Forward and Futures Pricing

Question 1

No income Formula

Answer 1

𝐹0 = 𝑆0𝑒𝑟𝑇
T in year

Question 2

Known income

Answer 2

𝐹0 = (𝑆0−𝐼)𝑒𝑟T

Question 3

Known yield

Answer 3

𝐹0 = 𝑆0𝑒(𝑟−𝑞)T

Question 4

Valuing a Forward/Future Contract

Answer 4

𝑓 = (𝐹0−𝐾)𝑒^−𝑟T

Question 5

Forward and futures contracts on currencies

Answer 5

𝐹0 = 𝑆0𝑒^(𝑟−𝑟𝑓)𝑇
rf is the value of the foreign risk-free interest rate

Question 6

Consider a four-month forward contract to buy a
zero-coupon bond that will mature one year from
today. The current price of the bond is $930. The
four-month risk-free rate of interest (continuously
compounded) is 6% per annum. Calculate the
forward price.

Answer 6

𝐹0 = 𝑆0𝑒𝑟𝑇
= 930 × 𝑒6%×4/12 = 948.79

Question 7

Consider a forward contract to purchase a couponbearing bond whose current price is $100. The forward
contract matures in 9 months. A coupon payment of
$2 is expected on the bond after 4 months. We assume
that the 4-month and 9-month risk-free interest rates
(continuously compounded) are, respectively, 6% and
7% per annum.

1) If the forward price is relatively high at $120, how
much can an investor gain?
* 2) If the forward price is relatively low at $90, how
much can an investor gain? Pg 10 revison notes

Question 8

Consider a 6-month futures contract on the
S&P500 (stock index). The current value of the
index is $1,400. What is the forward price if the
dividend yield is 3% per annum and the risk-free
rate is 5%?

Answer 8

𝐹0 = 𝑆0𝑒
(𝑟−𝑞)𝑇 = 1400𝑒
(0.05−0.03)×0.5 = $1,414.07

Question 9

A long forward contract on a non-dividend-paying stock was
entered into some time ago. It currently has six months to
maturity. Given that r = 0.10, 𝑺𝟎 = 25, T = 0.5, and K = 24,
calculate the six-month forward price, F0, and the value of
the forward contract, f.

Answer 9

𝐹0 = 𝑆0𝑒𝑟𝑇
= 25𝑒0.1×0.5 = $26.28
𝑓 = (𝐹0−𝐾)𝑒−𝑟𝑇
= 26.28 − 24 𝑒−0.1×0.5 = $2.17

Question 10

Suppose that an individual
starts with 1,000 units of
foreign currency. The 2-year
interest rates in Australia and
the United States are 3% and
1%, respectively, and the spot
exchange rate is 0.7500 USD
per AUD.
* Suppose first that the 2-year
forward exchange rate is
0.7000 or 0.7600. What is the
riskless profit for an
arbitrageur?

Answer 10

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