What is the forward price of a stock

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Derivatives and Risk Management Assignment -

Q1. What is the 6 month forward price of a stock, whose current price is $ 30, and is not expected to pay a dividend within 6 months? The riskless interest rate is 12%, continuously compounded. What if the stock is expected to pay a dividend of $2 after 3 months, and after 6 months? (Assume that the stock will be delivered Ex-Dividend against the forward contract, i.e. the receiver of the stock will not be entitled to the dividend paid at the same time as the delivery.)

Q2. If the 3 month interest rate is 9% and the 6 month interest rate is 10% (both with continuous compounding), then what are the prices of the 3 month and 6 month pure discount bonds? What is the forward price which will be agreed, to buy in 3 months time, the pure discount bond to mature in 6 months' time? What is the corresponding forward interest rate, with continuous compounding?

Q3. With the rates as in Question 2, what is the 6 month forward price of a bond with face value $1000, coupon 10% spot price $900, and which pays coupons on a quarterly basis? (Thus, the bond pays $25 every 3 months. Assume that the bond has just paid a dividend.)

Q4. Assume I can borrow at 5.1% and lend at 4.9% in domestic currency, and I can borrow at 7.1% and lend at 6.9% in foreign currency. (All rates with continuous compounding. Also, I can buy F$1 at spot for DS 2.01, and I can sell F$1 for at spot D$1.99. (F$ "Foreign dollar"; DS - "Domestic dollar".) What is the lowest price at which I would be allowed to buy FSs 1 year forward, without having an arbitrage opportunity? What is the highest price at which I would be allowed to sell FSs 1 year forward?

Reference no: EM132183819

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