Questions tagged [calibration]
The calibration tag has no usage guidance.
111
questions
0
votes
1answer
51 views
Interest rate swap valuation date convention
When we value interest rate derivatives on any date $t$, we can estimate our future payments using some calibrated forward curve $f_s$, where $s$ is the spot date, and discount these back to $t$ using ...
1
vote
1answer
46 views
Zero-coupon bond price under Rendleman-Bartter Model
let's say that I have simulated the interest rate using the Rendleman-Barttermodel, (which is not the best for rates I know) and then I want to simulate paths for the bond paying 1 at maturity:
$$...
5
votes
1answer
123 views
How frequently is local volatility calibrated to implied vol surface, in practice?
This has two related questions -
How frequently do equity derivative traders re-mark the implied volatility surface -
(i) once a day (e.g. at start of trading day, or end-of-day), or
(ii) ...
2
votes
1answer
121 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 ...
0
votes
0answers
39 views
Parameter estimation and calibration
I am not sure if I understand calibration correctly. Consider a CIR model, suppose I want to estimate the parameters $a,b,\sigma$, I can use a method such as this.
However I understand that ...
0
votes
0answers
54 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 ...
1
vote
0answers
41 views
How to migrate Octave Levenberg-Marquardt algorithm to Accord.Net (C#)
I am trying to migrate Matlab (Octave) Levenberg-Marquardt algorithm to Accord.Net (C#) but struggling to match input parameters
For example this simple example available in the documentation here:
...
2
votes
1answer
112 views
zero-shift SABR vega and re-calibration of SABR
I have a zero-shifted SABR model, where I need to confirm if the model is generating the calibration and vega's correctly.
The underlying model is the standard SABR lognormal (there is normal as well)...
2
votes
1answer
228 views
LSV model calibration with only few quotes per maturity
At this link I have asked what is the market standard when pricing options in different asset classes. Based on the answers, the standard for FX and equities seems to be the local-stochastic ...
1
vote
0answers
50 views
Effective duration and recalibration
I am calculating the effective duration of an interest rate instrument with optionality. I do the following
calibrate an interest rate model to market data: discount curve and ATM swaption vols
use ...
1
vote
1answer
285 views
python scipy optimize minimize arguments for Implied Volatility
I am having some trouble getting the 'correct' solution to a function where I am trying to utilize scipy.optimize.minimize.
In the code below, I create a function <...
7
votes
0answers
63 views
Quanto basket payoff
I have a payoff that is the worst of the returns two indices: S&P500 (SPX) and Euro Stoxx 50 (SX5E).
$\pi = \min \left\{\left(\frac{\text{SPX}_\tau-\text{SPX}_0}{\text{SPX}_0}\right),\left(\frac{\...
4
votes
1answer
301 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 ...
1
vote
1answer
160 views
CIR calibration
I'm using a CIR short rate model to forecast interest rate paths.
I've been thinking and also searching online about different ways of estimating its parameters (a, b and sigma). While there are a ...
3
votes
2answers
113 views
Statistical estimation vs Stochastic calibration of models
I have never been able to deduce the precise differences between model building from the statistical perspective and the stochastic processes/calibration perspective. I can only infer that these are ...
9
votes
0answers
344 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
votes
1answer
86 views
Ho & Lee yield curve fitting with zero coupon bond market prices
The Ho & Lee model for interest rates is given by the SDE:
$$
\mathrm d r = \eta(t) \mathrm d t + c\,\mathrm d X
$$
The calibration function for $\eta(t)$ is given by
$$
\eta^*(t)=c^2(t-t^*)-\...
4
votes
1answer
292 views
Intuition for the Effect of Vol of Vol in Heston Model on Volatility Surface
I was hoping someone could describe the economic/mathematical intuition behind the effect that the vol of vol parameter has on the volatility surface, in particular the slope to maturity. Take for ...
0
votes
1answer
143 views
Calibrate SABR-LMM using only data from Bloomberg?
I'm exploring the SABR-LMM model. In particular, have been trying to study the effect of the parameters and their time evolution.
However, the data seems to be a major issue here. Prices for caps/...
2
votes
0answers
109 views
Bootstrapping and Curve Calibration Objective Function
I'm confused about the form of the objective function for some global curve calibration. It seems simple enough: minimized the squared loss of the price of the input instruments and the price ...
2
votes
0answers
51 views
Interest model calibration and binomial trees
Are there any good books for beginners on calibrating interest rate models and creating binomial trees based on these interest rate models and using them in pricing
1
vote
0answers
86 views
Autocall Calibration
I'm trying to price autocalls.
In theory my pricing method is ok (I followed Bouzoubaa's book procedure) but I'm not sure I read anything on calibration of autocalls. Basically my question is what ...
2
votes
1answer
498 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
716 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, ...
3
votes
0answers
82 views
Change of measure when calibrating real-world dynamics
If I want to simulate a process (say, a set of forward rates) under a real-world measure, can I use option prices / implied vols to calibrate some of the parameters and do I need to change the measure ...
