Question

Consider the European digital option that pays a constant H if the stock price is above strike price X at maturity and zero otherwise. Assuming stock price S follows the following SDE under physical measure dS Assuming the risk-free rate is constant r. Please write down the price of this option and explain how it is related to the price of the standard Black-Scholes European call option.

Answer 1

As per guidelines first question is answered

Price of this option

C = e−rτE ( QI{ST >K} = Qe−rτP{ST > K} = Qe−rτN(d2)

d2 = ln(S/K)+(r − q − σ2/2)τ /σ √τ

Black scholes model can be used for calculating European rate interest call options which assumes that price of the futures follows geometric Brownian motion . Future price= security providing continuous dvidend yield equal to r