The tag has no usage guidance.

learn more… | top users | synonyms

9
votes
2answers
5k views

How to calibrate Hull-White from zero curve?

I am interested in calibrating a Hull-White model to the market. I do not, however, have data on anything except the market zero curves, as all derivatives are being traded OTC. My plan is to ...
9
votes
1answer
1k views

How to 'calibrate' simple pricing models for equity index options and equity options?

I am interested in doing some research on plain vanilla equity options and equity index options. I have historical data for these options. I also happen to have market maker 'fair price' (bid and ask) ...
7
votes
3answers
971 views

Option Pricing Model Calibration In Practice

I'm curious how an option pricing model like the Heston model is calibrated in practice. Here's how I imagine it happens: Let's say I have access to the most recent option prices on a given stock ...
7
votes
1answer
395 views

How do you calibrate a poisson arrival rate process?

Many papers in the microstructure literature assume an order arrival rate of the form $\lambda^a(\delta) = \lambda^b(\delta) = Ae^{-k\delta}$ That is, an order that's placed $\delta$ away from the ...
7
votes
1answer
411 views

How does one estimate theta in the Ho-Lee model from a yield curve?

I have a yield curve constructed using linear interpolation with data points every 3-months for US treasuries. I would like to use that calibrate a Ho-Lee model, but I can't wrap my head around how ...
7
votes
1answer
241 views

Are there “live” uses of the Generalized Method of Moments or are they all academic?

I see the Generalized Method of Moments suggested in numerous academic papers as a way to calibrate stochastic volatility models. However, any decent trading shop is going to calibrate to observable ...
6
votes
1answer
73 views

Calibration of nested pricing models consistently on two different classes of derivatives

Hi everyone, I'm programming in MATLAB and I have the following optimization problem in calibrating several nested specifications of pricing models. Summary: I have two pricing models ($1$ and $2$, $...
6
votes
3answers
367 views

What is an acceptable error on implied volatility?

Given an implied volatility surface (on equity indexes) and a calibrated model, what is the range of error on implied volatility a trader would accept ? This obviously depends on the model used to ...
5
votes
1answer
206 views

Model calibration to illiquid assets when pricing options with long maturities

Let us assume one is interested in pricing an option with a very long maturity (up to 20 or 30 years) on a liquid underlying. The market won't have liquid quotes for the higher maturities. Still you ...
5
votes
2answers
482 views

How to calibrate a volatility surface using SVI

I've read the following paper by Gatheral and Jacquier and have several question regarding the calibration of a volatility surface in a arbitrage free way and some theoretical aspects. Let me first ...
5
votes
1answer
189 views

Calibration Merton Jump-Diffusion

Consider the following SDE $dV_t = rV_tdt +\sigma V_t dW_t + dJ_t$ where $J_t$ is a Compound poisson process with log-Normal jump size $Y_i$. How am I supposed to calibrate this model to CDS spreads?...
4
votes
4answers
1k views

Other means of calibrating Heston models

I understand that the simplest way of calibrating a Heston model for volatility surface is to use Monte-Carlo to simulate the vol and stock price trajectories and then use the observed price to do a ...
4
votes
1answer
149 views

Libor Market Model Calibration

Currently I am doing a research on the plain vanilla multi-curve framework Libor Market Model meaning that no stochastic volatility is involved. I had the idea to calibrate to the swaption market. In ...
4
votes
1answer
181 views

Parameter estimation using martingale measures - include real world data?

Please note: I posted this in nuclearphynance first, but didn't get any replies. For desks which sell exotics it is common practice (as far as I know it) to calibrate the model (Stochastic Volatility,...
4
votes
1answer
504 views

Calibrating Hull-White using volatility data

I would like to calibrate Hull-White model using volatility data.I am using [Park (2004)] paper as a reference. He suggests to minimize the following objective function: where the first term is ...
3
votes
1answer
79 views

Calibration of Heston model

I would like to calibrate the Heston model and I am wondering which are the most common approaches used in the literature. Any suggestions (references from the main stream literature, notes or ...
3
votes
1answer
59 views

Numerical Optimizer Matlab Calibration LMM

I am trying to mimimize the following function in order to calibrate the Libor Market Model $$\sum_{i=1}^{n} \left(\sigma_i^{market}-\sigma_i^{Reb}\left(a,b,c,d,\beta\right)/\sqrt{T_i}\right)^2,$$ ...
3
votes
1answer
337 views

Stress Testing Methods

I'm working on the following task: Given quarterly data: a time series representing the 1-year realized (10 years of data) rates of default on a portfolio of mortgages a slew of ...
3
votes
1answer
299 views

Which approach is better for modeling option exercise strategies, rational or behavioral?

