Questions tagged [heston]
A type of stochastic volatility model developed by associate finance professor Steven Heston in 1993 for analyzing bond and currency options. The Heston model is a closed-form solution for pricing options that seeks to overcome the shortcomings in the Black-Scholes option pricing model related to return skewness and strike-price bias.
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Heston++ with QuantLib
Is it possible to implement in QuantLib the Heston++, hence, the Heston with a displacement factor? Thanks!
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Parameters bounds for Heston model calibration
Still working on my master thesis and I have a question I have been looking at for some time but can't find a good reason.
I am looking to follow the steps of Horvath et al. (2019) in order to ...
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Heston Model Sensitivity Qualitative Property
Consider the following Heston model:
$$\begin{aligned}
\mathrm{d}S_t&=rS_t\mathrm{d}t+\sqrt{v_t}S_t\mathrm{d}B_{1,t}\\
\mathrm{d}v_t&=-\kappa(v_t-\bar{v})\mathrm{d}t+\sigma_v\sqrt{v_t}\mathrm{...
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Forward variance in rough heston model
When calibrating or trying to approximate the rough heston model by a neural network, why is it done according to the hurst parameter, the correlation, the volatility of volatility and the forward ...
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Independence of log-returns under Heston model
I first precise that I am new to QuantSE.
Heston is a widely used moodel but I have some doubts on it and I couldn't find a proper answer on the internet.
How can we prove that Heston in not and ...
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Areas of research in calibration of stochastic volatility models
I am working on a thesis in deep calibration of the Heston model, and I wanted to include a section on the historical work, before the use of neural networks in this area.
Thus, I was wondering what ...
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Deep calibration in the Heston Model
I am doing my master thesis on deep calibration in the Heston Model, and after reading a few academic paper (eg. Horvath et al. 2019) on the subject I understand pretty well the procedure and the ...
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How calculate expectation and variation of stochastic integral Based on Heston model?
I was calculated Heston volatility model. But I think it is wrong.
$dS_t = \mu dt + \sqrt V_t dW_t^s$
$dV_t = k(\theta - V_t)dt + \sigma \sqrt V_t dW_t^v$.
$dW^s_t dW^v_t = \rho dt$
take integral to ...
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Volatility surface
When fitting/calibrating a option model like heston to option data, what are some useful data handling to do?
The basic thing is to remove all options with no trade/volume, but how many maturities ...
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Master Thesis about Heston vs. Duan option pricing model
I would like to write my master's thesis on volatility in option pricing. My idea was to compare the stochastic volatility model of Heston 1993 with the GARCH option pricing model of Duan 1995. For ...
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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 ...
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Vol Smile Call/Put Wing calibration
Is call/put wing volatility smile calibration approach used in practice? To calibrate an index (SPY) using only more liquid OTM calls/puts, to kind of use an "if" condition on K to S0 to ...
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In the Stochastic-Local Volatility (SLV/LSV) calibration procedure, which surface is used when calibrating the Leverage function
Before we match the leverage function $L(S_t,t)$ to the implied volatility surface generated from the market, we are supposed to calibrate the pure Heston parameters, $(\theta, \kappa, v_0, \rho, \xi)$...
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Gatheral pseudo-probabilities inverse Fourier transform
Im having some trouble with the discussion about the pseudo-probabilities in Gatheral's book. In chapter 2, it reads
Taking the inverse transform using equation (2.8) and performing the complex ...
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Monte Carlo simulation for OTM options under stochastic volatility
I'm looking to simulate the stochastic price and volatility process (Heston model) using some form of Euler method for Monte Carlo approximation of option prices. The results that I get are acceptable ...
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Heston model characteristic function
The characteristic function of $x=ln(S_T)$ in the framework of Heston model is guessed to be: $$f_j(\phi,x,v)=e^{C_j(\tau,\phi)+D_j(\tau,\phi)+i\phi x}$$
The call price is guessed to have the form: $$...
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Cleaning data before fitting the Heston SVM
This is more of a generic question regarding data cleaning. I have implemented the Heston SVM, and I am attempting to fit it to some historical option data. With simple cleaning of the implied ...
