Questions tagged [hullwhite]
The hullwhite tag has no usage guidance.
4
votes
1answer
147 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
votes
0answers
136 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 ...
2
votes
0answers
65 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-...
0
votes
2answers
216 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
0answers
54 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
162 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
62 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 ...
2
votes
1answer
151 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 ...
0
votes
0answers
137 views
Zero Coupon Bond Price under Hull White Model (One Factor)
While pricing Zero coupon bond using One Factor Hull White model. how to determine this value using real world example. θ(t)=F_t (0,t)+(σ^2 (1-e^(-2at) ))/2a
0
votes
0answers
28 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?
0
votes
0answers
33 views
How to examine the impact of the parameters in the Hull White Model on the yield curve
I want to examine the yield curve resulting from the 2 Factor Hull-White model. Is there any way to examine the influence of the parameters on the yields curve without calibrating the model?
0
votes
0answers
35 views
Impact analysis of parameters in the 2 Factor Hull White Model
Through the 2-Factor-Hull White Model you can model the yield curve if you have the parameters $a, b, \sigma, \eta$ given.
Is there any way to measure the impact of these parameters on the yield ...
2
votes
1answer
291 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
445 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
2answers
280 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
134 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 ...
2
votes
1answer
270 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:
$$dr(t) ...
0
votes
0answers
64 views
hybrid models with FX
I am working with an hybrid model:
$S_f(t)$: is a foreign Equity in a foreign currency f.
S follows a BlackScholes model:
$dS_f(t) = S_f(t) r_f dt + \sigma_1 S_f(t) dW_1(t) $
$r_f$ follows a hull ...
1
vote
1answer
584 views
Details of calibration of Hull-White model
Consider the one-factor Hull-White model
$$
\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
405 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 ...
0
votes
1answer
644 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
412 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
866 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
108 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 ...
6
votes
1answer
396 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:
$$d \ln r = \left[\theta(t) + \cfrac{\sigma'(t)}{\sigma(t)}\ln r \...
2
votes
2answers
384 views
Time dependent parameters in Hull-White model
Hull-White:
$$d r = [\theta(t) - ar]d t + \sigma d W_t.$$
There is a statement in John Hull's book:
The advantage of making $a$ or $\sigma$, or both, functions of ...
5
votes
2answers
646 views
Fixing mean reversion parameter in the 1F HW model
I am trying to calibrate the 1 factor Hull White model to ATM swaptions. The strategy which I use is to minimise the sum of squared difference between model and market prices for the swaptions on the ...
2
votes
1answer
299 views
Why Hull White 2 Factor model can't capture vol skew?
Is there a way to stay with the short rate model (like HW2F or G2++) but extend it to capture vol term structure (vol smile or skew). What happens if I calibrate HW2F to OTM swaptions? (I don't want ...
1
vote
0answers
275 views
How to calculate mean reversion values for Hull White tree calibration on MATLAB?
As part of a time series analysis, I'm writing a MATLAB program to create a Hull White tree, for the purpose of pricing a coupon-bearing bond.
While using the function hwvolspec (volatility ...
0
votes
1answer
801 views
Zero-coupon bond price volatility with one factor Hull White interest rate model
I have been trying to understand the H&W model expression for zero coupon bond price volatilities:
$\nu_B(t_0,t_M)=-\frac{\nu_r}{m}(1-e^{-m\tau_{0,M}})$,
where $\nu_B(t_0,t_M)$ is zero coupon ...
2
votes
1answer
595 views
FX Hull-White model
A model for FX, presented in Interest Rate Models, Brigo and Mercurio (2006), has the following dynamics:
\begin{align}
dr_t^d&= \lambda_d(\theta_d(t)-r_t^d)dt+\eta_d dW_t^d\\
dr_t^f&= [\...
7
votes
1answer
628 views
Calibrating a two-factor Hull-White model using Neural Networks
So I have the following short-rate model
$$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
437 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 ...
3
votes
1answer
444 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 ...
4
votes
0answers
250 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 ...
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
760 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 ...
1
vote
1answer
674 views
LIBOR rates from Vasicek/Hull-White model?
I am somehow puzzled by the following problem:
LIBOR rates are forward rates for an interbank loan for 1M or 3M (let's limit the range of possibilities to these two cases). Assuming that I have ...
4
votes
1answer
1k 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
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$$
where $b$ and $c$ are constants and $a(t)$ an arbitrary function of time $t$.
If Zero Coupon Bond $Z(...
6
votes
2answers
582 views
Whites Reality Check for Pair Trading
I want to use the Monte Carlo Method described in Aronsons book Evidence based Technical Analysis to test if a given pairs trading strategy is useless.
First step there is to randomize the returns of ...
6
votes
0answers
418 views
Callable bond price sensitivity to Hull-White volatility changes
I'm using classic Hull-White model for short term interest rate dynamic:
$$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 ...
2
votes
1answer
209 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 ...
1
vote
0answers
40 views
number of trades - flaw in White Reality Check?
I went through Whites paper of the reality check for multiple strategy testing.
To summarize at a simple example:
I have 2 strategies, s1 and s2.
s1 gives 2 signals and therefore 2 returns, s2 gives ...
2
votes
2answers
2k 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 ...
4
votes
1answer
424 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 ...
2
votes
2answers
623 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}\...
3
votes
1answer
989 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
1answer
351 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
325 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 ...
