Questions tagged [hullwhite]
The hullwhite tag has no usage guidance.
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Understanding simple calibration of Hull-White process
I've encountered issues with understanding how to calibrate the Hull-White model without Quantlib package. I want to calibrate this model for the time series of short-rate ($r_1, \cdots,r_n$).
I will ...
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Step by step integration of the Hull-White SDE
I'm struggling to understand the integration process of the Hull-White equation:
\begin{equation}
dr(t)=[\nu(t)-ar(t)]dt+\sigma dW(t)
\end{equation}
In the majority of the references that I have ...
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Hull-White Matlab code
Can someone help me with a code of Hull-White model to price derivatives, in which we use A(t,T), B(t,T) and P(t,T)-the discount factor?
Thank you.
I already have this code, that doesn´t work.
...
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Calibrating Hull White volatility on swap rate volatility
I'm strugling with the Hull-White 1F model. I'am trying to calibrate the volatility with the swap rate volatility. Here is the model I'am curently working on :
$$
\begin{align}
dr_t = a(b-r_t)dt + \...
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Hull-White model with multiple times involved
Consider a pair of currencies $d, f$ (domestic and foreign, respectively) for which we use independent Hull-White models for their rates,
$$dr_d=(\theta_d-a_dr_d)dt+\sigma_ddW_d,$$
$$dr_f=(\theta_f-...
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Euribor 3M simulation
I am required to simulate the trajectory of the Euribor3M rate as it is crucial for determining the future cash flows of my derivative instrument. I've received guidance to employ the Hull-White model....
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Bond option price under hull-white model with different settlement and expiration dates
I am aware of bond option (lets say, call option) price formula under Hull-White model, for example, here -
https://www.applied-financial-mathematics.de/sites/default/files/Teaching/...
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Forward ZC bond with Hull-White model
I am interested in finding the price of a forward zero coupon bond B(t0,t1,t2) under the Hull-White model. To arrive at this result, it makes sense to proceed in this way:
calculate ...
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Multiple factor Hull-While and yield curve deformation
I am currently studying rate models and I understand that the One-Factor model has some incompleteness: The yield-curve can only be shifted.
But I don’t understand what parameter controls this shift ( ...
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Pricing a swaption in a Hull-White model with two curves
Let's say the forward swap rate $s_t$ is equal to $$s_t = \frac{\sum_{j=1}^N \delta_j^{\textrm{float}} P_{t,T_j^{\textrm{float}}}^{\textrm{disc}} L_t^{[T_{j-1}^{\textrm{float}},T_j^{\textrm{float}}]}}{...
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Instantaneous forward rate function to use in HJM framework
HJM framework uses the instantaneous forward rate $f(t,T)$ in the resulting dynamics and pricing formulas (like in Hull-White or Ho-Lee model).
But clearly market does not have an $f(t,T)$ formula, so ...
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Derive the convexity adjustment for inflation YoY swap with unconventional payoff
I'm trying to solve for the convexity adjustment for an inflation YoY swap with unconventional payoff, where $I_i$ is CPI at time i:
$Notional * ([I_i/I_{i-1}]^{Day Count Fraction} - 1)$
In the normal ...
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Are instantaneous short rates compatible across models?
If I calibrate the Vasicek's yield curve to the Nelson-Siegel's (NS) yield curve, can I assume that $r_V(0) = r_{NS}(0) = \beta_0 + \beta_1$ or not?
NS short rate:
$r_{NS}(S) = β_0 + β_1 e^{-S/\tau} + ...
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Simulating Hull-White Model in Python
I first simulated the short rate in the Vasicek model using the following code, which is equivalent to simulating the following normal distribution $r_{t} \sim N\left(r_{0}e^{-at} + b\left(1-e^{-at}\...
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Zero-coupon bond price in the risk-neutral word
In Hull's technical note (http://www-2.rotman.utoronto.ca/~hull/technicalnotes/TechnicalNote31.pdf), on page 3, in the third row from the bottom, a plus sign suddenly appears before σ dz in an ...
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Convexity adjustment for inflation
I'd like to prove the following equation:
$\mathbb{E}\left[\frac{e^{\int_0^{T_1} y_s d s}}{e^{\int_0^{T_2} r_s d s}}\right]=\frac{\mathbb{E}\left[e^{\int_0^{T_2} r_s d s}\right]}{\mathbb{E}\left[e^{\...
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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 ...
CommunityBot
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QuantLib: null term structure set to this instance of index
I'm playing around with QuantLib and trying to price an interest rate cap using HW 1F model.
...
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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 ...
CommunityBot
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How to calibrate short-rate model (Hull-White) using historical domestic IBOR curve without other derivative price? [duplicate]
I'm trying to calibrate Hull White model in VietNam market to value IRS, CSS products which are not publicly traded.
dr(t)=(θ(t)−αr(t))dt+σ(t)dW(t)
I only ...
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Workaround for Hull-White short rate model in market without swaptions
Every time I search calibration methods in short-rate models such as Hull-White, I always find information on how to do it with swaptions market data. Yet, I can't find anything about how to do it in ...
CommunityBot
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Interest Rate Calibration and Backtesting under Fed's raising rates 2022-2023
With the Fed raising interest rates so fast and so drastically, classical interest rate models such as the Black Karasinski (BK), Hull-White (HW), etc., may have trouble calibrating to current rate ...
