(d2) = cumulative normal probabilities. sigma 2  = annualized variance of the continuously                  compounded return on the underlying. r = continuously compounded risk-free rate.
Inputs of the BS Formula Before we can use and understand the BS  formula we need to understand its inputs. The price of the underlying asset. The exercise price. The risk-free rate. The ‘volatility’ of the underlying asset. The time to expiration.

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Inputs of the BS Formula Which input is unobservable? THE VOLATILITY !! How do we estimate it? Historical estimation. Implied estimation.
Historical Estimation This type of estimation ASSUMES that the  volatility of the underlying asset is  constant over time. Steps: Take a sample of say, daily cont.  compounded returns:                 r i  =  ln(S i /S i-1 )  for i = 1,…..n.

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Historical Estimation
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BlackScholes - The Black-Scholes Formula By Dr Fernando Diz...

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