Question

A three-year long forward contract is entered into when the spot price of an investment asset is $30 and the risk free rate for all maturities. (With continuous compounding is 10%. the asset provides an income of $2 at the end of the first year and $2 at the end of the second.

a) what is the 3 year forward price?

b) what is the initial value of the forward contract?

c) Two and a half years later, the spot price of the asset is $35 and the risk free rate for all maturities is 8% (with continuous compounding). what are the forward price and the value of the forward contract?

Answer 1

Case a: 3 Year Forward Price

Spot price of the asset = $30

risk free rate = 10%

no. of years = 3

Forward price (F) = S * e^{(r * t)}

where, F = forward rate; S = spot rate; r = risk free rate; t = time period; e = 2.7183

F = $30 * (2.7183)^{(10% * 3)}

= $30 * (1.349862)

F = 40.49585

Case b: Initial value of the forward contract:

Forward contracts do not require early payment or down payment since no money changes hands at the initial agreement, so no value can be attributed to it.

Case c: Two and half years later spot price is $35 and risk free rate is 8%:

Spot price after 2.5 years = $35

risk free rate = 8%

Here we are assuming that the forward rate for the 3rd year is to be calculated. Hence 2.5 years is completed then the remaining period of time would be 0.5 years.

F = S * e^{(r * t)}

F = $35 * (2.7183)^{(8% * 0.5)}

F = $35 * 1.040811

F = $36.42839