3
votes
0answers
277 views
Calibration of Cox-Ingersoll-Ross process that hits zero (Feller condition violation)
I'm considering a Cox-Ingersoll-Ross (CIR) process
$$
dx_{t} = \alpha\left(\theta - x_{t}\right)dt + \sigma \sqrt{x_{t}}\,dW_{t}\,,\qquad \alpha,\beta,\sigma > 0
$$
which by assumption has $2\...
1
vote
0answers
31 views
amount of data - option pricer calibration
A practical question. When you calibrate an option pricer (whatever the model is), do you use data from several days or just one day (last trading day)? I noted some papers use data from one single ...
3
votes
1answer
467 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:
$$dr(t) ...
5
votes
0answers
230 views
Dupire's calibration
I'm trying to implement a method for calibrating the local volatility model (Dupire's one). I'm working on the paper from Andreasen and Huge : Volatility interpolation (SSRN). Is this considered to be ...
1
vote
0answers
83 views
Calibrating Heston paremeters based on market data for Implied Vol for Call options
Several questions have been asked in here regarding calibration in Heston yet I have not found what I have been looking for, so I will ask:
I am looking at a Heston model:
$$dS_t=\lambda \sqrt{v_t}...
1
vote
1answer
766 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
$$
\theta(t) = \...
16
votes
0answers
647 views
Local Stochastic Volatility - Break even levels
In Chapter 12 of his excellent book Stochastic Volatility Modeling, Lorenzo Bergomi discusses the topic of local-stochastic volatility models (LSV).
As most of you are probably aware of, the idea is ...
1
vote
1answer
1k views
How to get set the theta function in the Hull-White model to replicate the current yield curve
I want to calibrate the HW one factor model to current market data. How do I set the function $\theta(t)$ in
$$
\mathrm{d}r(t) = \kappa(\theta(t)-r(t))\mathrm{d}t+\sigma\mathrm{d}W(t)
$$
to ...
3
votes
0answers
139 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
312 views
Ill-posed problem: Local volatility calibration. Regularization vs Smoothing
I have asked my question on Mathematics site of Stack Exchange but maybe I will get the answer rather here.
I am working on inverse problem - calibration of local volatility (financial application). ...
8
votes
1answer
251 views
Heston model reparametrisation
It is well-known that calibrating Heston to the vanilla market is not as easy as it seems: some parameters are "interdependent" and the objective function exhibit plateaus in the parameter space (at ...
2
votes
0answers
181 views
Calibration of real-world drift for PFE
It is well-known that for the calculation of potential future exposure (PFE), real-word probability measure should be used to scenario-generation and risk-neutral measure is used for revaluation; see ...
2
votes
1answer
481 views
Calibration by monte carlo, should I fix my seed?
I am calibrating a 3-parameter stochastic model to options market data via Monte Carlo simulation. Let the parameter set be denoted by $\bar{\theta}$. (this is not a simple Black-Scholes type model, ...
4
votes
2answers
911 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 ...
1
vote
0answers
551 views
Heston Model Calibration
I've calibrated the Heston Model using options data and I was wondering if the parameters I've obtained are stable enough. Also, is Feller condition imposed, when calibrating the Heston Model, in the ...
2
votes
1answer
478 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 ...
5
votes
1answer
2k views
Vasicek model calibration
I am trying to calibrate Vasicek model, i.e. to determine the parameters $\kappa, \mu, \bar{\mu}$ and $\sigma$ where the process dynamics are given through
$$ dr_t=\kappa\left( \mu - r_t\right) dt+\...
1
vote
0answers
122 views
Multi objective optimization Swaption/Caplets joint Calibration
People suppose that we have a two asset type portfolio optimization (as Intrument Type 1 and 2).
In the each portfolio refered by the instrument type there are 2 asset so we have four asset in total.
...
3
votes
0answers
474 views
Equations for multicurve calibration with OIS discounting
I am trying to calibrate my forecast and discount curves using the multi-curve approach with OIS discounting. To do so, I have a implemented multivariate Newton-Raphson root finder. I am finding a bit ...
2
votes
1answer
184 views
Practical way to estimate price sensitivity to unexpected earnings (i.e., post-earnings drift)?
Post-earnings announcement drift is a well documented anomaly in financial research. In 2017 May NBER paper, Replicating Anomalies, the authors found that anomalies related to standardized unexpected ...
8
votes
1answer
242 views
Is a common approach to calibration reasonable?
"Model Calibration" article in Encyclopedia of Quantitative Finance states that
. . . a common approach for selecting a pricing measure $\mathbb{Q}$ is to choose, given a set of liquidly ...
2
votes
1answer
275 views
ATM i.r. Caps - Black vol calibration
I'm provided the forward curve and time 0 prices of ATM Caps.
Volatility is 1-factor Gaussian HJM model with specification:
$$
\sigma(t, T) = \nu \exp \{ \beta (T − t) \}
$$
Now, I need to ...
0
votes
1answer
212 views
Calibration of Monte Carlo value?
I wish to calibrate the Heston model parameters to a given smile. Trouble is, I have Heston implemented as a Monte Carlo simulation, and not some deterministic pricing function.
So, how do we ...
7
votes
1answer
741 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
124 views
How to prrice a European swaption with floor?
I'm wondering how we can price a european swaption with a floor on the floating leg.
Assuming that we use the HW 1 factor model, how we can simultaneously calibrate the swaption ( on swap rate ...
