3. First Semester Examinations FINMSUDS June. 2021 NOTE: For the remaining questions, we revert to the asset situation of positive interest rates. Question 3. In this question you should work to an accuracy of 4 decimal places for all quantities. (a) Your rst task is to use software of your choioe to select a number K which is uniformly distributed in the internal [95, 105] and a number 1' which is uniformly distributed in the interval [035,037]. These will be the values of the strike price and risk-free rate (p.a., continuously compounded) which you will use for the remainder of this question. Your values of course will be unique to you. Report these values as your solution to Part (a). [2 marks] In what follows you will consider a 1-year European put option on a stock whose price is currently $10!], and has a volatility of 25% pa. The exercise price of the option is the value If you found in Part (a) and the risk-free rate with continuous compounding is the value 1* you found in Part (a). (b) Construct a Cox-RoasHubmstein binomial tree with n. = 3 equal time steps for the stock price movements. State clearly the formulae that you use for the eonstruetion. ['2 marks] (c) What is the ak-neutral probability distribution? State clearly the formulae that you use and the value of the probability. [1 mark] (de Write at each node the values of the option, calculated using the risk-neutral probability distribution. State clearly the formulas that you use for the values. [1 mark]