Ross model

The above conclusions were based on calculations and measurements taken from a variety of ices [68]. They offer the prospect of defining a potential for the water molecule that not only satisfactorily reproduces structural data but also generates an acceptable DOS. At present the LR model appears to offer considerable promise in this direction. The local structure of water is often considered to be ice-like and a good model for ice would be an obvious candidate for the structure and dynamics of water. Indeed there are some indications that the two peaks are present in the INS of liquid water, but shifted to lower energies, 24 meV and 32 meV [79]. Therefore, it is appropriate to briefly review the consequences that this model would have for the liquid state of water. Of course this process is by its very nature speculative but it does draw out the intriguing number of unusual properties of water that can be addressed through the Li/Ross model. 

Chen R, Scott L (1995) Inters Rate Options in Multifactor Cox-lngersoll-Ross Models of the Term Structure. Journal of Derivatives 3 53-72. 

Although formally published in 1985, the Cox-Ingeisoll-Ross model was being circulated in academic circles from the mid-1970s onwards, which would make it one of the earliest interest-rate models. 

In this chapter, we have considered both equilibrium and arbitrage-free interest-rate models. These are one-factor Gaussian models of the term structure of interest rates. We saw that in order to specify a term structure model, the respective authors described the dynamics of the price process, and that this was then used to price a zero-coupon bond. The short-rate that is modelled is assumed to be a risk-free interest rate, and once this is modelled, we can derive the forward rate and the yield of a zero-coupon bond, as well as its price. So, it is possible to model the entire forward rate curve as a function of the current short-rate only, in the Vasicek and Cox-Ingersoll-Ross models, among others. Both the Vasicek and Merton models assume constant parameters, and because of equal probabilities of forward rates and the assumption of a normal distribution, they can, xmder certain conditions relating to the level of the standard deviation, produce negative forward rates. 

Brown, R., Schaefer, S., 1994. The term structure of real interest rates and the Cox, Ingersoll and Ross model. J. Financ. Econ. 35, 2-42. 

When calcnlating option prices in a one-factor model, a frequently made assnmption is that the process is driven by the short rate often with a mean reversion featnre linked to the short rate. There are several popnlar models which fall into this category, for example, the Vasicek model, and the Cox, Ingersoll, and Ross model both of which will be discussed in more detail later. Calculating option prices in a two-factor model involves both the short- and long-term rates linked by a mean reversion process. 

Ren-Raw Chen and Louis Scott, Pricing Interest Rate Options in a Two-Factor Cox-Ingersoll-Ross Model of the Term Structure, The Review of Financial Studies 5, no. 4 (1992), pp. 613-636. 

Although published officially in 1985, the Cox-Ingersoll-Ross model was described in academic circles in 1977, or perhaps even earlier, which would make it the first interest rate model. Like Vasiceks it is a one-factor model that defines interest rate movements in terms of the dynamics of the short rate. It differs, however, in incorporating an additional feature, which relates the variation of the short rate to the level of interest rates. This feature precludes negative interest rates. It also reflects the fact that interest rate volatility rises when rates are high and correspondingly decreases when rates are low. The Cox-lngersoll-Ross model is expressed by equation (4.11). 

In the next section we construct the equation analogous to (31) for the ecological function following the Gutkowicz-Krusin, Procaccia and Ross model outlined here. 

Brown, R., and S. Schaefer. 1994. The Term Structure of Real Interest Rates and the Cox, Ingersoll and Ross Model. Jourrutl of Financial Economics 35(1) 3 2. 

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