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Finite difference method for the Heston model using the ADI scheme
I am trying to implement the ADI FDM scheme for the heston and I am following The Heston Model and Its Extensions in Matlab and C#. They have the scheme:
$$U'(t) = \textbf{L}U(t),$$
$$\textbf{L} = A_0 ...
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Feller Condition in the Heston Model
I understand that for MC simulations we require the Feller Condition otherwise the simulation becomes unstable when approximating the events when $v_t<0$, but for semi-analytical solution and using ...
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Wrt speed, how optimised is QuantLib's Heston pricing class?
I have a pricing formula that is 300x the speed of the QuantLib's Heston pricing class. Is it incredibly slow?
For context, on a slow 1.6 GHz Dual-Core Intel Core i5 processor, my method can reliably ...
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Calibrating the Heston with the Levenberg-Marquardt algorithm
I am trying to implement the Levenberg-Marquardt algorithm similarly to Cui et al. Full and fast calibration of the Heston stochastic volatility model, 2017 here (although using a different method to ...
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Efficient Method of Moments(EMM) for Stochastic volatility model
We are attempting to calibrate the parameters of the Heston model via EMM on historical stock price returns. However, we are first trying a simple stochastic volatility model using EMM.
We have come ...
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Calibration of $\rho$ in the heston model
When calibrating the Heston model, the gradient of the price of the call/cost function wrt $\rho$ (correlation between $S$ and $V$), is a lot less than the other parameters like $v_0$ and $\bar{v}$. ...
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Heston Calibration - how far OTM can an option be before it's not considered ATM anymore?
I have been doing reading and supposedly implied volatility of ATM options with 1-2 week expiries are reasonable vols to use as your $V_0$ when calibrating a Heston model.
Firstly, why would it be ...
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COS method for Wishart Heston Model
NOTE: This code is a piece of code I am using for a master's thesis, so I do not expect someone to do the work for me, but I gladly accept suggestions of any kind.
However, I am trying to get the ...
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Heston model using YUIMA package
I am trying to estimate a Heston model using the Yuima package, but i am in trouble.
This is my script:
...
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Reference request about stochastic volatility model
I'm fiddling with estimation of stochastic volatility models and have build up a somewhat flexible framework using indirect inference.
I would like to try and throw a lot of different continuous ...
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Characteristic Function for Wishart Heston Model
I don't know if this is the right place (at most they will close the post). Anyway, I am trying to implement the characteristic function of the Heston Wishart Stochastic Volatility model illustrated ...
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Calibration of Heston using implied vol as $v_0$
I am looking at the difference if you calibrated the heston from market data using objective function minimisation.
In scenario 1, I calibrate all the parameters from market data
In scenario 2, I ...
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Can Heston volatility model be used to calculate VaR or CVaR?
I'm just a beginner and third-year statistics major student. Based on what I read in some journal, most common model that used to calculate VaR or CVAR is GARCH. Is there any possibility that I can ...
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Implied volatility of Below intrinsic value Heston prices for deep calibraiton
I am trying to generate implied volatility surfaces for European call in the Heston model. I get below intrinsic values for deep ITM, so about 2% of my surface has below intrinsic prices, which doesn'...
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How to modify the Heston Model such that we can modify the wings of the volatility surface?
In Heston model, if my intuition is correct, increase in sigma (volatility of volatility parameter) would increase the kurtosis and correlation factor between returns and volatility dictates the skew ...
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Neural Network to learn Heston Model parameters
I am trying to solve this question:
Write down pseudocode to learn a local stochastic volatility for finitely many
given option prices: assume a Heston stochastic variance and parametrize
local ...
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Typical values Heston parameters for FX options
I am not as familiar with FX options as I am with equity index options.
For the purposes of numerical testing/experiments I'd appreciate if somebody could tell me what are typical parameter values for ...
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Complex Integral in Rouah's Heston book
I have a silly question regarding complex calculus, in which I'm a bit rusty at the moment. In F. Rouah's book The Heston Model and Its Extensions in Matlab and C# the following appears:
Now evaluate ...
