Financial Mathematics- Assignment one

1.An investor enters into a short cotton futures contract when the futures price is 50 cents per
pound. The contract is for the delivery of 50, 000 pounds. How much does the investor
gain or lose if the cotton price at the end of the contract is (a) 48.20 cents per pound;
and (b) 51.30 cents per pound?

2. You would like to speculate on a rise in the price of a certain stock. The current stock
price is $29 and a 3-month call with a strike of $30 costs $2.90. You have $5, 800 to
invest. Identify two alternative strategies, one involving an investment in the stock and
the other involving investment in the option. What are the potential gains and losses
from each?

3 The price of gold is currently $500 per ounce. The futures price for the delivery in one
year is $700. An arbitrageur can borrow money at 10% per annum. What should the
arbitrageur do? Assume that the cost of storing gold is zero.

4. Describe the payoff from the following portfolio: a long forward contract on an asset and a
long European put option on the asset with the same maturity as the forward contract
and a strike price that is equal to the forward price of the asset at the time the portfolio
is set up

5. A long forward contract is equivalent to a long position in a European call option and a
short position in a European put option.” Explain this statement.