The number of trading days between March 25, 2024, and January 17, 2025 (Give your answer as a whole number of days) 106 Calculate the time in years, based on trading days rather than calendar days, between March 25, 2024, and January 17, 2025. (Give your answer as a decimal, to 4 d.p.) 0.2904 Generally, a rule of thumb to be used for finding historical volatility is to use the same number of trading days going backwards as there are going forwards until the expiration date of the option. In this exam, however, we will make a simplifying assumption that there are 10 months until the expiration of the option, and collect 10 months of data. In a separate spreadsheet, download daily adjusted close stock prices from May 30, 2023, to March 25, 2024. Calculate daily (log) returns using the prices. Hence, calculate the annualized historical volatility for your stock. (Give your answer as a percentage, to 3 d.p.) Problem 2 46.146% Using the U.S. Department of the Treasury's Daily Treasury Par Yield Curve Rates, write down: The risk-free interest rate (US Treasury rate) on March 25, 2024, for 6 months (Give your answer as a percentage, to 3 d. p.) 5.360% The risk-free interest rate (US Treasury rate) on March 25, 2024, for 1 year (Give your answer as a percentage, to 3 d.p.) 5.000% Interpolating between these two values, calculate an appropriate risk-free interest rate for use in a pricing model for an option maturing on January 17, 2025. (Give your answer as a percentage, to 3 d.p.) Using a 10-step binomial tree model, calculate the price of an American put option on your stock maturing on January 17, 2025, with the strike price that is closest to being at-the-money (from Problem 1(ii)) and a volatility of 25%. (Give your answer in dollars, to 4 d. p.)