## Value of a long forward contract (continuous)

**The value of a long forward contract with no known income and where the risk free rate is compounded on a continuous basis is given by the following equation: **

f = S_{0} – Ke^{-rT}

Where

S_{0 }is the spot price

T is the remaining time to maturity

r is the risk free rate

K is the delivery price which is set in the contract

For example, if the spot price is 30, the remaining term to maturity is 9 months (0.75 years), the continuously compounded risk free rate is 12% and the delivery price is 28, then the value of the forward contract will be:

f = 30 – 28e^{-0.12×0.75}= 4.41

You may calculate this in EXCEL in the following manner:

**Value of a long forward contract (discrete) **

The value of a long forward contract with no known income and where the risk free rate is compounded on a discrete basis is given by the following equation:

f = S_{0} – K(1+r)^{-T}

For example, if the spot price is 30, the remaining term to maturity is 9 months (0.75 years), the discretely compounded risk free rate is 12.50% and the delivery price is 28, then the value of the forward contract will be:

f = 30 – 28×(1+12.5%)^{-0.75}= 4.37

You may calculate this in EXCEL in the following manner:

**Value of a long forward contract (continuous) which provides a known income **

f = S_{0} – I – Ke^{-rT}

where I is the present value at time 0 of the known income on the investment assets.

For example, let us assume that the present value of the known income at time 0 is 2. The rest of the details are the same as for a forward contract (continuous) with no known income mentioned earlier. The value of the forward contract will be:

f = 30 -2- 28e^{-0.12×0.75}= 2.41

You may calculate this in EXCEL in the following manner:

**Value of a long forward contract (continuous) which provides a known yield **

f = S_{0}e^{-qT} – Ke^{-rT}

where q is the known yield rate provided by the investment asset.

For example, let us assume that the yield on the investment is 5%. The rest of the details are the same as for a forward contract (continuous) with no known income mentioned earlier. The value of the forward contract will be:

f = 30 e^{-0.05×0.75}– 28e^{-0.12×0.75}= 3.31

You may calculate this in EXCEL in the following manner:

**Value of a forward foreign currency contract **

f = S_{0}e^{-rfT} – Ke^{-rT}

where r_{f} is the value of the foreign risk free interest rate when the money is invested for time T.

For example, let us assume that the foreign risk free interest rate is 2%. The rest of the details are the same as for a forward contract (continuous) with no known income mentioned earlier. The value of the forward contract will be:

f = 30 e^{-0.02×0.75}– 28e^{-0.12×0.75}= 3.96

You may calculate this in EXCEL in the following manner: