Call and put options on an asset are available with an exercise price of Kes 150. The optionsexpire in 75 days, and the volatility is 0.40. The continuously compounded risk-free rate is 3.5percent,...

Call and put options on an asset are available with an exercise price of Kes 150. The optionsexpire in 75 days, and the volatility is 0.40. The continuously compounded risk-free rate is 3.5percent, and there are no cash flows on the underlying. The precise Black-Scholes-Merton valuesof these options at different underlying prices are as follows.a) From the Black-Scholes-Merton model, obtain the approximate values of the call delta and putdelta if the underlying asset price is Kes 140.b) Using the call delta and put delta obtained in Part A and the call and put prices given in theproblem for the asset price of Kes 140, calculate the approximate new call and put prices for ai) Kes 5 increase in the price of the underlying assetii) Kes 25 increase in the price of the underlying assetc) Based on a comparison of your answers in Part B with the actual call and put prices givenin the problem, what can you say about the approximations based on delta?


Page 1 KENYATTA UNIVERSITY SCHOOL OF BUSINESS DEPARTMENT OF ACCOUNTING AND FINANCE FOR 2ND SEMESTER 2020/2021 ACADEMIC YEAR BAC 309: FINANCIAL DERIVATIVES Instructions on or before 23rd September, 2021 without FAIL creativity, free thinking, robust discussion that is independent. It will be tested for similarity-so one should do his/her work independently. Indicate the name in full, registration number, telephone number and your email on top page. 1. Question One Consider a hypothetical futures contract in which the current price is Kshs 1,060. The initial margin requirement is Kshs 50, and the maintenance margin requirement is Kshs 40. Mr Ingati goes long 20 contracts and meets all margin calls but does not withdraw any excess margin. a) When could there be a margin call? b) Complete the table below and explain any funds deposited. Assume that the contract is purchased at the settlement price of that day so there is no mark-to-market profit or loss on the day of purchase. c) How much are your total gains or losses by the end of day 6? Day Beginning Balance Funds Deposited Futures Price Price Change Gain/Loss Ending Balance 0 1060 1 1055 2 1070 3 1045 4 1050 5 1020 6 1010 Page 2 2. Question two Call and put options on an asset are available with an exercise price of Kes 150. The options expire in 75 days, and the volatility is 0.40. The continuously compounded risk-free rate is 3.5 percent, and there are no cash flows on the underlying. The precise Black-Scholes-Merton values of these options at different underlying prices are as follows. a) From the Black-Scholes-Merton model, obtain the approximate values of the call delta and put delta if the underlying asset price is Kes 140. b) Using the call delta and put delta obtained in Part A and the call and put prices given in the problem for the asset price of Kes 140, calculate the approximate new call and put prices for a i) Kes 5 increase in the price of the underlying asset ii) Kes 25 increase in the price of the underlying asset c) Based on a comparison of your answers in Part B with the actual call and put prices given in the problem, what can you say about the approximations based on delta? Question three Consider an asset that trades at Kshs 1000 today. Call and put options on this asset are available with an exercise price of Kshs1000. The options expire in 275 days, and the volatility is 0.45. The continuously compounded risk-free rate is 3 percent. a) Calculate the value of European call and put options using the Black-Scholes-Merton model. Assume that the present value of cash flows on the underlying asset over the life of the options is Kshs 42.5. b) Calculate the value of European call and put options using the Black-Scholes-Merton model. Assume that the continuously compounded dividend yield is 1.5 percent. Asset Price Call Price Put Price Kes 140 6.572 15.497 Kes 145 8.769 12.694 Kes 165 21.135 5.06