Questions tagged [calibration]

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Calibration period

I want to calibrate some model to market data. This could fx be Bates, Kou, Black-Scholes, etc. So, for each model we have a set of parameters which need to be estimated through calibration. Now, my ...
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Initial forward variance curve calibration

Let $V_t^{T_1, T_2}$ be the forward variance swap rate for the period $[T_1, T_2]$, seen from $t$ (see for instance Lorenzo Bergomi's Smile Dynamics II) and let $\xi_t^T = V_t^{T,T} = \frac{\partial}{\...
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How does one calibrate a Vasicek model to actual cap prices?

I am trying to calibrate a Vasicek model given by $$ dr(t) = k[\theta - r(t)] dt + \sigma dW(t), \quad r(0) = r_0 $$ where $k, \theta, \sigma, r_0 > 0$. I am using the book by Brigo and ...
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Put-Call parity with dividends (OTM options) [closed]

The put-call parity with dividends is given as $$ C + K\mathrm{e}^{-r \cdot T} + D\mathrm{e}^{-r \cdot t} = P + S_{0}, $$ where $t$ denotes the time between now and when the dividend is paid, i.e, $t \...
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3 votes
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Useful methods to avoid degenerate calibration? (Heston model in my case)

I have implemented a Levenberg-Marquardt(LM) based method to calibrate the Heston model against market data by minimizing a weighted $L^2$-norm of differences of market vs model prices. Pretty ...
1 vote
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Implied volatility from local volatility versus market implied volatility

Does the local volatility flattens the (existing not forward) skew faster than what we observed in the implied volatility surface? The process is: Get market implied volatilities Fit a IV model (i.e. ...
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1 vote
1 answer
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A better calibration method available?

i'm facing a new and interesting task: We are calculating a time series of (hypothetical) behavioral portfolios, for which i need a few parameters to calculate the portfolio's weights in each asset. I'...
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Double exponential parametrization of a correlation matrix

I'm implementing a LIBOR Market Model with stochastic volatility following this book and ran into a problem trying to parametrize the forward-forward and volatility-volatility correlation matrices ...
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9 votes
1 answer
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The Holy Grail of Volatility Modelling: The SPX & VIX - Why?

I am currently researching a pre-print article by Julien Guyon & Jordan Lekeufack (2022): Volatility Is (Mostly) Path-Dependent. Their model is quite impressive in both its simplicity, as well as ...
3 votes
1 answer
120 views

Sabr Calibration not fitting the market volatility

I am trying to calibrate SABR but I do not fit the given volatility. ...
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0 votes
0 answers
50 views

Probability of touching barrier and stochastic interest rates

I am trying to figure out the impact of the stochastic interest rates on the price of barrier option. I was reading the book "FX Barrier Options" by Zareer Dadachanji and in the section ...
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1 vote
2 answers
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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 ...
2 votes
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Best way to extrapolate on implied volatility

I am doing some standard svd calibration to mark market implied vols in difference to a previous volatility surface. For longer term maturities where there is no market data, I am extrapolating ATM ...
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76 views

Estimating market price of interest rate risk under CIR model

My goal is to find the market price of risk associated with the interest rate under the CIR model whose stochastic differential equation under the physical measure is given: \begin{eqnarray}\label{...
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2 votes
3 answers
357 views

Calibrate the SABR model to the implied volatility surface

I'm currently trying to calibrate the SABR model. The question I have is that when I consider papers and other websites I only come across cases where the SABR parameters are calibrated to the implied ...
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1 vote
1 answer
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Pricing caps/floors on backward-looking USD SOFR with forward-looking LIBOR model

The payoff of a cap/floor is calculated as a payoff of constitutient caplets/floorlets. The SABR volatility model has the implied volatility approximations of Hagan et al. $$\sigma^f_{IV}\approx \...
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3 votes
1 answer
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Calibration of a volatility smile model on a partial smile

I'm using a well-known SABR model in order to build an implied volatility surface of caps/floors on a very illiquid market which is entirely missing OTM quotes. What happens to SABR implied smile/...
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Italy Zero Coupon Yields

I am looking for historical data for Treasury bills and bond yields for Italy on a monthly or daily basis. Where can I get this data?
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Calibrating Heston model using implied volatilities

I'm trying to understand how the authers of a paper calibrated their model. We got data on European type options on the S&P500-index period from early 2005 to mid-2009. We have daily data on ...
1 vote
1 answer
159 views

Statistical metric to measure how well does the volatility surface fit the market

Suppose that I have a model for implied volatility surface and want to figure out required recalibration frequency based on historical quotes. Since I have a large range of strikes and tenors over a ...
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1 answer
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Double Heston model calibration in Christoffersen's paper uses 52 sets of market data (each set as of a different date). Why?

In the paper on Double Heston model (2009) from Peter Christoffersen, they say: "Our focus is on explaining why a two-factor model works better than a one-factor model for the purpose of option ...
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Why would one need forward prices to perform derivatives pricing?

I am trying to understand the purpose of inputs the software of my company is using. Amongst others it needs calibration instruments, a model type, initial values of the respective underylings and a ...
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Why calibrate vol based on consensus?

I am starting to work on building vol surfaces using implied vols on the short run mixed up with consensus vols ran through a whole bunch of interpolation/calibration/smoothing process. Although I ...
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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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1 vote
1 answer
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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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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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1 answer
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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 ...
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1 vote
1 answer
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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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1 vote
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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+\...
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1 vote
1 answer
133 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 ...
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4 votes
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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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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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1 vote
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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 ...
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1 vote
1 answer
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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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1 answer
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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 ...
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2 votes
1 answer
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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 ...
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1 vote
1 answer
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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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1 vote
1 answer
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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\...
1 vote
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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 ...
1 vote
2 answers
591 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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2 answers
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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 ...
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2 answers
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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, $$\...
4 votes
1 answer
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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 votes
1 answer
854 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 ...
1 vote
0 answers
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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 ...
1 vote
0 answers
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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 ...
1 vote
0 answers
349 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 ...
1 vote
0 answers
307 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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1 answer
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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 ...
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1 answer
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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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