Questions tagged [calibration]
The calibration tag has no usage guidance.
173
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38 views
Option pricing when stock price follows binomial tree
Assume that the stock price is currently trading at $S_0$. It is known that the stock price follows a binomial tree, such that its price will be either $S_0e^{\theta_u}$ or $S_0e^{−\theta_d}$ over the ...
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21 views
Calibrate Local Volatility model to price quanto options
I have a Local Volatility model. I compute the LV surface $\sigma_{S}^{local}$ on vanilla option of $S$. Assume the vol of foreign exchange is constant and know, and the correlation equity/FX is known....
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1answer
189 views
Can't fit Bloomberg volatility smile with pysabr. What am I doing wrong?
I want to make sure that I can properly use SABR model on 1-period interest rate options, i.e. caplets, therefore I attempted to get lognormal volatilities for 4%, 6%, ATM, 8%, 10% strikes for 3Mx6M ...
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26 views
Should one calibrate SABR model on caps or caplets?
I want to build a volatility surface for caps on a 3M index implied from SABR model. I have a set of cap normal volatilities for a range of strikes (4%, 6%, 8%, 10% and ATM) and maturities (1, 2, 3, 4 ...
1
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1answer
53 views
In which scenario would we end up with more than one $\mathbb{Q}$ after calibrating an incomplete model?
Reading the literature I see that quite an effort is made to price derivatives in an incomplete setting. I see stuff like efficient hedging, indifference pricing, choosing $\mathbb{Q}$ by considering ...
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49 views
Calibrate 1-factor Gaussian HJM model on forward rates and ATM caps prices
I'm trying to solve the following problem as a part of the Interest Rate Models course
The algorithm that I'm following is
derive simple rates from the given forward rates via $L(0, T_i) = \frac{(1+\...
1
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1answer
50 views
Inverting the Black formula for Cap price to find Black implied volatility
I'm solving the following problem as a part of Interest Rate Models class on Coursera
I'm having a hard time using nonlinear root solver to invert the Black formula for Cap price in order to obtain a ...
4
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0answers
96 views
Why calibrate volatility Models to volatility surfaces rather than underlying's historical price data?
I'm trying to grasp the rationale for calibrating stochastic volatility models (i.e. Heston model) to empirical IV data from market prices. Doesn't this assume that the options are fairly priced and ...
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1answer
65 views
Why are implied parameters preferred over expectations of future implied parameters?
For example, when we price options on assets under the Heston model, we often compute the volatility of the volatility of the price of those assets implied by the market at time $t=0$ using the market ...
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0answers
39 views
Question on model recalibration upon a spot shift scenario analysis
I am given a plot of the fair value of a complex derivative against a scenario spot shift for a range odd possible shifts (-40% to 40%). Let us say the pricing model is a local vol model. I am unable ...
1
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1answer
102 views
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. ...
0
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1answer
69 views
When are parameters calibrated using one option type applicable to price other option types on the same underlying?
I am coding up some basic models to show prospective employers, but I am forced to guess "what is done in practice" since I don't yet work in the industry. I am implementing various ...
2
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1answer
372 views
Risk Neutral Valuation, Drifts and Calibration
Lets consider a pricing model like Vasicek.
Apparently, if you calibrate a derivatives pricing model to market prices this gives you risk neutral parameters. Its not clear to me as to WHY this will ...
1
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1answer
162 views
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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1answer
120 views
Calibration of Heston model with stochastic short rate
I have following Heston model with stochastic short rate:
\begin{eqnarray*}dS\left(t\right)&=&r\left(t\right)S\left(t\right)dt+\nu\left(t\right)S\left(t\right)dW^{S}\left(t\right)\\dr\left(t\...
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0answers
22 views
Interest rate caps and floors - where to get data [duplicate]
Hey I need some prices of interest rate caps and floors for model calibration. Where can I get (or eventually buy) data?
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0answers
64 views
Can you calibrate the Heston model using stock price trajectories?
I'm interested in calibrating the Heston model so I was reading about it online. All procedures I could find was using market prices for European call options and using the (semi-)closed-form ...
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2answers
169 views
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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1answer
112 views
Theoretical and practical drawbacks of using Deep Learning for calibration and pricing
I am investigating the suitability of using deep learning for pricing and calibration for the full implied volatility surface. Such examples of their application are in papers here and here. During ...
0
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2answers
164 views
Calibrating OU parameters using AR(1)
I have a mean reverting time series and want to find the Ornstein-Uhlenbeck (OU) parameters of it. I researched the internet and found that we can calibrate the model as a simple AR(1) process,
$$\...
3
votes
1answer
170 views
Stochastic Volatility vs Vanna-Volga
I'm working on the calibration of the Heston Stochastic Volatility Model for some FX option data for my bachelor thesis and I was asked "Why should people use Heston instead of other simple ...
2
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1answer
211 views
calibration of a local volatility model
Generally speaking, when calibrating a local volatility model a la Dupire to European vanilla calls, should I use the numerically (PDE or Monte Carlo) solved price for the vanilla call in the cost ...
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0answers
50 views
calibration of local volatility to
I'm looking to understand the practical details of calibrating local volatility to option prices for a range of different expiries using the Dupire local volatility equation. Would appreciate some ...
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0answers
67 views
MatLab code does not work for Heston model calibration
I am trying to calibrate Heston model on some data and I have the following code. Code is supposed, after it reads the data, to give back 5 parameters. However, I get an empty answer from MatLab. Does ...