This question is most relevant to the evaluation of embedded options, such as the refinancing option granted to borrowers in the mortgage and bank loan markets, or the call option present in some ...
3
votes
2answers
172 views

Interpretation of Drift

Consider the common model of stock prices given by a geometric Brownian motion (GBM), which follows the SDE $$ dS(t) = \mu S(t) dt + \sigma S(t) dW(t). $$ Below is a plot of a simulation of such a ...
3
votes
2answers
195 views

How to get around flat likelihood function when calibrating GBM parameters?

I want to calibrate jointly the drift mu and volatility sigma of a geometric brownian motion, $$\log(S_t) = \log(S_{t-1}) + (\mu - 0.5*\sigma^2) \Delta t + \sigma*\sqrt{\Delta t}*Z_t$$ where $Z_t$ ...
3
votes
1answer
53 views

Calibration of 1F Hull White short-rate model to market data

I want to calibrate the Hull White 1 factor short rate model to market data. The main purpose is to simulate interest rate paths, which I will use to calculate the net pv of banking liabilities. Some ...
3
votes
1answer
83 views

Estimating $\mu$ - only increasing $T$ improves estimate?

Assuming an asset price $S$ follows a geometric Brownian motion (GBM), the log returns $R$ are distributed as $$ R_i := \log\left(\frac{S_i}{S_{i-1}}\right) \sim \mathcal{N}\left(\left(\mu - \frac{\...
3
votes
0answers
52 views

Calibration of Merton's jump diffusion model

Setting In my financial engineering project I'm working on a new calibration formalism for jump-diffusion models and in particular Merton's jump diffusion model. A jump diffusion process $\{X(t), t \...
2
votes
3answers
475 views

How to estimate parameters of geometric brownian motion with time-varying mean?

Does anyone know how to estimate $A$, $\sigma_1$,$\sigma_2$ from the following system? $$dx = \mu_t x dt + \sigma_1 x dB_x$$ $$d\mu = A(\bar\mu - \mu) dt + \sigma_2 dB_\mu$$ Variation in $x$ could ...
2
votes
3answers
613 views

Calibration of a GBM - what should dt be?

I have a time series of daily data that I want to calibrate GBM parameters $\mu$ and $\sigma$ to. Using the discretized solution $$ S_{t_{i+1}} = S_{t_i}\exp\left(\left(\mu - \frac{\sigma^2}{2}\...
2
votes
2answers
122 views

Is there any template of hull white one-factor calibration model?

Recently I would like to look for excel template of hull white one-factor calibration model using swaption data for my urgent task? However, it seems that I cannot find suitable one in the web. ...
2
votes
2answers
708 views

Local volatility SVI parametrization

In this paper Gatheral presents the following parametrization of the implied total variance $w(k,T) = \sigma_{BS}(k,T)^2T$ for each slice $k \mapsto w(k,T)$: $$ w(k) = a + b\{\rho (k-m) + \sqrt{(k-m)^...
2
votes
1answer
418 views

Commonly used vol surface calibration model in the industry

I have 2 questions: What is the most commonly used equity option pricing model? I learned jump diffusion at school, read about Hensen and a few other models online. I am actually only calibrating ...
2
votes
1answer
215 views

LMM. Calibration to swaptions by Brigo and Morini. Volatility of swaption that matures at T=0

I'm reading Brigo D., Mercurio F. Interest Rate Models - Theory and Practice (Springer, 2006)(ISBN 3540221492) and also a source article on LMM cascade calibration to swaptions by Brigo and Morini. I ...
2
votes
0answers
35 views

Volatility Parametrization Libor Market Model - Underspecified Model?

Does the volatility parametrization that I have chosen give an underspecified model? Which volatility parametrization in the Libor Market Model would suit the best for the particular case described ...
2
votes
0answers
90 views

How to calibrate volatility surface for Interest Rate Cap&Floor pricing

I'm using Black model to do interest rate Cap & Floor pricing. The volatility is determined by using the bootstrapping methodology. However, afterwards, how should I do the calibration, or ...
2
votes
0answers
103 views

Calibration of Heston version of CIR

I'd like to calibrate a variant of Heston model for interest rates which is describe by this couple of SDE \begin{aligned}dr_t&=a(b-r_t)+\sqrt{r_t}\sigma_t dW_t^1 \\ d\sigma_t&=k(\theta-\...
2
votes
0answers
137 views

Calibration of Hull White One factor model in F.C.Park paper

I want to ask a question with reference to a paper from below link http://www.cmpr.co.kr/asset/research_material/implementing_interest_rate_models.pdf Minimization specified in Page 14: Mean ...
2
votes
0answers
71 views

How to compare market values with model values after calibration?

