During a summer internship, you have secured a position at a brokerage firm to temporarily replace their options pricing specialist who is on vacation. The manager urgently asks you to complete the unfinished work of this specialist, which involved evaluating an American put option. This put option is used to hedge the exposure arising from the shares of the company FICTIVA that are currently held by the brokerage firm. The specialist leaves on her desk a paper where she indicates her working hypotheses: The put option has a two-year maturity The exercise price is $42 The current market price of one FICTIVA share is $40 FICTIVA shares have an annual volatility of 10% The risk-free interest rate is currently 5% (continuously compounded) The method used for pricing options is a two-step binomial tree a) Determine the possible prices of the FICTIVA share at the end of each of the next two years. b) Using the previously determined prices, determine the value of the put option at each node of the two-step binomial tree using the risk-neutral approach. c) Imagine that it is a European put option, find its price at each node of the two-step binomial tree using the risk-neutral approach. d) Use the Black-Scholes formula to find the price of the European put option. e) Are your answers for questions c) and d) different or similar? Briefly explain.d) Use the Black-Scholes formula to find the price of the European put option. e) Are your answers for questions c) and d) different or similar? Briefly explain.