How to implement the hull white rate model?
The Hull-White tree is a general algorithm for the discrete-time implementationof diffusion models of the form dx(t) = (θ(t)−κ(t)x)dt+σ(t)dW. (3.1) Ifx=r, we get the Hull-White spot rate model. The aim is to develop a discrete-time version that has the following properties.
How are caps and floors priced in the hull white model?
Because interest rate caps/floors are equivalent to bond puts and calls respectively, the above analysis shows that caps and floors can be priced analytically in the Hull–White model. Jamshidian’s trick applies to Hull–White (as today’s value of a swaption in the Hull–White model is a monotonic function of today’s short rate).
How to make a hull white interest rate tree?
The construction of the Hull-White tree involves two stages. The first stage involves defining a new variable x* obtained from x by setting both θ(t) and the initial value of x. equal to zero. The process for x* is: dx* = −ax * dt +s dz (2) We construct a tree for x* that has the form shown in Figure 1.
When was the first hull white model made?
The first Hull–White model was described by John C. Hull and Alan White in 1990. The model is still popular in the market today. The model is a short-rate model. In general, it has the following dynamics:
Is the hull white model Gaussian or bivariate?
The Hull-White Model The process X in (3.2) is Gaussian. As shown in Ostrovski [20] the variables X t and´t s X y dy are bivariate normal distributed conditionally on X s with well known mean and variance. We define
Is the Black Scholes Hull White model exact?
The Black-Scholes Hull-White Model The generation of the scenarios (underlying and interest rate) in this case has been done using an exact schemes described in Ostrovski [20], with a few changes in order to incorporate the correlation between underlying and interest rate.