Questions tagged [hullwhite]
The hullwhite tag has no usage guidance.
104
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Incorporating Accrued Interest to price fixed income callable bonds in short rate models
I am using the DerivaGem software provided by Hull & White (available at DerivaGem 4.00a) in Options, Futures & Other Derivatives. I am attempting to back propagate a bond to obtain the ...
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Calibrating the mean reversion parameter of the short-rate-model Black-Karasinski
When modelling the term structure of interest rates, one widespread possibility is using the Black-Karasinski(BK) model, which is given by the following stochastic process
$$dln\,r=[θ(t)−a\,ln\,r]dt+σ(...
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Hull-White model for yield curve prediction
I am using the Hull-White model (extended version of Vasicek) to predict Canadian zero-coupon bond yield curves. Most of the time the model does a pretty good job of fitting the real curve in terms of ...
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Approximating second derivatives at boundary of finite difference scheme
The Question
I am implementing a finite difference scheme for the Heston-Hull-White PDE:
\begin{align}
\frac{\partial u}{\partial t} &= \frac{1}{2}s^2v\frac{\partial^2 u}{\partial s^2 } + \frac{1}{...
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How do I calculate Hull White's Theta from the discount curve?
The Question
I'm currently implementing the a finite difference method for the Hull-White model, shown below:
$$\mathrm{d}r(t)=\lambda[\theta(t) − r(t)]\mathrm{d}t + \sigma\mathrm{d}W(t)\tag{1}$$
This ...
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0
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Dealing with the ru term in an ADI Finite Difference Scheme
I'm trying to code up the algorithm from this paper. The paper presents an ADI algorithm for pricing options in the Heston-Hull-White model.
The starting point is the Heston-Hull-White PDE, given ...
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1
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113
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Why should future short rates tend towards the current term structure of interest rates?
I'm currently looking at the Hull-White model reproduced below:
$$\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. ...
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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.
...
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2
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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
...
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1
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Hull White 1 Factor Formulas with Time Dependent Variables
In John Hull's "Options Futures and Other Derivatives" I see that bond prices in Hull White 1 Factor model are specified as the following:
$P(t,T) = A(t,T)e^{-B(t,T)r(t)}$
where
$B(t,T) = \...
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1
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Calibrating Hull-White 1 Factor
I have been trying to learn HW1F on my own, out of nothing more than genuine curiosity during my twilight years, and I'm confused on the issue of calibrating. I don't know why, but all the research ...
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1
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What is the definition of "co-terminal swaptions"? why they are important in the calibration process?
could anyone help me understand the definition of "co-terminal" swaptions? What are they? Can you provide an example to illustrate? And why such instruments are important in model ...
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Calibrate Hull-white one factor model with swaption in analytical formula
I've been trying to calibrate Hull-white one factor model with swaption but I have a trouble making closed form solution of swaption
Below is the part of paper I've been referencing to
https://people....
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Implication of Humped Spot Curve on future spot curve(s)
I'm currently implementing a G++ model (Two Factor Hull & White model with constant parameters) on zero curve bootstrapped from USD IRS.
Currently, USD IRS is humped at 30 years; swap rate goes up ...
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how to get 3 month Forward rates from Hull white model simulation?
I implemented the Hull White one factor model in Monte Carlo simulation, and got the short rate on each node (time step =1month). my question is how to get the forward rate from the short rate? I am ...
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Hybrid Models - Hull white with Heston / SchobelZhu / BS
I was looking at literature and found that for hybrid models, most of the literature only gives hybrid models where the volatility of the interest rate process(e.g Hull White) is constant.
Is there a ...
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1 Factor Hull And White Swaption Calibration
I'm trying to calibrate a Hull and White model with constant volatility, mean reversion and theta such that the model can reproduce the initial Term Structure. I'm using this python code adapted from &...
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1
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QuantLib - Calibrating Hull White one-factor on negative interest rates
I have been working with the QuantLib Python package for some days now. Currently, I am working on calibrating a Hull White one-factor model for short rates. I am calibrating the model on the yield-...
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Hull white model calibration - constant mean reverse factor and sigma
I setup a HW 1F model using Monte Carlo simulation with constant mean reversion and volatility factors. When I calibrate to a series of swaptions ( 1x4yr;2x3yr;3x2yr;4x1yr),the last three swaption ...
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Hull-White Monte Carlo simulation - mean reversion function
Quite new to implementing Hull white model in Monte Carlo simulation, hope to get help for 1. how to get the function $\theta$ in the following formula (the function used to match initial term ...
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Hull-White model applied in practice
I'm reading about the Hull-White model, I understand the math behind it and logic but what I am struggling to understand is how it's actually used in practice ? How can we combine it with technics ...
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Quantlib: How do I price a ZC bond using the Hull White model?
I am trying to use QuantLib to model short rate and looks like QL has some material here
http://gouthamanbalaraman.com/blog/hull-white-simulation-quantlib-python.html
I have been able to simulate ...
