BSM model. It is Oct 22, 2023 and you consider trading options on a security priced at $47 with standard deviation on the continuously compounded returns of 17%. The options are European with a strike price of $41 and expiration date Apr 5, 2024. The continuously compounded risk-free rate associated with the expiration is 5%. Assume that the security is a non-dividend paying stock and the Black-Scholes model is appropriate for pricing. Notes: 1. The cumulative standard normal table is available on Moodle. 2. Use full accuracy in all the calculations except for finding N (d1,2). These values are supposed to come from the table, which has 2 decimals accuracy. Thus, if you are using Excel you must round the arguments of N (d1,2) to 2 decimals. 3. Wherever needed, use = 3.14 a. What is the value of the call option? $ Number Round your answer to two decimal places. b. What is the value of the put option? $ Number Round your answer to two decimal places. c. What is the number of call option contracts necessary to delta-neutral hedge 8,000 shares of the stock (with a sign!)? Number contracts Round your answer to the nearest integer d. What is the put gamma for a stock price movement from $47 to $47.87 Number Round your answer to two decimal places e. What is the value of the call scaled vega for a given shift in volatility from 17% to 16.4% ? $ Number Round your answer to two decimal places