Questions tagged [hullwhite]
The hullwhite tag has no usage guidance.
90
questions
2
votes
1answer
88 views
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 ...
4
votes
2answers
407 views
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 ...
0
votes
1answer
128 views
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 ...
0
votes
0answers
56 views
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,...
1
vote
0answers
50 views
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 ...
0
votes
0answers
32 views
How to implement CallableFloatingRateBond in QuantLib?
Is there anybody has any idea (or any C++ code) to implement the pricer for the CallableFloatingRateBond in QuantLib. I want to discount and forecast the cash flows on the tree using the Hull White ...
0
votes
0answers
47 views
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 ...
2
votes
1answer
98 views
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 ...
0
votes
0answers
53 views
Option pricing PDE Black Scholes one-factor Hull-White (or Vasicek) model
I am trying to find the option pricing PDE of the Black Scholes one-factor Hull-White (or Vasicek) model using a self-financing portfolio strategy. The system is as following
\begin{equation*}
\begin{...
1
vote
0answers
16 views
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 ...
0
votes
0answers
83 views
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 ...
0
votes
0answers
18 views
Jarrow-Yildrim like model with G2++
I would be interested in if there exists a Jarrow-Yildrim like model, but based on two factors like the G2++ model. If there is no particular description available yet, would it be possible to extend ...
1
vote
1answer
111 views
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 ...
1
vote
1answer
106 views
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 ...
0
votes
0answers
24 views
Theta function in the Black Karasinski model to replicate the current yield curve?
I am trying to replicate a research paper "Gas Storage valuation using a Monte Carlo method"
Gas storage valuation using a monte carlo method
which is to me a not very complex but technical ...
1
vote
1answer
102 views
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 ...
1
vote
0answers
129 views
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 ...
2
votes
2answers
265 views
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$...
1
vote
1answer
146 views
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 ...
2
votes
1answer
304 views
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 ...
-1
votes
1answer
113 views
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-...
1
vote
1answer
539 views
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 ...
0
votes
0answers
117 views
Swap rate in the annuity measure and Martingale Representation Theorem
As we know, swap rate evolves as a martingale in the appropriate annuity measure. Martingale representation theorem says if I can find a Brownian motion in the annuity measure and the swap rate is ...
2
votes
1answer
228 views
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. ...
2
votes
1answer
531 views
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 ...
2
votes
0answers
106 views
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}...
1
vote
0answers
106 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 ...
2
votes
1answer
281 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 ...
3
votes
0answers
599 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)
.
...
2
votes
2answers
327 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,...
1
vote
1answer
587 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 ...
3
votes
1answer
1k views
Calibration of Theta, A(t) and B(t) of Hull White 1Factor model
Iām simulating interest rates via the HullWhite One factor model. To simulate the short rate Iām using the code from the Quantlib Python Cookbook, chapter 15 and beyond (By Goutham Balaraman and Luigi ...
5
votes
1answer
624 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 ...
11
votes
1answer
793 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 ...
3
votes
0answers
169 views
How can I estimate the time-varying Īø 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-...
3
votes
2answers
943 views
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
...
2
votes
1answer
101 views
Convert Short rate from HW simulation into Swap rates
I am trying to price an exotic option that requires me to simulate 10 yr swap rates. I have calibrated a 1 factor HW model to swaption prices. However, my understanding is that the HW model describes ...
0
votes
1answer
588 views
Estimation of market price of risk of short interest rate under the Hull-White model
I think I am a bit confused. I intend to estimate the market price of risk the short interest rate, say, under the Hull-White model. I have the following two questions.
Is it correct to state state ...
1
vote
0answers
76 views
A basic question about short-rate models
Sorry, if it's a very rudimentary question. I mainly practice tax but have to deal with financial transactions from time to time where I have to benchmark option prices. I have usually used Hull's ...
3
votes
1answer
299 views
Hybrid Heston-Hull White Model
I am wondering if anyone could recommend a few good papers on hybrid heston-hull white models, in particular with respect to the approximation of model European options for calibration. Literature on ...
1
vote
0answers
378 views
Zero Coupon Bond Price under Hull White Model (One Factor)
While pricing Zero coupon bond using One Factor Hull White model:
$$dr(t) = \left(\theta(t) - a r \right)dt + \sigma dW(t)$$
How to determine the value of $\theta(t)$ using real world example:
$$Īø(t)=...
1
vote
0answers
67 views
Relation between BDT volatility and Hull-White one factor Volatility
Is there any mathematical relationship between the volatility of spot rates calibrated from Lognormal model and the volatility of spot rates calibrated from HW one factor model?
2
votes
1answer
964 views
Hull White Tree Calibration 2
This is actually to extend the question I asked previously and to follow up Bernd's answers.
This is the original link:
Instruments for calibrating Hull White Model
1.
As Bernd mentioned, it's ...
3
votes
1answer
1k views
Instruments for calibrating Hull White Model
I have a few questions regarding hull white calibration, specificly for the trinomial tree model.
1.I am wondering what are the ideal instruments could be used for hull white model calibration? Cap, ...
1
vote
0answers
139 views
European Call Option Modelling under 2 factor Hull White interest rates
I have modelled the yield curve through the two factor Hull White Model. Now I want to implement in Matlab the price development of a ATM-Call-Option (European).
Has someone an idea how to combine ...
3
votes
3answers
630 views
Monte-Carlo simulation Hull-White process: physical and risk-neutral measure
From Monte-Carlo simulation Hull-White process I get paths in risk-neutal measure. How can I get paths in physical measure?
1
vote
1answer
312 views
Lattice pricing of derivatives under multi curve framework (OIS and LIBOR)
My goal is to price various derivatives resetting to 1M and 3M LIBOR via using a lattice. I have calculated an OIS curve for discounting and adjusted 1M and 3M LIBOR forward curves to be consistent ...
3
votes
1answer
899 views
Proof behind solution for theta in Hull-White with time-dependent volatility and mean reversion?
I'm studying the following paper on Hull-White model calibration:
Hull-White paper
In this paper they study the general form of the HW model with time-dependent mean reversion and volatility:
$$dr(t) ...
1
vote
1answer
1k views
Details of calibration of Hull-White model
Consider the one-factor Hull-White model
$$
\mathrm{d}r(t) = (\theta(t)-\kappa r(t))\mathrm{d}t + \sigma\mathrm{d}W(t)
$$
When one calibrates the model to market data one chooses
$$
\theta(t) = \...
1
vote
1answer
1k views
Hull-White Extension of Vasicek Model
I am reading the book Interest Rate Models by Brigo and Mercurio and try to understand the Hull White Model Extended Vasicek Model. They start off by defining the instantaneous short-rate process ...
