Questions tagged [calibration]
The calibration tag has no usage guidance.
125
questions
2
votes
1answer
74 views
how does stochastic volatility models generate smiles?
When calibrating call price with the BS-model, we achieve some parameters and especielly we achieve $\sigma^*$.
Now, lets say I will price call options using these parameters. Then we achieve, lets ...
2
votes
0answers
83 views
Stochastic Volatility Models Real World Calibration
I am trying to find some research pertaining to the historical (or real world) calibration of stochastic volatility models.
For example, in applications such as counterparty credit risk (IMM) or ...
0
votes
0answers
50 views
PD calibration using Bayes formula
When calculating ECLs for loans under IFRS 9, one of the requirements is that the PD estimates have to be Point-in-time ($PD_{PIT}$) rather than through-the-cycle ($PD_{TTC}$).The setting is as ...
2
votes
1answer
95 views
Hull-White calibration volatility as a function of time
I need some help for the parametrization of the volatility parameter in the Hull-White model.
I have the necessary Caplet vols and I calibrated the HW model to match the Caplet and hence the Cap ...
0
votes
1answer
52 views
Calibrating Heston model parameters using the Active-set method and Levenberg–Marquardt
Background: We're estimating the parameters of the Heston model from current market data of options. This is to be implemented using the active-set method (see section 16.5 here) and the Levenberg-...
2
votes
1answer
104 views
SABR Calibration
I need to generate the Volatility Surface of call options on S&P500 index, my
dataset contains implied volatilities regarding various expiration dates for various strike prices.
My doubt is, ...
3
votes
1answer
76 views
QuantLib: Which CalibrationHelper to use for Normal Volatilities
I am using the SwaptionHelper class to create the swaptions.
Reading the documentation: https://www.quantlib.org/reference/class_quant_lib_1_1_swaption_helper.html
I realize that one of the ...
0
votes
1answer
71 views
Constructing Daily Term Structure
I am very new to QuantLib and am trying to do Swaption Model calibration following the example here:http://gouthamanbalaraman.com/blog/short-interest-rate-model-calibration-quantlib.html
Appreciate ...
0
votes
0answers
43 views
Black-Scholes model - Calibration of the risk-free rate
I know there is a lot of content about this topic, but I have not seen a post which gives a satisfying answer to my problem.
I am trying to hedge a European call option with real market data under ...
1
vote
1answer
117 views
Why co-terminal swaptions are that important?
Usually Hull & White is calibrated to co-terminal swaptions. When asking why specifically co-terminal, I get the response that it is just a choice and it depends on the use we intend to do with ...
1
vote
1answer
55 views
Calibrate a model parameter with an error function
Suppose I want to find the implied volatility using an option model from market prices. Surely I can find the implied volatility for each strike price ($k$ different strike prices) for a given ...
0
votes
0answers
24 views
CDS ISDA Pricing (usage of accrued in calibration)
I am looking to understand the ISDA CDS Pricing Model for a 1Y "Buy Protection" CDS with Coupon = Quoted Spread = 100bp. Numbers are from Bloomberg.
Cash-Flow Matrix
...
1
vote
0answers
42 views
Calibration using only strike price
I have a binary option and want to calibrate it's BS pricing model. I only have a series of Strike Price vs the Option price, no knowledge on time to maturity, volatility, risk free rate or the ...
1
vote
0answers
35 views
Procedure of model calibration
Say that your end goal is to price an equity exotic derivative under both Heston and the local volatility models (Black Scholes model with vola dependent on strike and underlying level). Do the ...
0
votes
1answer
83 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
61 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
176 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
161 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
50 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
91 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
52 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
228 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
285 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
59 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
407 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
1answer
102 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
424 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
193 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
140 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 ...
10
votes
1answer
434 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
104 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
412 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
169 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
138 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
56 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
97 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
654 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
909 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
93 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 ...
5
votes
1answer
360 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
602 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:
$$dr(t) ...
5
votes
0answers
248 views
Dupire's calibration
I'm trying to implement a method for calibrating the local volatility model (Dupire's one). I'm working on the paper from Andreasen and Huge : Volatility interpolation (SSRN). Is this considered to be ...
1
vote
0answers
88 views
Calibrating Heston paremeters based on market data for Implied Vol for Call options
Several questions have been asked in here regarding calibration in Heston yet I have not found what I have been looking for, so I will ask:
I am looking at a Heston model:
$$dS_t=\lambda \sqrt{v_t}...
1
vote
1answer
883 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
$$
\theta(t) = \...
17
votes
0answers
733 views
Local Stochastic Volatility - Break even levels
In Chapter 12 of his excellent book Stochastic Volatility Modeling, Lorenzo Bergomi discusses the topic of local-stochastic volatility models (LSV).
As most of you are probably aware of, the idea is ...
4
votes
1answer
1k views
How to get set the theta function in the Hull-White model to replicate the current yield curve
I want to calibrate the HW one factor model to current market data. How do I set the function $\theta(t)$ in
$$
\mathrm{d}r(t) = \kappa(\theta(t)-r(t))\mathrm{d}t+\sigma\mathrm{d}W(t)
$$
to ...
3
votes
0answers
152 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
344 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). ...
9
votes
1answer
294 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 ...