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0answers
138 views
Heston Model Calibration with MatLab: model prices do not fall in the bid-ask range
I am currently implementing the MatLab code reported below for the calibration of Heston Model. The code seems fine and, by reading the paper where I took the code, I was able to calibrate and price ...
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101 views
Vasicek Model With Jumps
I'm trying to calibrate a mean-reverting, jump diffusion model using the outline provided on page 11 here:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.40.3489&rep=rep1&type=pdf
...
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0answers
117 views
Calibrate Geometric Brownian Motion of trading volume time series
Let's say I'm modeling the trading volume of a stock price (e.g. Apple Inc.) to follow a Geometric Brownian Motion and I want to estimate the parameters (i.e. drift and volatility) using historical ...
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1answer
55 views
Calibration when characteristic function is not known
The prices of the call and put options can be quickly calculated using many methods using the form of the characteristic function. But how to calibrate a model when we don't know the characteristic ...
1
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1answer
195 views
Calibration Hull-White
This is more a conceptual question around calibration. My objective is to calibrate a 1-factor Hull White model, and my question relates to calibrating a and sigma (both constants) to swaptions.
Let's ...
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0answers
266 views
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 &...
3
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0answers
94 views
Explicit expression for option prices in SABR?
I am trying to get a grip of the current state of research regarding option pricing in the SABR model.
Am I correct in that, so far, there is no known general formula for the option price in the SABR ...
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0answers
76 views
Derivation of $u=e^{\sigma\sqrt{dt}}$ and $d=e^{-\sigma\sqrt{dt}}$
Anyone could provide me a proof of how, starting from $\frac{dS_T}{S_t}\sim \operatorname{N}(\mu dt,\sigma^2 dt)$ with $p:=\frac{e^{rdt}-d}{u-d}$, we can obtain the parameters $u$ and $d$ as from ...
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1answer
266 views
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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0answers
54 views
Carr-madan vs COS method vs other methods
Hey during calibration we have to calculate option prices very fast. The most popular method was developed by Carr-Madan, but COS method also is very popular. The problem is for example with Variance ...
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1answer
133 views
Heston model on currency
We could have the formula for Heston model for currency as (under the Risk-neutral measure for $r_d$) -
$dS_t = \left( r_d - r_f ...
4
votes
2answers
451 views
Forward skew generated by Local Vol model
I'm digging into the properties of the Local Vol model and I become confused with statements made by authors in papers/textbooks (without explanations) like, "The forward skew in local vol model ...
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0answers
66 views
Two questions about COS method
Hey I have some problem with COS method. Here is the paper of Fang and Oosterlee https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.466.267&rep=rep1&type=pdf
Why in table 1.1 they ...
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1answer
44 views
Calibration data selection - basic rules
Hey I found following rules for selecting data for calibration (source: "Kou Jump Diffusion Model: An Application to the Standard and
Poor 500, Nasdaq 100 and Russell 2000 Index Options" by ...
6
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1answer
172 views
How to choose the martingale measure in incomplete markets
Hey I know that when market is incomplete, then we have to choose an equivalent martingale measure (I heard about Escher Transform martingale measure, Mean correcting martingale measure, minimal ...
0
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1answer
85 views
How to estimate the risk-free rate when pricing options - calibration
I would like to calibrate my model to the current call option prices (with 17 different maturity times) but I don't know how to choose a risk-free rate in this case.
3
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1answer
141 views
PnL due to model recalibration and its relationship with hedging error
Consider the case where at t=0, I calibrate my model to the market, but at t=1 my model is no longer able to recover the price in the market, so it needs recalibration. Say I have delta hedged my ...
4
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1answer
109 views
How to calibrate models with unbounded parameter space
I am calibrating the Heston model with sequential quadratic programming algorithm. It turns out that the volatility surfaces I am calibrating to can be fit very well with extreme values of mean ...
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0answers
115 views
Bond Options Calibration to market volatility using SABR Model
I'm trying to calibrate bond option implied volatility from SABR model to market volatilities, I tried calibration in python but the smile isn't correctly matching with market volatility?
Any help is ...
2
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0answers
47 views
Local v/s global calibration for a Bermudan Option (calibrate co-terminals vs entire matrix)
I am quite new to rates modeling and I have a question on the pros and cons of calibrating to larger set of vanilla instruments v/s calibrating to an exotic's 'natural' hedges. For example, I could ...
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0answers
21 views
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 ...
3
votes
2answers
766 views
What does it mean to "calibrate vols"
As a beginner, it can sometimes be hard to discern what different terms and phrases mean in QF. I've heard multiple people such as academics and market-makers say things like "calibrate vols" or "...
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0answers
330 views
Libor Market Model with SABR Calibration
What is the industry practice in calibrating SABR Libor Market Model? Do you first calibrate the SABR model using market data and then implement the libor market model with the calibrated parameters?
...
3
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1answer
175 views
Heston Monte Carlo or FFT Pricing
I am trying to better understand the Heston model and its implementation. It seems like a lot of people use the FFT method for calculating the call prices during the Heston calibration, but the Monte ...
7
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1answer
615 views
Implied vol and model calibration for an american option on a dividend paying stock - is there a market standard pricing model?
In terms of calibrating a pricing model to observed prices for American options on a dividend paying stock, is there a standard way of doing this in practice?
My initial thought was to use CRR ...
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0answers
29 views
Goodness of Calibration Test
are there some tests which are usually performed in order to ensure that a calibration procedure is sound? That is, say you have a model depending on N parameters and one tries to fit them in order to ...
