6. A European style digital option pays one unit of currency if ST K. Find the Black Scholes price for a digital option as a function of o (the stock volatility), r (the risk free rate), S. (the spot price), and K. Hint: This uses the Black Scholes theory (log-normal stock price) but not the Black Scholes formula. Express St in terms of the exponential of a Gaussian (identify the mean and variance) or in terms of a standard normal. Then write the event that the option is in-the- money (has a non-zero payout) in terms of this Gaussian. Then write the the probability of a payout in terms of the cumulative normal (the N function). Remember to discount. 6. A European style digital option pays one unit of currency if ST K. Find the Black Scholes price for a digital option as a function of o (the stock volatility), r (the risk free rate), S. (the spot price), and K. Hint: This uses the Black Scholes theory (log-normal stock price) but not the Black Scholes formula. Express St in terms of the exponential of a Gaussian (identify the mean and variance) or in terms of a standard normal. Then write the event that the option is in-the- money (has a non-zero payout) in terms of this Gaussian. Then write the the probability of a payout in terms of the cumulative normal (the N function). Remember to discount