Questions tagged [calibration]

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62 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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159 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 &...
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53 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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73 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
113 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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35 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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88 views

Are Levy models useless after the financial crisis of 2008?

I calibrated (by minimizing RMSE) the Black Scholes, VG and CGMY models to data from 2005 (before the crisis) and to data from 2020. The results surprised me. I do not understand why for data from ...
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41 views

Carr and Madan algorithm to avoid arbitrage in oprion prices

Hey in this text (https://arxiv.org/abs/1107.1834) in section 7 is described an algorithm which can delete options which generate an arbitrage. $C_ij$ is call option price with strike $K_i$ and ...
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39 views

How to prepare data for calibration

I want to calibrate different models by minimizing RMSE. When I use data from Schoutens (2003) everything is OK i.e I get reasonable parameters. The problem appears when I try to calibrate models to ...
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15 views

Call options data from 18 April 2002 (Schoutens 2003)

Hey I would like to calibrate different models to call options prices from 18 April 2002. Schoutens used this data for calibration but unfortunately he write only months (screen). What can i do in ...
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30 views

Regularized model Calibration - Penalty term

Hey I want to calibrate model by minimizing $$\arg \min_{\theta}\frac{1}{n}\sum(\text{market price}-\text{model price}(\theta))^2$$ where $n$ is the number of options. This is ill-posed problem and I ...
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1answer
84 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 ...
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2answers
157 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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54 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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28 views

Kou model calibration

Hey I want to calibrate Kou model (with 5 parameters to estimate). I am using the brute and fmin functions in Python. In the Black Scholes model, the calibration took literally a few seconds (only one ...
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43 views

Calibration of the Ho Lee model in Excel only based on historical treasury rates (3 months)

I would like to calibrate the Ho Lee model $dr_t=θ_tdt+σdW_t$ with $θ(t)= F_t(0,t)+σ^2$ in Excel based on a time series of 3-month treasury rates and then compare the real time series with that ...
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72 views

Calibration and comparison of the Vasicek model and Ho-Lee model

I would like to calibrate the Hoo-Lee model and the Vasicek model to a historical interest rate series and compare the interest rate development of both models with the historical interest rate series....
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1answer
35 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 ...
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1answer
112 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 ...
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1answer
71 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.
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48 views

Black Scholes model calibration

the only parameter in the Black Scholes model that needs to be estimated is the volatility. Which approach is correct: Estimation of volatility from daily log returns Estimating volatility by ...
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15 views

website for downloading data for model calibrating [duplicate]

I'm looking for a website from which I could download data to calibrate the model to evaluate options. I've heard that quandl is free for non-commercial use, but I've heard of Yahoo finance too. Which ...
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1answer
91 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 ...
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1answer
76 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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74 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 ...
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0answers
29 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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41 views

calibration of correlation in vasicek model

how can I calibrate the correlation by numerical integration of the normal bivariate distribution assuming that the standardized asset returns of two firms are described by the single-factor Vasicek ...
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17 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 ...
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2answers
484 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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113 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? ...
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1answer
90 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 ...
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1answer
201 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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24 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 ...
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65 views

Calibration of G2++ two factor interest rate model using Kalman filtering

I'm trying to use the Kalman filter to calibrate a G2++ interest rate model in R. I'm reading "Implementing interest rate models: A practical guide" by Park F.C. (2004) where he provides details on ...
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1answer
75 views

CEV Model Primer

Could someone please point out to a good primer on CEV model? I am trying to get a basic grasp of the model: The dynamics, advantages & disadvantages, for which payoff it is usually used (Hybrid ...
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1answer
136 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 ...
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128 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 ...
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0answers
273 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 ...
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1answer
313 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 ...
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1answer
109 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-...
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1answer
151 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, ...
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1answer
290 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 ...
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1answer
173 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 ...
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1answer
594 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 ...
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1answer
61 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 ...
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49 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 ...
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66 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 ...
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1answer
188 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 ...
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1answer
112 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: $$...
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256 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) ...