An ounce of gold currently trades for $1500 in the spot market. A contract to deliver 100 ounces of gold 3 months from today currently trades at a forward price of $1522 per ounce. It will cost $2 to store 1 ounce of gold each month, payable at the end of the month. You have access to risk-free borrowing and lending at a 4% interest rate.

a) Use a replicating portfolio to derive the no-arbitrage forward price for delivery 3 months from today. Be sure to use a payoff table to show that your two portfolios have the same payoffs.

b) Based on your results in part a), there is an arbitrage opportunity. Construct a set of transactions today that costs nothing today, but generates a guaranteed positive cash flow 3 months from today. What is your total profit? Prove both: zero cost today, riskless future profit.

t=0

t=T Maturity in 3 months

S0= $1500

ST - $6

Long FWD

ST-F

Buy a bpnd @ RF rate that pays F

PV(F) = F/1.04^(3/12)

+F

Borrow @ RF rate so that we owe

- $2 @ T=30

- $2 @ T=60

- $2 @ T=90

PV(-2) = -2/1.04^(3/12)

PV(-2) = -2/1.04^(2/12)

PV(-2) = -2/1.04^(1/12)

-$6

$1500 = = F/1.04^(3/12) - 2/1.04^(0/12) - 2/1.04^(2/12) - 2/1.04^(1/12)

$1514.7801+$2+$2.013116+$2.006547=$1520.7997737= F

The forward price is mispriced it should be priced @ $1520.7997737 per ounce.

Asset

Price @ 0

Payoff @ T

Gold

Buy gold -$1500

Short @ +$1522

Borrow @ RF rate

+$1500

-$1520.7997737

Portfolio

0

+$1.200226303

Yes, there is an Arbitrage opportunity you can make $120.02 per 100 ounces of gold in three months.

i just want to confirm my answes