Assist showing calculations
1.4 Exercise 1.5 X is a positive stochastic continuous variable with probability distribution func- tion (PDF) F(x) = P(X x). c) Calculate the Laplace Transform f*(s) = Efe ]= , e-f(x)dr. d) Calculate the expected values m = E[X], E[X*]. k = 0, 1,2. ..., the vari- ance or. the standard deviation ox and the coefficient of variation c = o/m, with and without the transform F* (s). Solution: a) For the calculation of f(x) we just need to differentiate:9. Stock ABC has the following characteristics: . The current price to buy one share is 100. . The stock does not pay dividends. European options on one share expiring in one year have the following prices: Strike Price Call option price Put option price 90 14.6 0.24 100 6.80 1.93 110 2.17 6.81 A butterfly spread on this stock has the following profit diagram. 6 4 2 80 85 90 95 100 105 110 115 120 -2 The continuously compounded risk-free interest rate is 5%. Determine which of the following will NOT produce this profit diagram. (A) Buy a 90 put, buy a 110 put, sell two 100 puts (B) Buy a 90 call, buy a 110 call, sell two 100 calls (C) Buy a 90 put, sell a 100 put, sell a 100 call, buy a 110 call (D) Buy one share of the stock, buy a 90 call, buy a 110 put, sell two 100 puts (E) Buy one share of the stock, buy a 90 put, buy a 110 call, sell two 100 calls. IFM-01-18 Page 6 of 105 10. Stock XYZ has a current price of 100. The forward price for delivery of this stock in 1 year is 110. Unless otherwise indicated, the stock pays no dividends and the annual effective risk-free interest rate is 10%. Determine which of the following statements is FALSE. (A) The time-1 profit diagram and the time-1 payoff diagram for long positions in this forward contract are identical. (B) The time-1 profit for a long position in this forward contract is exactly opposite to the time-1 profit for the corresponding short forward position. (C) There is no comparative advantage to investing in the stock versus investing in the forward contract. (D) If the 10% interest rate was continuously compounded instead of annual effective, then it would be more beneficial to invest in the stock, rather than the forward contract.Determine which, if any, of the following positions has or have an unlimited loss potential from adverse price movement in the underlying asset, regardless of the initial premium received. 1. Short 1 forward contract II. Short 1 call option III. Short 1 put option (A) None (B) I and II only (C) I and III only (D) II and III only (E) The correct answer is not given by (A), (B), (C), or (D) IFM-01-18 Page 14 of 105 27. DELETED 28. DELETED 29. The dividend yield on a stock and the interest rate used to discount the stock's cash flows are both continuously compounded. The dividend yield is less than the interest rate, but both are positive. The following table shows four methods to buy the stock and the total payment needed for each method. The payment amounts are as of the time of payment and have not been discounted to the present date. METHOD TOTAL PAYMENT Outright purchase A Fully leveraged purchase B Prepaid forward contract C Forward contract D Determine which of the following is the correct ranking, from smallest to largest, for the amount of payment needed to acquire the stock. (A) C