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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 ...
CommunityBot
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Implication of Humped Spot Curve on future spot curve(s)
I'm currently implementing a G++ model (Two Factor Hull & White model with constant parameters) on zero curve bootstrapped from USD IRS.
Currently, USD IRS is humped at 30 years; swap rate goes up ...
CommunityBot
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Derivations of the pricing PDE for the Heston-Hull-White or Heston-CIR models
Consider the hybrid model given by
$$dS=(r-q) S dt + \sqrt{v} S dZ_1$$
$$dv = \kappa_v (\theta_v - v) dt + \sigma_v \sqrt{v} dZ_2$$
$$dr = \kappa_r (\theta_r - r) dt + \sigma_r r^p dZ_3$$
with ...
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Calibrating Hull-White model
So I have the following short-rate model
$$dX_t = a_1X_tdt + \sigma_1dW_t$$
$$dY_t = a_2Y_tdt + \sigma_2dB_t$$
$$r_t = X_t + Y_t + f(t)$$
with $X_0 = Y_0 = 0$ where $W$ and $B$ are Brownian motions ...
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Hull White Tree Calibration 2
This is actually to extend the question I asked previously and to follow up Bernd's answers.
This is the original link:
Instruments for calibrating Hull White Model
1.
As Bernd mentioned, it's ...
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How to calibrate Hull-White from zero curve?
I am interested in calibrating a Hull-White model to the market.
I do not, however, have data on anything except the market zero curves, as all derivatives are being traded OTC. My plan is to ...
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Approximating second derivatives at boundary of finite difference scheme
The Question
I am implementing a finite difference scheme for the Heston-Hull-White PDE:
\begin{align}
\frac{\partial u}{\partial t} &= \frac{1}{2}s^2v\frac{\partial^2 u}{\partial s^2 } + \frac{1}{...
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How do I calculate Hull White's Theta from the discount curve?
The Question
I'm currently implementing the a finite difference method for the Hull-White model, shown below:
$$\mathrm{d}r(t)=\lambda[\theta(t) − r(t)]\mathrm{d}t + \sigma\mathrm{d}W(t)\tag{1}$$
This ...
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Hybrid Models - Hull white with Heston / SchobelZhu / BS
I was looking at literature and found that for hybrid models, most of the literature only gives hybrid models where the volatility of the interest rate process(e.g Hull White) is constant.
Is there a ...
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Deriving the Heston-Hull-White PDE
I'm trying to derive the Heston-Hull-White PDE. The correct backwards PDE is equation (1.3) of this paper on page (2). I will begin deriving the forward PDE, but switching between the two is trivial.
...
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Why should future short rates tend towards the current term structure of interest rates?
I'm currently looking at the Hull-White model reproduced below:
$$\mathrm{d}r = \lambda(\theta(t)-r)\mathrm{d}t + \sigma\mathrm{d}W(t)\text{.}\tag{1}$$
I have a simplistic understanding of the model. ...
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Dealing with the ru term in an ADI Finite Difference Scheme
I'm trying to code up the algorithm from this paper. The paper presents an ADI algorithm for pricing options in the Heston-Hull-White model.
The starting point is the Heston-Hull-White PDE, given ...
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Calculating the short rate from the discount curve
I'm currently looking at some code that implements the Hull-White model. As one of the inputs, the code accepts a table of discount factors at various dates.
Time in Years
Discount Factor
0
1
0.003
...
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Hull White 1 Factor Formulas with Time Dependent Variables
In John Hull's "Options Futures and Other Derivatives" I see that bond prices in Hull White 1 Factor model are specified as the following:
$P(t,T) = A(t,T)e^{-B(t,T)r(t)}$
where
$B(t,T) = \...
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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 ...
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Calibrating Hull-White 1 Factor
I have been trying to learn HW1F on my own, out of nothing more than genuine curiosity during my twilight years, and I'm confused on the issue of calibrating. I don't know why, but all the research ...
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What is the definition of "co-terminal swaptions"? why they are important in the calibration process?
could anyone help me understand the definition of "co-terminal" swaptions? What are they? Can you provide an example to illustrate? And why such instruments are important in model ...
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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,...
CommunityBot
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Calibrate Hull-white one factor model with swaption in analytical formula
I've been trying to calibrate Hull-white one factor model with swaption but I have a trouble making closed form solution of swaption
Below is the part of paper I've been referencing to
https://people....
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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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how to get 3 month Forward rates from Hull white model simulation?
I implemented the Hull White one factor model in Monte Carlo simulation, and got the short rate on each node (time step =1month). my question is how to get the forward rate from the short rate? I am ...
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1 Factor Hull And White Swaption Calibration
I'm trying to calibrate a Hull and White model with constant volatility, mean reversion and theta such that the model can reproduce the initial Term Structure. I'm using this python code adapted from &...
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QuantLib - Calibrating Hull White one-factor on negative interest rates
I have been working with the QuantLib Python package for some days now. Currently, I am working on calibrating a Hull White one-factor model for short rates. I am calibrating the model on the yield-...
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Hull white model calibration - constant mean reverse factor and sigma
I setup a HW 1F model using Monte Carlo simulation with constant mean reversion and volatility factors. When I calibrate to a series of swaptions ( 1x4yr;2x3yr;3x2yr;4x1yr),the last three swaption ...
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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 ...
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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 ...
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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 ...
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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 ...
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