Questions tagged [hullwhite]

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16
votes
2answers
963 views

Applicability of PCA to get historical volatilities to calibrate interest rates trees

My question in short is as follows: can I take main principal component of historical covariance matrix and use it as historical volatilities when fitting a binomial tree? Here's more detailed ...
14
votes
2answers
12k views

How to calibrate Hull-White from zero curve?

I am interested in calibrating a Hull-White model to the market. I do not, however, have data on anything except the market zero curves, as all derivatives are being traded OTC. My plan is to ...
9
votes
0answers
371 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 ...
7
votes
1answer
2k views

On short-rate-models: Black-Karasinski (with constant parameters) compared to Vasicek

When modelling the term structure of interest rates, one widespread possibility is using the Black-Karasinski model, which is given by the following stochastic process $$d\ln{r}=[\theta(t)-a(t)\ln{r}]...
7
votes
1answer
492 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 \...
7
votes
1answer
788 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 ...
7
votes
2answers
619 views

Whites Reality Check for Pair Trading

I want to use the Monte Carlo Method described in Aronsons book Evidence based Technical Analysis to test if a given pairs trading strategy is useless. First step there is to randomize the returns of ...
6
votes
1answer
3k views

Extended Hull White Interest Rate Model for Zero Coupon Bond

Let's take the following three SDEs: $$dr=u(r,t)dt + w(r,t)dX$$ $$u(r,t)=a(t)-br$$ $$w(r,t)=c$$ where $b$ and $c$ are constants and $a(t)$ an arbitrary function of time $t$. If Zero Coupon Bond $Z(...
6
votes
0answers
534 views

Callable bond price sensitivity to Hull-White volatility changes

I'm using classic Hull-White model for short term interest rate dynamic: $$dr(t)=[\theta(t)-\alpha(t)r(t)]dt+\sigma(t)dW(t)$$ (Notation is quite intuitive, anyway I am using the same as Wikipedia ...
5
votes
2answers
1k views

Why is the mean time-dependent in the Hull-White interest rate model?

In the Vasicek interest-rate model, the interest rate reverts to a constant mean. This makes sense to me. In my conception, the mean ought to be time-invariant, since interest rates don't follow an ...
5
votes
1answer
2k views

Consequence of negative mean reversion of hull white one factor model

I tried to calibrate the data for hull-white one-factor model. Sometimes, I get negative estimate of mean reversion factor after the calibration process. When I plug the negative mean reversion factor ...
5
votes
1answer
1k views

Calibrating Hull-White using volatility data

I would like to calibrate Hull-White model using volatility data.I am using [Park (2004)] paper as a reference. He suggests to minimize the following objective function: where the first term is ...
5
votes
1answer
1k views

How does the 2-factor Hull White model propagate the forward rates curve?

I've been trying to get a grasp on some of the basics of interest rate modeling, and am looking to simulate rates using the 2 factor Hull White model, which I am aware offers a more realistic model of ...
5
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 ...
5
votes
1answer
1k views

Reasonable Hull & White parameters

I am using a Hull & White model to simulate forward rates on US swap curve from the 1.10.2012. This is a part of a bigger picture, and I am interested in some reasonable values for the parameters ...
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 ...
4
votes
4answers
10k views

Simulating the short rate in the Hull-White model

What is the best way to simulate the short rate $r(t)$ in a simple one factor Hull White process? Suppose I have $$ dr(t) = (\theta(t)-\alpha r(t))dt+\sigma dW_t $$ where $\theta(t)$ is calibrated ...
4
votes
1answer
532 views

Extended CIR and discretization

Did someone know how to discretize this process efficiently : $dX(t) = \kappa [\theta(t)-X(t)]dt + \sigma \sqrt{X(t)}dW(t)$ I am looking for something more sophisticated than the trivial Euler ...
4
votes
1answer
371 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 ...
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 ...
4
votes
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
votes
1answer
537 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) ...
3
votes
1answer
1k views

Zero coupon bond pricing under Extended Hull & White

How do you price zero coupon bond in extended Hull & White model by solving the Bond Pricing Equation??
3
votes
2answers
543 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 ...
3
votes
1answer
902 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 ...
3
votes
1answer
395 views

Calibration of Hull White One factor model in F.C.Park paper

I want to ask a question with reference to a paper from below link http://www.cmpr.co.kr/asset/research_material/implementing_interest_rate_models.pdf Minimization specified in Page 14: Mean ...
3
votes
1answer
369 views

Estimating mean reversion

I've read in some places that mean reversion parameters for a rates model, eg Hull White, can be estimated directly from the current yield curve. However I've not been able to find anything more on ...
3
votes
1answer
228 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 ...
3
votes
0answers
228 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) . ...
3
votes
0answers
108 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-...
3
votes
0answers
146 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 ...
3
votes
0answers
289 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 ...
3
votes
0answers
651 views

Reasoning for Bloomberg's short rate volatilty calculation

Bloomberg, in its documentation, explains that it calculates the short rate volatility for its Hull White implementation by multiplying the e.g. 10y IRS rate (divided by 100) by the 10y cap vol. Why? ...
2
votes
1answer
591 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 ...
2
votes
2answers
844 views

Why does the short rate in the Hull White model follow a normal distribution?

Consider Hull White model $dr(t)=[\theta(t)-\alpha(t)r(t)]dt+\sigma(t)dW(t)$ when we solve the SDE above we have $r(t)=e^{-\alpha t}r(0)+\frac{\theta}{\alpha}(1-e^{-\alpha t})+\sigma e^{-\alpha t}\...
2
votes
2answers
527 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
2answers
130 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,...
2
votes
1answer
812 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, ...
2
votes
1answer
555 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 ...
2
votes
1answer
69 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
140 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 ...
2
votes
1answer
571 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
230 views

Function A(t,T) in one-factor Hull-White model

I am struggling with Hull-White model now and have the following question: in the lecture notes under the link below I see how A(t,T) and B(t,T) are being derived. This requires the solution of ...
2
votes
2answers
3k views

Historical calibration of Hull-White model

I have a question concerning 1-factor Hull-White model. For my master project I need to calibrate it to compute Counterparty credit risk metrics. I know that the model might be calibrated either for ...
2
votes
0answers
54 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}...
2
votes
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 ...
2
votes
2answers
413 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
3k views

Normal vs Lognormal Short Rate models

Are there any general arguments to decide whether it is better to use a model with a normal or a lognormal distribution of the short rate? E.g. Hull-White with a normal and Black-Karasinski with a ...
1
vote
1answer
209 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 ...
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 ...