Basic Forward Payoffs and Pricing
Problem Set – Not collected or graded
FINC416, September 12, 2014
- The current 3-month forward price for gold is $1229/troy oz. Complete the payoff table at delivery for someone who enters a long gold forward contract at F=$1229 for each of the following potential spot prices:
Spot price at expiration (ST) / Payoff per troy oz.
$1160
$1180
$1200
$1220
$1240
$1260
- The current 3-month forward price for silver is $18.54/troy oz. Complete the payoff table at delivery for someone who enters a short silver forward contract at F=$18.54 for each of the following potential spot prices:
Spot price at expiration (ST) / Payoff per troy oz.
$17.00
$17.50
$18.00
$18.50
$19.00
$19.50
- Suppose the current spot price of an asset is S0= $32.00/unit. The continuously compounded rate at all terms is r=5% per annum. Holding the asset entails no other cash flows or convenience yields (δ=0). Calculate the forward price for this asset at the following terms:
Term (days) / F0,T/ unit
30
60
90
180
365
- Suppose the current spot price of an asset is S0= $32.00/unit. The continuously compounded rate at all terms is r=5% per annum. The holder of the asset earns a continuously compounded dividend of 2.5% per annum (δ=2.5%). Calculate the forward price for this asset at the following terms:
Term (days) / F0,T/ unit
30
60
90
180
365
- Suppose the current spot price of an asset is S0= $32.00/unit. The continuously compounded rate at all terms is r=5% per annum. The holder of the asset pays a continuously storage cost of 0.5% per annum (λ=0.5%), but there is no convenience yield. Calculate the forward price for this asset at the following terms:
Term (days) / F0,T/ unit
30
60
90
180
365
- Suppose the current spot price of an asset is S0= $32.00/unit. The continuously compounded rate at all terms is r=5% per annum. The holder of the asset pays a continuously storage cost of 0.5% per annum (λ=0.5%), but there is a continuously compounded convenience yield of 10% per annum (c=10%). Calculate the forward price for this asset at the following terms:
Term (days) / F0,T/ unit
30
60
90
180
365
- Suppose the current spot €/$ rate is 1.52345. At all term lengths, US$ deposits earn 4% and € deposits earn 3%, both continuously compounded per annum. Calculate the forward €/$ rate at the following terms:
Term (days) / F0,T/ unit
30
60
90
180
365
- Suppose the spot price of asset X is S0= $22.80 per unit, and the current 90-day forward price is $22.00 per unit.
- What can we say about the relationship between the 90-day risk-free return, r, and the lease rate, δ, associated with the asset?
- Suppose the interest rate, r=16%, and the lease rate δ=24%. Does an arbitrage opportunity exist? How would you exploit it?
- The current stock price of ABC is $64.33. ABC will pay dividends of $1.32 per share in 50 days, 141 days, 233 days, and in 325 days. What is the forward price on ABC stock for delivery in 265 days if the continuously compounded risk-free return is 4% per annum?
- A trader enters 12 short 1-year forward contracts on gold today at F=1298/troy oz. Each contract is on 100 troy ounces. The trader is required to put 8% of the notional value of the position in a margin account today when they entered the position. The margin account earns 1.5% interest compounded continuously per annum.
- What is the initial margin required by the trader on this position today?
- Suppose the very next day’s settlement price for gold is $1312/oz. What would be the new balance in the trader’s margin account?