Letter

MODUL 3

FATIMA MUHAREMOVIC 3 A

5.23

A) I = $1 * e-0.08*2/12+ $1 * e−0.08×5/12 = $1.9540

F0 = ($50 − $1.9540) * e−0.08×0.5 = $50.01.

The initial value of the forward contract is zero. When the compounding

frequency is ignored the dividend yield on the stock equals the risk-free rate of interest.

B) In three month:

I = $1 * e−0.08*2/12 = $0.9868

f = −($48 − $0.9868 − $50.01 * e−0.08*3/12) = $2.01

($48 − $0.9868) * e−0.08*3/12 = $47.96.

5.26

Suppose the F0 is the one-year forward price of gold. If F0 is relatively high, the

trader can borrow $250 at 6%, buy one ounce of gold and enter into a forward contract to

sell gold in one year F0.

The profit made in one year is

F0 − 450 * 1.06 = F0 – 477= F0= 477

If F0 is relatively low, the trader can sell one ounce of gold for $249, invest the proceeds at

5.5%, and enter into a forward contract to buy the gold back for F0.

The profit is

449 * 1.055 − F0 = 473.695 − F0= F0= 743.695

This shows that there is no arbitrage opportunity if the forward price is between $473.695

and $477.

5.14

The theoretical futures price for a contract deliverable in two months is

0.8000 * e-(0.05−0.02)× 2/12 =0.8040

The actual futures price is, therefore, too high. An arbitrageur would buy Swiss francs and

short Swiss francs futures.

5.12

The theoretical futures price is 400*e(0.10-0.04)*4/12 = 408.08

The actual futures price is only 405. This shows that the index futures price is too low relative to the index. The correct arbitrage strategy is Buy futures contracts.

5.9

A) The forward price: F = S*er(T-t) = 40*e0.10 = 44.207. The initial value of the forward contract is zero.

B) The delivery price K is 44.207. The value of the contract after six months is

f = S – K*e-r(T-t) = 45 – 44.207*e-0.10*0.5 = 2.94895

The forward price is: F = S*er(T-t) = 45e0.10*0.5 = 47.307