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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 curve is a function graph in finance that defines the prices at which a contract for future delivery or payment can be concluded today. For example, a futures contract forward curve is prices being plotted as a function of the amount of time between now and the expiry date of the futures contract (with the spot price being the price at time zero).
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 reason for the change is that, post-crisis, the overnight rate is the rate paid on the collateral (variation margin) posted by counterparties on most CSAs. 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".
For each single forward rate the model corresponds to the Black model. The novelty is that, in contrast to the Black model, the LIBOR market model describes the dynamic of a whole family of forward rates under a common measure. The question now is how to switch between the different -Forward measures.
These, in turn, are functions of the volatility(s) of the forward rates. [28] A "simple" discretized expression [29] for the drift then allows for forward rates to be expressed in a binomial lattice. For these forward rate-based models, dependent on volatility assumptions, the lattice might not recombine.
Forward volatility is a measure of the implied volatility of a financial instrument over a period in the future, extracted from the term structure of volatility (which refers to how implied volatility differs for related financial instruments with different maturities).
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.