Questions tagged [hullwhite]

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1answer
80 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 ...
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1answer
47 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-...
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1answer
73 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 ...
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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
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1answer
114 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. ...
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1answer
210 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 ...
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0answers
57 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
77 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
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1answer
148 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 ...
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0answers
79 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 ...
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0answers
302 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) . ...
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2answers
143 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,...
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0answers
128 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....
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1answer
268 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 ...
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0answers
399 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
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1answer
390 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 ...
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0answers
382 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
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0answers
112 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
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2answers
550 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 ...
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0answers
61 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
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1answer
381 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 ...
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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 ...
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1answer
234 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 ...
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0answers
275 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)=...
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0answers
57 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
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1answer
605 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
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1answer
849 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, ...
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0answers
115 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
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2answers
448 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?
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1answer
222 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
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1answer
566 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) ...
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1answer
832 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) = \...
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1answer
695 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
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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
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1answer
577 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-...
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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 ...
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0answers
150 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
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1answer
495 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 \...
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2answers
556 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 ...
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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
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1answer
574 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 ...
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0answers
324 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 ...
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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 ...
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1answer
825 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&= [\...
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1answer
809 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 ...
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1answer
635 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 ...
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1answer
605 views

Hull-White formula on wikipedia, correct?

The distribution for the short rate in Hull-White model on Wikipedia is: But the same equation in Damiano's Interest Rate Models - Theory and Practice is: Q: I ...
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0answers
290 views

Hull White 2 factors and non Markov interest rates

I am studying the calibration of the 2 factors Hull White model on Brigo and Mercurio's book. They point out that, using cap volatilities, the value of $\rho$ is almost minus one and this means that ...
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1answer
1k views

Hull White Stochastic Volatility Model in Matlab

I'm trying to code the Hull White stochastic volatility model using matlab and somewhere my code seems to mess up. I've coded the SABR model as well and that's working fine. When I compare prices ...
3
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1answer
926 views

Calibration of 1F Hull White short-rate model to market data

I want to calibrate the Hull White 1 factor short rate model to market data. The main purpose is to simulate interest rate paths, which I will use to calculate the net pv of banking liabilities. Some ...