Explain and show in FULL detail: Assume the Black-Scholes framework. At time t =

ANSWER: We are 95% confident that the population difference between these proportions is between –13.37% and 15.55%.

ID: 2711219 • Letter: E

Question

Explain and show in FULL detail:

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

V (S,t) = Ke^(r(Tt))N(d2).

Assume that at t=0,you are told d2 =0.

Also, If the initial number 0 of shares of the stock for your hedging program is = 1/2

Calculate

1. (a) 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:

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

ANSWER:

We are 95% confident that the population difference between these proportions is between –13.37% and 15.55%.

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