Questions tagged [hullwhite]
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77
questions
0
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1answer
25 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
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0answers
41 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 ...
1
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0answers
68 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
57 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
93 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
54 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
107 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
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0answers
33 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
123 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. ...
1
vote
1answer
242 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
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0answers
62 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}...
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0answers
80 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
160 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 ...
0
votes
0answers
88 views
Fitting to Market Data in Extended Vasicek / Hull White
I need your help for my task.
I need to calibrate to the market data for Hull White model for Zero Coupon Bond Price. I refer to John Hull and Alan White paper. I want to ask you a few questions and ...
3
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0answers
355 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
164 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,...
0
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0answers
139 views
Calibration of 1-factor Hull-White model using Jamshidians trick - see my code
So, I'm trying to calibrate the Hull-White 1-factor model given Black swaption volatilities that I have from the Bloomberg terminal. I'm following the Jamshidian method as described in this thesis (3....
1
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1answer
305 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 ...
1
vote
1answer
451 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 ...
4
votes
1answer
420 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 ...
9
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0answers
398 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
119 views
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-...
2
votes
2answers
579 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
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0answers
63 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
401 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
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0answers
69 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
240 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
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0answers
279 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:
$$θ(t)=...
1
vote
0answers
59 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
647 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 ...
2
votes
1answer
896 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
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0answers
119 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
2answers
463 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
237 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
595 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
869 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
$$
\theta(t) = \...
1
vote
1answer
723 views
Hull-White Extension of Vasicek Model
I am reading the book Interest Rate Models by Brigo and Mercurio and try to understand the Hull White Model Extended Vasicek Model. They start off by defining the instantaneous short-rate process ...
4
votes
1answer
1k views
How to get set the theta function in the Hull-White model to replicate the current yield curve
I want to calibrate the HW one factor model to current market data. How do I set the function $\theta(t)$ in
$$
\mathrm{d}r(t) = \kappa(\theta(t)-r(t))\mathrm{d}t+\sigma\mathrm{d}W(t)
$$
to ...
1
vote
1answer
609 views
Monte-Carlo simulation Hull-White process
I have one question about Monte-Carlo simulation Hull-White process, maybe you can give me some advice.
I constructed a Hull-White process using Python and QuantLib.
Now I want to construct a Hull-...
4
votes
2answers
1k views
Implementation of one-factor Hull-White short interest rate model
I am looking for implementation in R, VBA, C++, Python (or in any other programming language) of one-factor Hull-White short rate interest model according to the following article:
Hull J. and White ...
3
votes
0answers
151 views
volatility term structure calibration
As is well known in order to calibrate an interest rate model (i.e. hull-white, LMM) i need to use the current market yield curve and volatility. But in the case I want to calibrate the model in a ...
7
votes
1answer
507 views
Black Derman Toy model: from tree to differential equation
The Black Derman Toy model of interest rates is usually introduced as the model governed by the stochastic differential equation:
$$d \ln r = \left[\theta(t) + \cfrac{\sigma'(t)}{\sigma(t)}\ln r \...
3
votes
2answers
578 views
Time dependent parameters in Hull-White model
Hull-White:
$$d r = [\theta(t) - ar]d t + \sigma d W_t.$$
There is a statement in John Hull's book:
The advantage of making $a$ or $\sigma$, or both, functions of ...
6
votes
2answers
1k views
Fixing mean reversion parameter in the 1F HW model
I am trying to calibrate the 1 factor Hull White model to ATM swaptions. The strategy which I use is to minimise the sum of squared difference between model and market prices for the swaptions on the ...
2
votes
1answer
609 views
Why Hull White 2 Factor model can't capture vol skew?
Is there a way to stay with the short rate model (like HW2F or G2++) but extend it to capture vol term structure (vol smile or skew). What happens if I calibrate HW2F to OTM swaptions? (I don't want ...
1
vote
0answers
326 views
How to calculate mean reversion values for Hull White tree calibration on MATLAB?
As part of a time series analysis, I'm writing a MATLAB program to create a Hull White tree, for the purpose of pricing a coupon-bearing bond.
While using the function hwvolspec (volatility ...
1
vote
1answer
1k views
Zero-coupon bond price volatility with one factor Hull White interest rate model
I have been trying to understand the H&W model expression for zero coupon bond price volatilities:
$\nu_B(t_0,t_M)=-\frac{\nu_r}{m}(1-e^{-m\tau_{0,M}})$,
where $\nu_B(t_0,t_M)$ is zero coupon ...
1
vote
1answer
844 views
FX Hull-White model
A model for FX, presented in Interest Rate Models, Brigo and Mercurio (2006), has the following dynamics:
\begin{align}
dr_t^d&= \lambda_d(\theta_d(t)-r_t^d)dt+\eta_d dW_t^d\\
dr_t^f&= [\...
7
votes
1answer
832 views
Calibrating a two-factor Hull-White model using Neural Networks
So I have the following short-rate model
$$dX_t = a_1X_tdt + \sigma_1dW_t$$
$$dY_t = a_2Y_tdt + \sigma_2dB_t$$
$$r_t = X_t + Y_t + f(t)$$
with $X_0 = Y_0 = 0$ where $W$ and $B$ are Brownian motions ...
1
vote
1answer
676 views
zero coupon bond pricing formula using Hull White
I am having some trouble to understand the derivation of the parameters of zero coupon pricing formula using Hull White. Specifically I am trying to understand how to get
--[1]
where is the ...
