Pricing a Forward-Forward Contract in Excel

A forward-forward is a type of forward contract that involves two delivery dates. The buyer agrees to purchase an underlying asset from the seller at a specified price on the first delivery date, and then sell it back to the seller at another specified price on the second delivery date. The difference between the two prices is the interest rate for the period between the two dates.

The pricing of a forward-forward contract depends on the spot price of the underlying asset, the risk-free interest rate, and the carrying costs of the asset. The forward price for the first delivery date is calculated by multiplying the spot price by a factor that accounts for the interest rate and the carrying costs. The forward price for the second delivery date is calculated by multiplying the forward price for the first delivery date by another factor that accounts for the interest rate and the carrying costs for the period between the two dates.

The forward-forward contract can be used to hedge against interest rate risk, or to speculate on the future movements of interest rates. For example, a borrower who expects interest rates to rise can enter into a forward-forward contract to lock in a lower interest rate for a future loan. A lender who expects interest rates to fall can enter into a forward-forward contract to lock in a higher interest rate for a future deposit.

Basic Theory

A forward-forward contract is an agreement between two parties to exchange cash flows at a future date. In the context of interest rates, it typically involves the exchange of fixed-rate cash flows for floating-rate cash flows. The basic formula for pricing a forward-forward contract is as follows:

$V = \frac{{C_{\text{fixed}} - C_{\text{floating}}}}{{(1 + r_{\text{floating}})^{t_2 - t_1}}}$

Where:

$V$ is the value of the forward-forward contract.
$C_{\text{fixed}}$ is the fixed interest rate.
$C_{\text{floating}}$ is the expected floating interest rate.
$r_{\text{floating}}$ is the discount rate for the floating cash flows.
$t_1$ is the starting time of the forward-forward contract.
$t_2$ is the ending time of the forward-forward contract.

Procedures

Determine Contract Terms: Define the terms of the forward-forward contract, including the fixed interest rate, the expected floating interest rate, and the contract period.
Calculate Floating Cash Flows: Estimate the future floating cash flows based on the expected interest rates.
Discount Floating Cash Flows: Apply the discount rate to the future floating cash flows to bring them to present value.
Calculate Contract Value: Use the formula mentioned earlier to calculate the value of the forward-forward contract.

Example Scenario

Let’s consider a scenario where Company A enters into a forward-forward contract with Company B. The contract terms are as follows:

Fixed interest rate ( $C_{\text{fixed}}$ ): 5%
Expected floating interest rate ( $C_{\text{floating}}$ ): 4.5%
Contract period ( $t_2 - t_1$ ): 2 years

Excel Calculation

Description	Formula	Calculation
Floating Cash Flows	$\text{Principal} \times \text{Expected Floating Rate}$	$1,000,000 * 4.5% = $45,000
Discounted Cash Flows	$\frac{\text{Floating Cash Flow}}{(1 + \text{Discount Rate})^t}$	$\frac{$45,000}{(1 + 4.5\%)^2} = $41,542.04$
Forward-Forward Value	$\frac{(\text{Fixed Rate} - \text{Discounted Cash Flow})}{(1 + \text{Discount Rate})^t}$	$\frac{(5\% - $41,542.04)}{(1 + 4.5\%)^2} = $58,457.96$

Result

The value of the forward-forward contract is $58,457.96.

Other Approaches

Yield Curve Approach: Instead of using an expected floating rate, you can derive the floating rate from the yield curve, providing a more market-driven estimate.
Monte Carlo Simulation: For a more sophisticated approach, you can use Monte Carlo simulations to model various interest rate scenarios and assess the impact on the forward-forward contract’s value.