Binary option under normal distribution
AAPL currently is trading at $100. A binary call option will pay you $1 if the price at expiration is above the strike price, $0 otherwise.
Risk-free rate of interest is zero.
a. Using data, you estimated a weekly standard deviation of 2.5% and 4-week standard deviation of 5%. Price the following binary options based on your estimation:
(1) and expiration in 1 week;
(2) and expiration in 4 weeks.
b. Assuming mean of zero, if a binary option with strike of $110 is priced at $0.15 four weeks before expiration, what is the implied volatility?