After calibration the G2++ model for interest (with swaption volatilities), I want to statistically test the quality of the calibration by comparing market to model values. What is the best way to ...
2
votes
0answers
106 views

Do some option pricing models allow for misspecification and what does it mean?

This is to some extent a theoretical question and maybe we can work together to produce some input and output. Diverse option pricing models are reported to be misspecified in various studies. One ...
2
votes
0answers
198 views

Dual curves and short rate calibration

When I calibrate a short rate model to market swaption vols, what curve am I getting when I plug in the calibrated parameters into the analytical formulae (assuming they exist for the model I'm ...
1
vote
3answers
317 views

Implied Vol vs. Calibrated Vol

Consider the Black-Scholes model, in which the log stock return over a time period $\Delta t$ is given by $$ \log(S_{i+1}/S_i) = (\mu - \sigma^2/2)\Delta t + \sigma \sqrt{\Delta t} Z_i, \qquad Z_i \...
1
vote
1answer
134 views

Calibration of non-mean-reverting OU process

I'm looking for some reference on how to calibrate a non-mean-reverting Ornstein-Uhlenbeck process to historical data using MLE or OLS. The model has the following SDE: $d\lambda(t)=a\lambda(t)dt+\...
1
vote
1answer
369 views

Good Model Calibration Books/Papers for Common Option Pricing Models

I am trying to find a good book which focuses on the model calibration. I just want to know generally, what are the most common methods of model calibration(such as Black-Scholes Model, Stochastic ...
1
vote
1answer
48 views

About the Feller Condition in Heston Calibration

I have noticed when reading (many) articles about Heston Calibration that not all (few actually) do care about the Feller condition. Below is a compilation of calibration results from some different ...
1
vote
1answer
40 views

SVI calibration, why fit to option prices and not implied volatilities

Bear with me. Related (very good) question: How to calibrate a volatility surface using SVI From this paper http://arxiv.org/pdf/1204.0646.pdf, page 21. Why does the recipe suggest fitting to option ...
1
vote
1answer
484 views

How to calibrate the Hull-White model using cap prices?

I'm given cap prices and swap rates, and i'm trying to calibrate the Hull-White model to them. I then want to use the model in order to price a swaption. I know that the model can be calibrated from ...
1
vote
0answers
17 views

Calibrating and simulating returns from a t-distribution

A slight twist (I hope) on the familiar problem of simulating log returns from a t distribution. My two questions concern calibration to sample data. First, one can infer the degrees of freedom in the ...
1
vote
0answers
176 views

Historical calibration of Hull-White model

I have a question concerning 1-factor Hull-White model. For my master project I need to calibrate it to compute Counterparty credit risk metrics. I know that the model might be calibrated either for ...
1
vote
0answers
75 views

Initial values for Heston Model calibration

I'm doing a Heston model in Matlab using simple Monte Carlo simulations (5.000 paths and 2 steps per day, simulating 360 days). When I try to calibrate the Heston parameters using fminsearch it takes ...
1
vote
0answers
107 views

Markov switching model estimation

We are testing Markov switching models to forecast risk regimes, similar to the paper by Kritzman, Page and Turkington. We find that in some cases the Baum-Welch algorithm converges very slowly or not ...
1
vote
0answers
122 views

What to do with linear regression or regression splines outside of the training range?

This is a cross-post from here In my question on a load forecast model using temperature data as covariates I was advised to use regression splines. This really seems to be a/the solution. Now I ...
1
vote
0answers
59 views

Should portfolio be optimized by marking to the future than marking to market (excluding currencies)?

Observing the negative interest bonds in Switzerland, Denmark, GErmany the value of higher presently (credit-free) outgoing cash flows seems less important than the value of lower future (credit-free) ...
0
votes
0answers
28 views

Calibration of Dothan Model to Yields

For both the Vasicek and CIR model the yields $R(t,T)$ and short rates $r_t$ have an affine relationship: $$ R(t,T) = \frac{B(t,T)r_t - A(t,T)}{T-t}, $$ where $A(t,T)$ and $B(t,T)$ are determined by ...