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The forward rate is the future yield on a bond. It is calculated using the yield curve . For example, the yield on a three-month Treasury bill six months from now is a forward rate .
The forward price (or sometimes forward rate) is the agreed upon price of an asset in a forward contract. [ 1 ] [ 2 ] Using the rational pricing assumption, for a forward contract on an underlying asset that is tradeable, the forward price can be expressed in terms of the spot price and any dividends.
When the volatility and drift of the instantaneous forward rate are assumed to be deterministic, this is known as the Gaussian Heath–Jarrow–Morton (HJM) model of forward rates. [ 1 ] : 394 For direct modeling of simple forward rates the Brace–Gatarek–Musiela model represents an example.
The SABR model describes a single forward , such as a LIBOR forward rate, a forward swap rate, or a forward stock price. This is one of the standards in market used by market participants to quote volatilities. The volatility of the forward is described by a parameter .
The forward values of the overnight rate can be read from the overnight index swap curve. "OIS-discounting" is now standard, and is sometimes, referred to as " CSA -discounting". See: Financial economics § Derivative pricing for context; Interest rate swap § Valuation and pricing for the math.
Note the dividend rate q 1 of the first asset remains the same even with change of pricing. Applying the Black-Scholes formula with these values as the appropriate inputs, e.g. initial asset value S 1 (0)/S 2 (0), interest rate q 2, volatility σ, etc., gives us the price of the option under numeraire pricing.
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The Smith–Wilson method is a method for extrapolating forward rates. It is recommended by EIOPA to extrapolate interest rates. It was introduced in 2000 by A. Smith and T. Wilson for Bacon & Woodrow.