# Questions tagged [hullwhite]

The tag has no usage guidance.

104 questions
Filter by
Sorted by
Tagged with
26 views

### Hull-White model for yield curve prediction

I am using the Hull-White model (extended version of Vasicek) to predict Canadian zero-coupon bond yield curves. Most of the time the model does a pretty good job of fitting the real curve in terms of ...
43 views

### Approximating second derivatives at boundary of finite difference scheme

The Question I am implementing a finite difference scheme for the Heston-Hull-White PDE: \begin{align} \frac{\partial u}{\partial t} &= \frac{1}{2}s^2v\frac{\partial^2 u}{\partial s^2 } + \frac{1}{...
63 views

### How do I calculate Hull White's Theta from the discount curve?

The Question I'm currently implementing the a finite difference method for the Hull-White model, shown below: $$\mathrm{d}r(t)=\lambda[\theta(t) − r(t)]\mathrm{d}t + \sigma\mathrm{d}W(t)\tag{1}$$ This ...
27 views

### Dealing with the ru term in an ADI Finite Difference Scheme

I'm trying to code up the algorithm from this paper. The paper presents an ADI algorithm for pricing options in the Heston-Hull-White model. The starting point is the Heston-Hull-White PDE, given ...
102 views

### Why should future short rates tend towards the current term structure of interest rates?

I'm currently looking at the Hull-White model reproduced below: $$\mathrm{d}r = \lambda(\theta(t)-r)\mathrm{d}t + \sigma\mathrm{d}W(t)\text{.}\tag{1}$$ I have a simplistic understanding of the model. ...
124 views

### Deriving the Heston-Hull-White PDE

I'm trying to derive the Heston-Hull-White PDE. The correct backwards PDE is equation (1.3) of this paper on page (2). I will begin deriving the forward PDE, but switching between the two is trivial. ...
144 views

### Calculating the short rate from the discount curve

I'm currently looking at some code that implements the Hull-White model. As one of the inputs, the code accepts a table of discount factors at various dates. Time in Years Discount Factor 0 1 0.003 ...
39 views

156 views

### How to solve these SDE Problems

Quuestion1. I make a solution $r(t)$ used by Ito's lemma $r(t)=e^{-a t}r(0)+\int _{0}^{t}e^{a (s-t)}\theta (s)ds+\sigma e^{-a t}\int _{0}^{t}e^{a u}\,dB^{1}(u)$ Is this right? and I try to make ...
424 views

### Proof of the Hull & White Model calibration

I have a question about the demonstration of the formula which states that: If we have an Hull & White Model for the short rate diffusion such that Then the model is fully calibrated if and only ...
819 views

### Implementation of Generalized Hull-White interest rate model

I am looking for implementation in R (or Matlab) of the Generalized Hull-White interest rate trinomial tree according to the following paper: Interest Rate Trees: Extensions and Applications (2017) . ...
599 views

### Hull-White zero-coupon bond price does not depend on the volatility?

So, today I started pricing zero-coupon bonds using the Hull-White model. An interesting feature is that when t = 0 the bond price does not actually depend on the volatility since the last term of A(0,...
938 views

### Hull white model Monte Carlo simulation Zero Coupon Bond

I am trying to use Hull White Model to price a zero coupon bond by Monte Carlo Simulation. The basic idea is under this equation: Under Hull White Model, I want to generate every short rate (r) and ...
2k views

### Calibration of Theta, A(t) and B(t) of Hull White 1Factor model

I’m simulating interest rates via the HullWhite One factor model. To simulate the short rate I’m using the code from the Quantlib Python Cookbook, chapter 15 and beyond (By Goutham Balaraman and Luigi ...
889 views

### why calibrate volatility and fix the mean reversion

I have had a few experiences or chats with teammates about the Hull-White model. The famous model has 2 parameters : The volatility The mean reversion Very often I hear that the mean reversion has ...
943 views

### Zero Coupon Bond prices in One Factor Hull White model

I implemented the one factor Hull White model for educational purposes and I calibrated the model from a given (made up!) yield curve: The Zero Coupon Bond Prices from this yield curve are: Taking ...