3. Binary option under normal distribution of price SP500 index currently is trading at 2,800. A binary call option will pay you $1 if the price at expiration is above the strike price, 50 otherwise, Binary put will pay you $100 if price at expiration is below the strike, and so otherwise. a. You believe in the next year, the price will follow a normal distribution with mean at current price and standard deviation of 20%, or 2000 20% - 400 points. What is the price of a binary CALL option with strike at 2,500 (2 points) b. You observed that a binary PUT with strike at 2400 with 1 year before expiration is priced at $10. What is the implied annual volatility (4 points)? 3. Binary option under normal distribution of price SP500 index currently is trading at 2,800. A binary call option will pay you $1 if the price at expiration is above the strike price, 50 otherwise, Binary put will pay you $100 if price at expiration is below the strike, and so otherwise. a. You believe in the next year, the price will follow a normal distribution with mean at current price and standard deviation of 20%, or 2000 20% - 400 points. What is the price of a binary CALL option with strike at 2,500 (2 points) b. You observed that a binary PUT with strike at 2400 with 1 year before expiration is priced at $10. What is the implied annual volatility (4 points)