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305
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Instantaneous correlation in the 2 factor Hull White model
I'm trying to understand which parameter controls the instantaneous correlation in the 2 F HW model. As in, correlation b/w 2 rates observed at the same time. My thinking is as follows:
$$Rate(1)=P(t,...
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Hedge robustness of the one factor Hull White model
I recently came across a quote in a book:
"All single factor models share the limitation that shifts in curve levels cause shifts in the package of vanilla options that are a good hedge for the ...
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A forward contract to buy a foreign currency can be handled by a linear model
In Hull's book, he says that: "An example of a derivative that can be handled by the linear model is a forward contract to buy a foreign currency." Then he continues with, "For the ...
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Implication of forward-rate dynamics when the short-rate follows a normal process
In the section 3.2.3 of the second edition of "Interest Rate Models - Theory and Practice" by Brigo and Mercurio, the forward-rate dynamics implied by the CIR model is derived as follow:
The ...
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Hull & White 1F - What is the appropriate calibration portfolio for Libor indexed structured note?
I'm wondering what is the best swaptions or caps portfolio I could use to calibrate the two parameters of H&W 1F model for a structured note with optionality on Libor underlying.
Let's suppose ...
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1k
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Trinomial Trees for Hull-White model
I am studying trinomial trees and trying to implement them in Python to compare them to the monte carlo simulation. I searched 3-4 hours in the web; but can't find any implementation on binomial or ...
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Current discount rate of Hull White One-Factor Monte Carlo Simulation
I have a question about the Hull-White One-Factor Monte Carlo Simulation. As we know under the Hull-White One-Factor Model, the short rate follows a random process. So basically, every simulation path ...
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Hull-White model: match between HJM framework and short model formulation
I need to show that the Hull-White model $$dr=(\theta(t)-ar)dt+\sigma dW^Q$$ corresponds to the Heath-Jarrow-Morton formulation $$df(t,T)=\alpha(t,T)dt+\sigma e^{-a(T-t)}dW^Q.$$
I obtained the drift ...
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490
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Two Factor Hull White Model Calibrate
I have a question about the optimizer method to calibrate the parameters of two factor hull white model. I have the analytical pricing formula for cap and market cap price. There are five parameters ...
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Pricing of the compound coupon bond with PDE
I am now studying finance math using Steven E.Shereve's book.
Using Interest Rate models, We can the price for zero-coupon with maturity price $1$ under Hull-White interest rate model[page 274] and ...
user43792
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2
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540
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Discount factor in Hull-White model
Consider a Hull-White model
$dr(t)=\left(\theta(t)-a(t) r(t)\right) dt + \sigma dW(t)$
with parameters
$a=0.1$
$\sigma=0.3$
$\theta(t)$ was calibrated to match
$P(0,t)=\exp(-\mu t)$
with: $\mu=0.2$...
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Formula for quantiles of swaprates in the 1-factor Hull-White model
Is there a closed formula to approximate the quantiles of swaprates in the 1-factor Hull White model?
Background
The Hull-White is a Gaussian model for the short rate. Its mean and covariance ...
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Hull-White calibration volatility as a function of time
I need some help for the parametrization of the volatility parameter in the Hull-White model.
I have the necessary Caplet vols and I calibrated the HW model to match the Caplet and hence the Cap ...
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1
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Hull White Cap/Floor calibration
I have a problem and I hope someone could help me.
I calibrated the Hull-White model to Caps and Floors from t=0 so the bond prices are equivalent to todays term structure.
See: Hull-White zero-...
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Why co-terminal swaptions are that important?
Usually Hull & White is calibrated to co-terminal swaptions. When asking why specifically co-terminal, I get the response that it is just a choice and it depends on the use we intend to do with ...
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Cap price as bond options
I am currently struggling with model calibration of the Hull-White (or Vasicek) model to Caps and Floors. My main problem is that I am confused about the notation.
In Brigo & Mercurio (2006, p. ...
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Implementation of the Hull and White short rate model
This is the first time I'm using quantlib, and I wanted to compare the velocity of quantlib with my own Python code.
I found a tutorial about Hull and White to generate the short rate paths with ...
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Hull White Equation Derivation
Hello I need your help.
I found the formula for deriving $A(t,T)$ and $B(t,T)$ in Hull White paper is like this
$BB_{tT} - B_{t}B_{T} - B_{T} = 0$ and
$ABA_{tT} - BA_{t}A_{T} - AA_{t}B_{T} + \frac{1}...
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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 ...
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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 ...
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937
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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)
.
...
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2
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809
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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,...
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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 ...
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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 ...
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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 ...
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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 ...
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How can I estimate the time-varying θ term in the Hull-White one factor model?
I am trying to simulate the prices of bond indexes (e.g. Barclays Aggregate, IBOXX sovereign, IBOXX corporates) using Monte Carlo assuming that they follow the SDE given by the Hull-White model (one-...
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2
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Hull White help needed
I've been trying to calibrate Hull-White 1 Factor & 2 Factor model using Caps but I've some major doubts about my methodology, and would really appreciate some help.
I am using these formulas
...
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