Risk mgmt at derivatives question regarding black scholes model. Attached is the question and Excel template.

Risk Management & Derivatives - FIN422 Assignment 3 This assignment is due at the end of the day on April 13. The assignment is to be completed in your assigned groups. Please have one group member turn in the completed assignment through D2L. Please turn in an Excel file with analysis and a Word file with answers to the questions. Everything in the Excel file based on the Black-Scholes model and binomial option pricing model must have calculations with the appropriate formulas with the exception of the answers in question 2.b.iii that come directly from the BOPMmacro.xls file. 1. Consider a July 2017 call option on Apple stock with a strike price of $150. The current AAPL stock price on March 30, 2017 is $143.93. The option has 114 days until expiration (such that T = 114 365 ). LIBOR for this period is 1.25%. AAPL has volatility of 18.9%. (a) Price the option using the Black-Scholes model. (b) Price the option using the Binomial Option Pricing Model. Use 10 subperiods in the 1 tree (such that each branch of the three covers 114 365 10 of a year). 2. Consider a June 2017 put option on SPY with a strike price of $230. The current SPY price 79 on March 30, 2017 is $236.29. The option has 79 days until expiration (such that T = 365 ). For this question, assume that LIBOR is currently 5% (that is greater than the actual LIBOR but it will help illustrate some features of the option pricing models). SPY has volatility of 15%. (a) Price the option using the Black-Scholes model. Does the Black-Scholes model assume that the option is European or American? Are exchange-traded options on SPY European or American options? (b) Price the option using the Binomial Option Pricing Model. Use 10 subperiods in the 79 1 tree (such that each branch of the three covers 365 10 of a year). i. Begin by pricing a European version of the SPY put option. Does this price dier from the Black-Scholes option value? Why? ii. Now price the American SPY put option. Your Excel file should have a formula at each node of the tree which automatically determines whether the option should be exercised early while pricing the option. Does the value of the American option dier from the value of the European option? Why? iii. With only 10 branches in the tree, the Binomial Option Pricing Model solution has not yet converged to the Black-Scholes solution (you can see this by comparing the European option values from the two models). Use the Excel spreadsheet BOPMmacro.xls given on Blackboard with the binomial option pricing model calculator. Calculate the European and American versions of the put option using this model 1 with 1000 steps in the tree. The European put value should be comparable to the Black-Scholes put value, and the American put value provides a value for the put which takes the early exercise provision into account. 3. The following table shows May 2017 put option premiums as of March 30, 2017 for SPY over a range of strike prices. The current SPY price is 236.29. The options expire in 51 days 51 (T = 365 ) and LIBOR is 1.05%. Strike Price $220 $225 $230 $235 $240 Put Premium $0.63 $0.98 $1.62 $2.82 $5.12 You will calculate the implied volatility of each option using Solver in Excel. Solver is useful for minimizing or maximizing various functions in Excel by changing some parameters. Solver should be on the Data tab. If it doesn't show up, you may need to tell Excel to install it (look it up on Google or Excel help). In this case, we want the Black-Scholes option value to equal the observed option prices. For each option, you can tell Solver to make the Black- Scholes option price (the \"objective\") equal to the observed option price from the table above. The only parameter that Excel should be able to change is the volatility parameter ( ), so Excel can only change that corresponding cell. Solver should the find the which makes the implied Black-Scholes option price equal to the observed price, and this number is the implied volatility of the option. (a) Calculate the implied volatility of each option using the Black-Scholes model. (b) Plot the implied volatilities as a function of the strike price. Are the in-the-money or out-of-the-money put options more expensive in terms of their implied volatilities? 2 Spot Price Risk Free Rate Volatility Option Maturity (years) Strike Option Type (c = call, p = put) Exercise Type (a = American, e = European) No. of Time Steps Option Price 100 0.05 0.2 0.5 120 c e 500 1.022927885 Calculate