Black-Scholes framework holds. At time t = 0 you write a T year at-the-money Eur

Question

Black-Scholes framework holds. At time t = 0 you write a T year at-the-money European digital option, value =

V (S, t) = Ker(T t)N(d2).

Assume that at T=0 you are told d2 = 0

Calculate: (a) the initial number 0 of shares of the stock for your hedging program.

(b) option, the standard deviation of the option using this 0.

in terms of the risk free rate r and the term T of the option, Explain:

(c) Do we also need to know for the underlying stock?

(d) What happens to your 0 as T ?

Black scholes equation: https://gyazo.com/2c5fe248b267a8479b3629d0658f20d5

Explanation / Answer

ANSWER:    

We are 95% confident that the actual mean difference between the appraised values and selling prices of all the houses sold in Grand Rapids is between -$3785 and $561.  

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