Home › CFA® Level I › Derivatives
CFA® Level I · Derivatives · free lesson
Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities
A forward's price is fixed when it is agreed, but its value changes every day afterward. This module shows how to value a forward at initiation, during its life and at expiration, including forwards on income-paying assets and currencies, and then turns to underlyings with many maturities: implied forward rates from the spot curve, forward curves for commodities, and forward rate agreements.
What you will learn
1. Distinguish the price of a forward contract from its value and calculate the value of a forward at initiation, during its life and at expiration for an underlying with no income or costs.
- Price: the fixed F_0(T) in the contract. Value: what the position is worth now.
- At initiation, value = 0 because F_0(T) is the no-arbitrage price.
- At expiration, V_T = S_T - F_0(T) for the long.
- During the life: V_t = S_t - F_0(T)(1 + r)^-(T - t) = PV of [F_t(T) - F_0(T)].
- The short's value is always the negative of the long's value.
2. Calculate the value during its life of a forward on an underlying with carry benefits or costs, including a currency forward.
- Adjust the current spot for remaining carry: subtract PV of income, add PV of costs.
- V_t = S_t - PV_t(I) + PV_t(C) - F_0(T)(1 + r)^-(T - t).
- Equivalent: discount F_t(T) - F_0(T) at the risk-free rate for the remaining time.
- Currency forward value = (F_t - F_0) x base notional, discounted at the price-currency rate.
- The value is in the price currency; the seller of the base currency has the opposite value.
3. Calculate implied forward rates from spot rates and interpret the term structure of forward prices, including contango and backwardation.
- (1 + z_B)^B = (1 + z_A)^A (1 + IFR_{A,B-A})^(B-A): investing long equals investing short and rolling at the forward rate.
- Forward growth factor between A and B = DF_A / DF_B.
- Upward-sloping spot curve: forward rates above spot rates; inverted curve: forward rates below.
- Contango: forward prices rise with maturity; backwardation: forward prices fall with maturity.
- Backwardation typically signals tight supply and a high convenience yield.
4. Describe forward rate agreements and calculate an FRA's fixed rate, settlement amount and value before settlement.
- An A x B FRA fixes the rate for a period from month A to month B; only the interest difference is paid.
- Long FRA: pays fixed, receives floating, gains if rates rise.
- At initiation the FRA rate equals the implied forward rate, so the value is zero.
- Settlement = (MRR - FRA rate) x period x notional, discounted at MRR if paid at the start of the period.
- Value before settlement = (new FRA rate - old FRA rate) x period x notional, discounted to today.
Module at a glance
- Forward price is fixed in the contract; forward value starts at zero and then moves with the underlying.
- Long value during the life: S_t - PV(income) + PV(costs) - F_0(T)(1 + r)^-(T - t).
- At expiration: V_T = S_T - F_0(T); the short's value is the negative.
- Currency forward value = (F_t - F_0) x notional, discounted at the price-currency rate.
- (1 + z_B)^B = (1 + z_A)^A (1 + IFR)^(B - A); rising spot curves imply higher forward rates.
- Contango: forward prices rise with maturity; backwardation: they fall, often with tight supply.
- An FRA locks in a future rate; the long pays fixed and gains when rates rise; discount start-of-period settlements.
This free module has 4 lessons, 13 practice questions with full explanations.