Financial math

QUESTION 1 QUESTIONS 1 (6 marks) The spot price of a non-dividend paying stock is 210 AED. The risk-free rate of interest is 4% per annum. Determine a Its 18-months forward price Fo b. The value of its forward contract on a long forward with 18-months to maturity with delivery price of 205 AED. c The value of its forward contract on a short forward with 18-months to maturity with delivery price of 245 AED. 2 (15 marks) The price of a financial asset "S" is 560 AED and its volatility is 65%. Assume that the annual risk free interest rate is 3%. The question is about pricing European options with sport price "S" and Strike price "K" using one-step binomial tree. d Find "c" the premium of a 20 months European call option on "s" when K-500 AED using one-step binomial tree. e Find "p" the premium of a 20-months European put option on "S" when K-500 AED using one-step binomial tree. f Compare c + Ke-rT to p + S g. Determine the 20-months forward price F. of "S". h. Find the value of "K" that makes c-p. d Hina "e the premium of a 20-months European call option on "S" when K-500 AED using one step binomial tree. e Find "p" the prernium of a 20-months European put option on "S" when K-500 AED using one step binomial tree. f. Compare c + Ke-rt to p+S g. Determine the 20 months forward price fo h Find the value of "K" that makes Cup. of "S". 3. (7 marks) The current price of a stock is 65 AED. The volatility of the stock is 90% and the risk free interest rate is 10%. Find the prerrium of a call option expiring after 6-months with strike K-80 AED using i a two-step binomial tree model. j. Black-Scholes formula