Questions tagged [hullwhite]
The hullwhite tag has no usage guidance.
125
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Quantlib Hull-White long term rate simulation
I have an idea of how to simulate short rate in Hull-White 1F model using QuantLib (Hull White Term Structure Simulations with QuantLib Python). I am not sure if there is any way to simulate a long-...
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1
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102
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Pick the price of plain bond off Hull-White Tree
Since we can use Hull-White tree to calculate the price of a option embedded bond, which can be achieved by the QuantLib pricing engine TreeCallableFixedRateBondEngine, can this engine be also used to ...
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54
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Impact of Skew on Bermudan Swaptions
I'm trying to understand the impact of different skew assumptions on the pricing of Bermudan swaptions, e.g. 10NC1 struck at K%.
It is often stated that the price of the Bermudan depends primarily on ...
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65
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How to deal with the deterministic $y$ in the d-dimensional gaussian model
Suppose that under the risk-neutral measure $\mathbf{Q}$ we have an HJM framework dynamics for the instantaneous forward rate $$df_{t,T} = \left(\ldots\right) dt + {}^t \sigma_f (t,T) d W^{Q}_t$$ ...
- 113
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60
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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 ...
1
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1
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100
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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 ...
- 61
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67
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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 :
$$
\begin{align}
dr_t = a(b-r_t)dt + \...
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42
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Hull-White model with multiple times involved
Consider a pair of currencies $d, f$ (domestic and foreign, respectively) for which we use independent Hull-White models for their rates,
$$dr_d=(\theta_d-a_dr_d)dt+\sigma_ddW_d,$$
$$dr_f=(\theta_f-...
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114
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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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1
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96
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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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63
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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 ...
- 1
1
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0
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38
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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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117
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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}}]}}{...
- 113
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57
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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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103
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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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67
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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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785
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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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115
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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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82
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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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1
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327
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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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39
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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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120
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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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2
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499
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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 ...
3
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1
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249
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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$$
with ...
- 57
2
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0
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62
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Approximating second derivatives at boundary of finite difference scheme
The Question
I am implementing a finite difference scheme for the Heston-Hull-White PDE:
\begin{align}
\frac{\partial u}{\partial t} &= \frac{1}{2}s^2v\frac{\partial^2 u}{\partial s^2 } + \frac{1}{...
- 21
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520
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How do I calculate Hull White's Theta from the discount curve?
The Question
I'm currently implementing the a finite difference method for the Hull-White model, shown below:
$$\mathrm{d}r(t)=\lambda[\theta(t) − r(t)]\mathrm{d}t + \sigma\mathrm{d}W(t)\tag{1}$$
This ...
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76
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Dealing with the ru term in an ADI Finite Difference Scheme
I'm trying to code up the algorithm from this paper. The paper presents an ADI algorithm for pricing options in the Heston-Hull-White model.
The starting point is the Heston-Hull-White PDE, given ...
- 437
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148
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Why should future short rates tend towards the current term structure of interest rates?
I'm currently looking at the Hull-White model reproduced below:
$$\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. ...
- 437
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770
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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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2
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584
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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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228
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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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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 ...
- 103
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1
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2k
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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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2
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2k
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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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1
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109
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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 ...
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0
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306
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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
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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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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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1
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2k
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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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410
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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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1
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930
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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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2
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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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1
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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 ...
- 179
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1k
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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,...
- 2,501
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93
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Hedge robustness of the one factor Hull White model
I recently came across a quote in a book:
"All single factor models share the limitation that shifts in curve levels cause shifts in the package of vanilla options that are a good hedge for the ...
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65
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A forward contract to buy a foreign currency can be handled by a linear model
In Hull's book, he says that: "An example of a derivative that can be handled by the linear model is a forward contract to buy a foreign currency." Then he continues with, "For the ...
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229
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Implication of forward-rate dynamics when the short-rate follows a normal process
In the section 3.2.3 of the second edition of "Interest Rate Models - Theory and Practice" by Brigo and Mercurio, the forward-rate dynamics implied by the CIR model is derived as follow:
The ...
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Hull & White 1F - What is the appropriate calibration portfolio for Libor indexed structured note?
I'm wondering what is the best swaptions or caps portfolio I could use to calibrate the two parameters of H&W 1F model for a structured note with optionality on Libor underlying.
Let's suppose ...
- 11
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1
answer
2k
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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 ...
- 11
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1
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413
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Current discount rate of Hull White One-Factor Monte Carlo Simulation
I have a question about the Hull-White One-Factor Monte Carlo Simulation. As we know under the Hull-White One-Factor Model, the short rate follows a random process. So basically, every simulation path ...
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