Interest rates are important in pricing market securities. Interest rates are also important at corporate level since most investment decisions are based on some expectations regarding alternative opportunities and the cost of capital—both of which depend on the interest rates. Interest rates are also closely watched by bond portfolio managers, who base their strategies around the direction of interest rates.
However, these rates cannot be obtained from market directly. Hence, portfolio managers have to rely on a model that tells how the interest rates change over time. This is known as interest rate mode.
There are many ways in which a dynamic model of the term structure can be derived. A term structure is defined as the set of interest rates derived from zero coupon market yields (which provide fixed and certain cash flows) by using a method called bootstrapping. The bootstrapping method is one of the basic and early methods used. The main problem, however, with this method is it can be used for bonds that have a fixed or certain cash flows (like government bonds), but most interest rate derivative securities do not have a fixed payoffs. Hence, for valuations of such interest rate derivatives we need to consider certain assumptions about the evolution of future interest rate.
Many term structure models have been developed considering these assumptions of interest rates. The models can be mainly divided into Arbitrage-free and equilibrium models.
Equilibrium models are models that describe the dynamics of the term structure by using fundamental economic variables that are assumed to affect the interest rates. These models calculate the prices at which a market reaches equilibrium i.e. at what prices the supply and demand balance and the market clears. Equilibrium models also consider the current state of the economy and portray the behaviour of the term structure of interest rates in such economic situation.
Arbitrage- Free Models:
An arbitrage-free model is a financial engineering model that assigns prices to derivatives or other instruments in such a way that it is impossible to construct arbitrages between two or more of those prices. Arbitrage-free models used for trading are generally calibrated to one or more market prices to preclude arbitrages between prices assigned by the model and those quoted prices.
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