Discussion on the Vasicek Model free essay sample

These models postulate alternative assumptions about the nature of the stochastic process driving interest rates, and deduct a characterization of the term structure implied by these assumptions in an efficiently operating market. These models can be categorised into two main models, arbitrage free models and equilibrium models. Arbitrage free Models These models match the observed prices in the market. These models does not allowed for arbitrage profits to be realized in the markets, by basing an arbitrage strategy on the on the values generated by the model and actual market prices. Models under this category include the Ho-Lee model and the Heath-Jarrow-Morton model. Equilibrium Models. The equilibrium models explain the term structure, based on economic fundamentals that affect the term structure. The models usually start off with the assumptions about economic variables leading to the derivation of a process for the short term rate r. The short term rate is than tested in order to observe the implications on bond prices and option prices (Hull, 2006). We will write a custom essay sample on Discussion on the Vasicek Model or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Restrictions are placed in order to derive bond and derivative prices to be derived (Fabozzi, 2007). Models under this category include the Cox-Ingersoll-Ross mode and the Vasicek model. This paper will attempt to explore the Vasicek, looking at the contribution, limitations as well as looking at how the Vasicek model was employed in other empirical studies. The Vasicek model Vasicek in 1977 developed a model which derives a general form of the interest rate structure term which is a yield based one factor equilibrium model. This model assumes that the short rate process follows a normal distribution, which incorporates mean reversion, is popular with certain practitioners as well as academics because it is tractable. The development of the model is based on an arbitrage argument similar to the works of Black and Scholes (1973) for option pricing. The model is formulated in continuous time, although some implications for discrete interest rate series were noted. The Vasicek model assumes that the risk neutral process for r is:- dr+a(b-r) dt + ? dz a, b and ? are constants. The short rate is pulled to a level b at rate a. This pull is a normally distributed stochastic term ? dz. If interest rates are high, this part of the equation will become negative and therefore, lead to a decrease in interest rates, and thus keeping interest rates at a certain targeted level (Zeytun and Gupta, 2007). If interest rates are too low, this part of the equation becomes larger, pushing interest rates higher, and avoiding a freefall in interest rates (Zeytun and Gupta, 2007). The left hand part of the equation is a disturbance term that affects the process of r(t). There are also compelling economic arguments in favour of mean reversions, that when interest rates are high, the economy tends to slow down and borrowers require less funds. This causes the rates to pull back to its equilibrium value which causes the rates to decline. On the other hand, when the rates are low, there tends to be high demand for funds from borrowers and rates tend to increase (Zeytun and Gupta, 2007). According to Vasicek (1977), the assumptions that is made is that the rate follows a Markov process, the value of the interest rate depends only on its current value and the market is assumed to be efficient.