Problem 8 Intro Managing Transaction Exposure Perfect Purchase is a U.S. electronics retailer importing consumer electronics from Japan. The company will need 10 million yen (¥) in one year to pay its suppliers. The firm expects the following exchange rate scenarios and probabilities: Scenario Spot rate Probability in one year A $0.0092 0.2 B $0.0098 0.5 C $0.0104 0.3 A call option on yen expiring in one year costs $0.00029 per yen and has an exercise price of $0.0098 per yen. Part 1 Attempt 1/10 for 10 pts. What is the total cost of hedging your payables with a call option (in $)? p+ decimals Submit About Blog Contact Instructor Guide Privacy © Accepi 2012-20 MacBook Air
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We can do this by multiplying each exchange rate scenario by its corresponding probability and summing them up. Expected exchange rate = (0.2 * $0.0092) + (0.5 * $0.0098) + (0.3 * $0.0104) Next, we need to calculate the total cost of hedging with a call option. Show more…
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Suppose a company in the US is buying some parts from a supplier in Japan. The US firm has to pay for the parts next month. Suppose they believe the value of the Yen-Dollar exchange rate in 1 month is given by the following probability distribution: they believe there is a probability of 0.22 that $1 will exchange for 85 Yen, there is a probability of 0.19 that $1 will exchange for 90 Yen, there is a probability of 0.35 that $1 will exchange for 95 Yen, and with the remaining probability that $1 will exchange for 100 Yen. What is the expected value of the number of Yen that $1 will exchange for?
Mauya M.
1) A stock price is currently $100. Over each of the next two six-month periods, it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a one-year European call option with a strike price of $100? 2) For the situation considered in the previous problem, what is the value of a one-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy put-call parity. 3) If the put option in the previous problem was American, would it ever be optimal to exercise it early at any of the nodes on the tree? Find the value of this American put option.
Sri K.
5a. Binomial Hedging. Consider a one-year European call option with a strike price K = $100 on a stock that has a current price of S₀ = $100 per share. The call option is the right to buy, but not the obligation to buy, at the strike price K. In one year the price of a share will either rise to Sᄉ = $120 or fall to Sᅂ = $80. In general, the up payoff is Cᄉ = max(Sᄉ - K, 0) and the down payoff is Cᅂ = max(Sᅂ - K, 0). Solve the following equations for N and B: NSᄉ + B = Cᄉ NSᅂ + B = Cᅂ where N is the number of shares of stock and B is the maturity value of a zero-coupon bond. Compute the value of the hedging portfolio (which gives the value, or price, of the call option) NS₀ + e⁻ʳᅯ B where the risk-free interest rate is r = .05 and t = 1 year in this problem. 5b. Binomial Pricing. The one-year forward value of the stock is assumed to be S₀eʳᅯ = pSᄉ + (1 - p)Sᅂ. Calculate the value of p, the "up" transition probability. This option’s value also can be computed as the value C₀ C₀ = e⁻ʳᅯ [pCᄉ + (1 - p)Cᅂ] after the up probability p has been computed in S₀eʳᅯ = pSᄉ + (1 - p)Sᅂ. C₀ is the present value of the expected payoffs of the option. Compute C₀ and thereby confirm that it is equal to the value of the hedging portfolio in part (a).
Adi S.
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