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(i) A forward contract with 12 months to maturity is written on an underlying stock. The stock price is $45, and it is expected to pay dividends of $2 after 6 months and $3 immediately prior to maturity. The relevant riskless rate of interest is 4%. Calculate the theoretical forward price and initial value of the forward contract and explain the forward pricing relationship. (ii) Provide a numerical example of an arbitrage strategy for situations where the forward is trading above, and below the theoretical forward price.
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- A forward contract with 8 months to maturity is written on an underlying share. The market price of the share is $34, and it is expected to pay dividends of $1.40 after 2 months and $2 immediately prior to maturity of the forward. The relevant riskless rate of interest is 4%. Calculate the theoretical forward price and initial value of the forward contract and explain the forward pricing relationship.Consider a 4-month forward contract for which the underlying asset is a stock index with value of 3, 825.97 and a continuous dividend yield of 0.5% Assume the continuous risk-free annual interest rate is 4.5%, a. Determine the no arbitrage forward price. $ Round your answer to the nearest cent b. Calculate the value of a long position if 2 month(s) later the index changes to 3, 825.97 and the risk-free rate is still 4.5% $ Round your answer to the nearest centSuppose the 1-year futures price on a stock-index portfolio is 1,914, the stock index currently is 1,900, the 1-year risk-free interest rate is 3%, and the year-end dividend that will be paid on a $1,900 investment in the market index portfolio is $40.a. By how much is the contract mispriced?b. Formulate a zero-net-investment arbitrage portfolio and show that you can lock in riskless profits equal to the futures mispricing.c. Now assume (as is true for small investors) that if you short sell the stocks in the market index, the proceeds of the short sale are kept with the broker, and you do not receive any interest income on the funds. Is there still an arbitrage opportunity (assuming that you don’t already own the shares in the index)? Explain.d. Given the short-sale rules, what is the no-arbitrage band for the stock-futures price relation-ship? That is, given a stock index of 1,900, how high and how low can the futures price be without giving rise to arbitrage opportunities?
- A stock is expected to pay a dividend of $1 per share in 2 months. An investor purchased a forward contract on the stock at a forward price of $50 some time ago. The contract now has 3 months to its delivery date. The stock is currently trading at $55 and the risk free rate is 4% on a continuously compounded basis. Consider the following statements. I. The price of a forward contract on the stock with 3 months to the delivery date is $54.55 II. The value of the investor’s forward position is $5.50 Which of the following is correct? (No excel pls) a. Statement I is incorrect, Statement II is correct. b. Both statements are correct. c. Both statements are incorrect. d. Statement I is correct, Statement II is incorrect.You observe that the settlement price of a one-year futures contract for 1 share of a dividend paying stock is currently at $52. The current stock price is $50 and the risk-free interest rate is 10% p.a. (compounded annually). It is also known that the dividend yield on the stock is 4% p.a. (compounded annually). Set up a strategy to realize an arbitrage profit today and show the initial and terminal cash flows from each position taken in the strategy. Assume that investors can short-sell or buy the stock on margin and that they can borrow and lend at the risk-free rate. Thank you!A stock is currently priced at $40. The risk-free rate of interest is 8% p.a. compounded continuously and an 18-month maturity forward contract on the stock is currently traded in the market at $38. You suspect an arbitrage opportunity exists. Which one of the following transactions do you need to undertake at time t = 0 to arbitrage based on the given information? Long the forward, short-sell the share and invest at risk-free rate Long the forward, borrow money and buy the share Short the forward, borrow money and buy the share Short the forward, short-sell the share and invest at risk-free rate
- Suppose a stock is currently (time t = 0) worth 100. Further, suppose the one year annually compounded interest rate is 2%, and the two year annually compounded rate is 3%. Find the following:a) The forward price for a forward contract on the stock with maturity year T1 = 1. b) The forward price for a forward contract on the stock with maturity year T2 = 2.c) The forward price for a forward contract with maturity T1 = 1 on a ZCB with maturity T2 = 2.d) The forward price for a forward contract with maturity T1 = 1 on a forward contract on the stock with maturity T2 = 2 and delivery price K = 101.The multiplier for a futures contract on a stock market index is $50. The maturity of the contract is 1 year, the current level of the index is 1,800, and the risk-free interest rate is .5% per month. The dividend yield on the index is .2% per month. Suppose that after 1 month, the stock index is at 1,820.a. Find the cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition always holds exactly.b. Find the holding-period return if the initial margin on the contract is $5,000The stock price of Top Gloves Bhd today is RM3.00. The call option on this stock with a strike price of RM2.00 and a 60 days maturity has an option premium of RM1.50. The put option with a strike price of RM2.00 and 60 days expiry possess a premium of RM1.20. The risk-free rate per annum is 5%. Required: (a) Prove that there is mispricing. (b) Suggest a suitable arbitrage strategy for this mispricing.
- Consider the futures contract on XYZ Inc. stock. Suppose that the annual dividend yield for the stock is 2.5% and the risk-free rate is 6.3%. Both rates are based on continuous compounding. The current futures price of the XYZ Inc. futures contract maturing in 18 months is $900 per share. Assume that the no arbitrage Futures-Spot parity when asset provides a known yield holds. What is the current spot price of XYZ Inc. per share? Please explain and show calculation. a. $934.39 b. $952.79 c. $850.13 d. $900.00 e. $944.371 A long forward contract on a dividend-paying stock was entered into some time ago. It currently has 6 months to maturity. The risk-free rate of interest (with continuous compounding) is 7% per annum, the stock price is 65 dirhams and the delivery price is 60 dirhams. The average dividend rate is 2%. (a) Determine the value of this long forward contract. (b) Determine also the value of the short forward contract in this casa. (e) What can be said about the relationship between these two values?Assume the Black-Scholes framework. Let S be a stock such that S(0) = 21, the dividend rate is δ = 0.02, the risk free rate is r = 0.05, and the volatility is σ = 0.2. (a) Calculate the expected payoff of a 6 month call with strike price 17. (b) Calculate the cost of such a call. (c) Calculate the cost of a 6 month put with strike price 17. (d) Calculate the price of a derivative that pays |S(0.5) − 17| in six months