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Feller Condition (Cox-Ingersoll-Ross) source
For the Cox-Ingersoll-Ross model $$\text{d}r_t = a(b-r_t)\text{d}t+\sigma\sqrt{r_t}\text{d}W_t$$ the condition (referred to as "Feller condition") $$2ab\geq\sigma^2$$ ensures that the solution is ...
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Time Dependent Heston model yields a runtime error in Quantlib (Python)
I am trying to fit a time dependent Heston model using Quantlib Python. I'm getting the following runtime error: Boost assertion failed : px !=0.
Can somebody help in this or is there an example of ...
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The little Heston Trap in DPS representation
I was wondering if the representation by Duffie, Pan, and Singleton (2000) is already accounting for the little Heston trap. DPS represent their 'general' discounted characteristic function as:
$$
\...
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Heston Riccati equation
Let
$$
\begin{align*}
dY_{t} &= \left(r - \frac{1}{2} V_{t}\right) dt + \sqrt{V_{t}}dW_{t}\\
dV_{t} &= \kappa(\theta - V_{t}) dt + \rho \sigma \sqrt{V_{t}}dW_{t} + \sigma\sqrt{1-\rho^{2}}\sqrt{...
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Piecewise constant Heston model Monte Carlo simulation
I am studying this time dependent Heston model
\begin{equation}
dS_t=(r-q) dt +\sqrt{V_t} dW_t^1 \\
dV_t=\kappa_t(\theta_t-V_t) dt + \sigma_t dW_t^2 \\
S_0=s_0\\
V_0=v_0\\
...
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Why fitting $\mathbb{Q}$ vs $\mathbb{P}$ measure Heston model if both fit to market
If both models fit their closed form formulas to market prices, why should I prefer a more complex model? ($\mathbb{Q}$ version has one extra parameter $\lambda$)
Do valuation with dynamics work ...
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Heston Process: Accept-Reject Sampling to Alleviate the Problem of Negative Variances
I've read even in recent papers, and on page 21 of the book "The Volatility Surface" by Jim Gatheral (2006), all the debate over whether to reflect or truncate negative variances whilst ...
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Heston formulae and characteristic function for FX options (or dividend paying yield)
I've seen the formulae for Call valuation with the Heston model for non-dividend paying Stocks.
How should I modify it to use it in an FX pair (which has two risk free rates: local currancy rate $r$ ...
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How to compute Vega in the Heston Model
I am computing European Option Sensitivity as: Delta, Vega and Gamma. I am using Heston Model to simulation spot and the variance.
While computing Delta and Gamma, I understand, we need to bump spot ...
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Vega in the Heston model
I'm trying to calculate the hedging quantities of the Heston model. I undestand that the replicating portfolio consist of one option, $V = V(S,v,t)$, $\Delta$ stocks and $\phi$ units of the option to ...
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Stochastic volatility with jumps [closed]
I'm reading the Duffie, Pan, and Singleton (2000) paper now and I've stumbled upon something that seems to me as an inconsistency. Whenever I look up the SVJJ model, I see that its log-transform is ...
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I can not calibrate Heston model
This is a code that I have used to calibrate Heston model. the following code describe the optimization algorithms used (genetic algorithm plus interior method)
...
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Most accurate Fourier transform method for extreme OTM options
I need to calculate vanilla options prices for extreme moneyness range of e.g. (0%,1000%) under the Heston model for various parameter values that satisfy Feller.
Which Fourier method (or other method)...
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Filtering SDE for Heston Volatility
Consider a GBM model with Heston volatility:
$$dS_t = \mu S_t dt + \sqrt{V_t} S_t dB_t^1$$
$$dV_t = \kappa(\theta-V_t)dt+\xi \sqrt{V_t}dB_t^2,$$
where $(B_t^1, B_t^2)$ is a correlated BM. Let
$$\...
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Using QuantLib Python to value FX options using stochastic volatility
I would like to use QuantLib (and in particular the python wrapper) to value FX option using the Heston model. Thanks to http://gouthamanbalaraman.com and all of the articles therein : in particular ...
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