(a) Consider a forward contract on an asset S with maturity T = 10 years. The asset S pays no dividends and the spot price at time 0 is S(0) = £56. The continuously compounded interest rate is r 2% per annuum. Calculate the forward price F(0, T). = (b) Consider the setting of (a). Suppose that you can enter a forward con- tract on S (long or short) with forward price of F(0, T) £70 and maturity T = 10. Assume that you are also allowed to trade any number of zero coupon bonds with maturity T 10, and any number of the underlying stock S. Construct = an arbitrage. (c) = Consider a 6-month forward contract written on 100Kg of coffee beans. Assume that the spot price is £10 per Kg and that the continuously compounded risk free rate is r 5% per annum. Suppose that storing the coffee beans incurs an unknown cost, due halfway the contract. What are the storage costs if the forward price is £1005? -
(a) Consider a forward contract on an asset S with maturity T = 10 years. The asset S pays no dividends and the spot price at time 0 is S(0) = £56. The continuously compounded interest rate is r 2% per annuum. Calculate the forward price F(0, T). = (b) Consider the setting of (a). Suppose that you can enter a forward con- tract on S (long or short) with forward price of F(0, T) £70 and maturity T = 10. Assume that you are also allowed to trade any number of zero coupon bonds with maturity T 10, and any number of the underlying stock S. Construct = an arbitrage. (c) = Consider a 6-month forward contract written on 100Kg of coffee beans. Assume that the spot price is £10 per Kg and that the continuously compounded risk free rate is r 5% per annum. Suppose that storing the coffee beans incurs an unknown cost, due halfway the contract. What are the storage costs if the forward price is £1005? -
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:3. (a)
Consider a forward contract on an asset S with maturity T = 10 years.
The asset S pays no dividends and the spot price at time 0 is S(0) = £56. The
continuously compounded interest rate is r = 2% per annuum. Calculate the
forward price F(0,T).
(b)
Consider the setting of (a). Suppose that you can enter a forward con-
tract on S (long or short) with forward price of F(0,T) = £70 and maturity
T = 10. Assume that you are also allowed to trade any number of zero coupon
bonds with maturity T = 10, and any number of the underlying stock S. Construct
an arbitrage.
(c)
(d)
Consider a 6-month forward contract written on 100Kg of coffee beans.
Assume that the spot price is £10 per Kg and that the continuously compounded
risk free rate is r 5% per annum. Suppose that storing the coffee beans incurs an
unknown cost, due halfway the contract. What are the storage costs if the forward
price is £1005?
-
Consider the following market: There are only two times t = 0 and
1 years. The annual continuously compounded interest rate is 5% per annum.
There is an asset S(t) such that if the market goes up, then S(1) = £1200, and
if the market goes down, then S(1) = £1000. A put option with maturity t = 1
and strike price £1150 written on S is a derivative which at time t = 1 pays the
holder min{S(1) — 1150, 0} pounds. In the market you can trade pounds and the
asset. Construct a portfolio that replicates the put option and use it to determine
the value at time t = 0 of such a put option, provided that S(0) = £1100.
t =
=
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