Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities
Refresher reading access
Introduction
Earlier lessons introduced forward commitment features, payoff profiles, and concepts used in pricing these derivative instruments. In particular, the relationship between spot and forward commitment prices was established as the opportunity cost of owning the underlying asset (represented by the risk-free rate) as well as any additional cost or benefit associated with holding the underlying asset. This price relationship both prevents arbitrage and allows a forward commitment to be replicated using spot market transactions and risk-free borrowing or lending.
n the first lesson, we explore the pricing and valuation of forward commitments on a mark-to-market (MTM) basis from inception through maturity. This analysis is essential for issuers, investors, and financial intermediaries to assess the value of any asset or liability portfolio that includes these instruments. The second lesson addresses forward pricing for the special case of underlying assets with different maturities, such as interest rates, credit spreads, and volatility. The prices of these forward commitments across the so-called term structure are important building blocks for pricing swaps and related instruments in later lessons.
Learning Outcomes
- explain how the value and price of a forward contract are determined at initiation, during the life of the contract, and at expiration; and
- explain how forward rates are determined for an underlying with a term structure and describe their uses.
Summary
- A forward commitment price agreed upon at contract inception remains fixed and establishes the basis on which the underlying asset (or cash) will be exchanged in the future versus the spot price at maturity.
- For an underlying asset that does not generate cash flows, the value of a long forward commitment before expiration is equal to the current spot price of the underlying asset minus the present value of the forward price discounted at the risk-free rate. The reverse is true for a short forward commitment. Foreign exchange represents a special case in which the spot versus forward price is a function of the difference between risk-free rates across currencies.
- For an underlying asset with additional costs and benefits, the forward contract MTM value is adjusted by the sum of the present values of all additional cash flows through maturity.
- Underlying assets with a term structure, such as interest rates, have different rates or prices for different times-to-maturity. These zero or spot and forward rates are derived from coupon bonds and market reference rates and establish the building blocks of interest rate derivatives pricing.
- Implied forward rates represent a breakeven reinvestment rate linking short-dated and long-dated zero-coupon bonds over a specific period.
- A forward rate agreement (FRA) is a contract in which counterparties agree to apply a specific interest rate to a future period.
1 PL Credit
If you are a CFA Institute member don’t forget to record Professional Learning (PL) credit from reading this article.