We consider the classical Black-Scholes model with single risky asset that follows a geometric Brownian motion:
where () is a standard Brownian motion, is the constant volatility, is the constant risk-free rate and is the initial asset price.
Under these conditions, for any the stock price is given by the following formula:
We consider a security with time to maturity and the payoff function:
Payoff of the form corresponds to a digital call options with strike price, .
We will consider several methods for computing the price of this security.
Parameters