Question

Problem 2. Forward prices and value [25 marks] a) [5] Suppose there is a 16 months Forward on 1 share of non- dividend paying stock traded in the market. Current stock prices are $50 and the Forward price is $57. What is the interest rate (continuously compounded) implied by the given Forward price? b) [6] Suppose that actual interest rates are 7% per annum (continuously compounded as well). Find the Fair price of Forward contract and explain your arbitrage strategy. Demonstrate your payoffs on the strategy. c) [6] Demonstrate your arbitrage strategy if actual rates are 11%. d) [8] Suppose you ended up Shorting that Forward contract in (a). 3 months later Forwards on the same asset with the same maturity date are traded at a fair price. Spot prices are $53 and the risk-free rate is 8%. Find the value of your position.

Answer 1

Solution-

(A) Forward price = $57 and Spot price = $50

Time to maturity = 16 months, then "i" will be calculated as-

57 = 50 * e^ (i * 16/12)

SO, i = 9.827%

(B) Suppose actual rate = 7% then implied forward price = 50 * e^ (0.07 * 16/12)

= $54.891

As this is less than $ 57 then we should go short in forward @57 and buy stock @ 50 in spot. This will require borrowing $50 now.

At maturity, payment for borrowing will be $54.891 and profit = $57-54.891

= $ 2.1086

(C) Suppose actual rate = 11% then implied forward price = 50 * e^ (0.11 * 16/12)

= $57.8984

As this is more than $ 57 then we should go long in forward @ 57 and sell stock @ 50 in spot. This will require investing $50 now.

At maturity, investment will give $57.8984 and profit = $57.8984 - 57

= $ 0.8984

(D) Forward prices of the contract expiring in 13 months will be-

53 * e^ (0.08 * 13/12)

= $ 57.798

The forward price in contract where we are short is $57 which is lower than forward prices now.

Hence the value of short position must be-

= 57 - 57.798

= - $0.798

Answers

Thanks!