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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1answer
57 views

Heston stochastic model - Intuition, why a price of a call would involved complex numbers?

I am new to stochastic volatility and Heston model and I don't understand why would a price of a call option involve complex numbers. I can see technically why but I don't see the intuition. I was ...
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18 views

Heston volatility surface in Python QuantLib

Does anyone have experience with the Python QuantLib function HestonBlackVolSurface? I'm trying to produce a 3D plot of the volatility surface as done in the ...
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Deriving coupling equation(s) for Heston Stochastic Volatility Model

In Bergomi Smile Dynamics (2003) Section 2.1 we are given the following coupled equations for the mean and for the variance of the hedger's portfolio: $ \begin{align*} \frac{dm}{dt} + \mathcal{L}m - ...
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37 views

QuantLib (Python) Heston model delta

is it possible to obtain the delta for Heston model with QuantLib-python? I am using AnalyticHestonEngine and simple European option/payoff. I am aware of the possibility of calculating numerical ...
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1answer
61 views

How to project 1 Year ATM Implied volatility for SPX 500 1Year from now? Final goal is to calculate 1 Year Call prices on SPX 500 1 year from now?

I have the historical data for 1Year ATM Implied Volatility on SPX 500. I want to simulate the 1 year call option prices 1 year from now. What methods and approaches do I need to use? (Heston,GARCH, ...
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160 views

How can I prove that the solution to the Heston SDE is a Markov process?

Consider the Heston model expressed as \begin{align} dS_t &= \mu S_t dt + S_t \sqrt{V_t} \big(\rho dW_t^{(1)}+\sqrt{1-\rho^2}dW_t^{(2)} \big); \tag*{(1)} \\ dV_t &= \kappa(\theta - V_t)dt + \...
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87 views

Simulation of Heston process Quantlib-Python

I am wondering weather there exists some method such that one can simulate sample paths for the Heston model in Quantlib-Python. I am currently working on a project that require simulations with the ...
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57 views

Approximate Asian option price under Heston Model

I am looking to see if there is a formula or a derivation at least of an approximation of an Asian (Average Price) option under the heston model of stochastic volatility. Please advise
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2answers
63 views

Heston Model and antithetic variables

I was implementing some variance reduction techniques for the heston model and came up with a question when implementing the antithetic variable technique. Namely, I was not sure if I had to implement ...
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1answer
58 views

Does the Heston calibration have to be done on an arbitrage-free surface?

In a similar way to local volatility? I'm trying to calibrate a surface, but the results aren't convincing, so I was wondering if it was necessary to first use a way to regulate it (splines, ...
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38 views

Benchmarking of models

Why do we need benchmarking adjustmenets for a model? Suppose, a trading desk is using Heston model for generating vol surface, then why do risk management uses various other models like IR Mean ...
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61 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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75 views

How are Autocallables modelled?

What models are used to price autocallables ? Should we talk about Heston/SABR models which talking about this topic ? Any reference link is welcome.
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60 views

Heston model with jumps in both variance and underlying dynamic

How can I build on Matlab a Heston model using characteristic function adding jumps in both variance and underlying dynamic ? Suppose that the number of jumps is Poisson-distributed but the jump size ...
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1answer
127 views

Heston calibration using Quantlib and Python: failure in BlackVarianceSurface function

I have an error when trying to use the fucntion BlackVarianceSurface from quantlib. Can you help me? the error is RunTime Error: dates must be sorted unique. ...
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150 views

evaluation of option pricing models based on Greeks empirical hedging effectiveness

I’ve studied many different pricing models (B&S, Vasicek, CIR, Merton jump, Heston, ecc), each of them gives as output a different price and different values for the Greeks. So, for example, if ...
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1answer
124 views

Compute implied volatility surface of a put option from a call option

Suppose the function double bsCall(double S0, const double &K, double T, double r, double sigma) computes analytically the Black-Scholes price of a call option ...
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How do I, as a student, discover whether (new) papers consist of important contributions?

I am a master's student and have just started reading research papers regularly for the first time. I usually browse articles on arXiv. One of the main difficulties I've run into is figuring out ...
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Double Heston Model - Gauthier & Possamai prices

has anyone successfully implemented the Double Heston model based on Fabrice Rouah's "The Heston Model and its extensions"? I am finding that writing up the Matlab code from his chapter on the ...
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1answer
155 views

Example of complex structured products on FX market?

Lately I have been working a lot with the vol smile and different stochastic volatility models with FX forwards data. Now I want to work with pricing examples through simulations. Can you suggest some ...
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Simulating volatility process in the Heston model using the relation between the CIR Process and Ornstein–Uhlenbeck processes

I am trying to simulate the volatility process in the Heston model using the relation between the CIR Process and Ornstein–Uhlenbeck processes. In fact, giving $\mathbf{X}$ a $n$-dimensional vector ...
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1answer
121 views

Difference between modelValue from HestonModelHelper and NPV() from VanillaOption

I am trying to calibrate an Heston model and price vanilla option using Quantlib 1.15 and Python 2.7. I use the following code ...
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66 views

Sticky Delta Property - Heston Model

Given the model in the picture, how can you verify the sticky delta property without any computational methods? I was told that it is possible to deduce it just looking at the model but frankly i have ...
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76 views

What is the model behind Heston-Nandi functions in the fOptions R package?

I am dealing with Heston model in R and for this purpose I am using the package fOptions from RMetrics. The calibration formula requires the specification of some parameters (omega, lamda, alpha, ...
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What adjustments need to be made to Heston model to price futures options? [duplicate]

My understanding for the Black Scholes model is that a few adjustments need to be made so that the BS model can be used to price futures. Hence the Black-76 model. What adjustments, if any, do we ...
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196 views

Pricing in the Heston Model

The dynamics of the Heston Model is \begin{align*} \frac{dS}{S} & = \lambda \sqrt{\nu} d W^S \\[0.5em] d \nu & = k (1- \nu )dt + \epsilon \sqrt{\nu} dW^\sigma \end{align*} where $\lambda$...
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Negative theta in Log-linear stochastic volatility model

I was asked to simulate the following geometric Brownian motion to get paths for the SPX stock price. the process follows a Log-Linear stochastic volatility. $dS_t = \mu S_tdt+e^VS_tdW_1 $ where ...
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414 views

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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141 views

Quanto basket payoff

I have a payoff that is the worst of the returns two indices: S&P500 (SPX) and Euro Stoxx 50 (SX5E). $\pi = \min \left\{\left(\frac{\text{SPX}_\tau-\text{SPX}_0}{\text{SPX}_0}\right),\left(\frac{\...
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1answer
603 views

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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124 views

Zero-rebate barrier option pricing under the Heston model

I'm trying to derive an approximation for the zero-rebate barrier option under the Heston model: $$dS_t=\mu S_tdt+\sqrt{v_t}S_tdW^S_t$$ $$dv_t=\kappa(\bar{v}-v_t)dt+\eta\sqrt{v_t}dW^v_t,\quad d\langle ...
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411 views

How to determine the risk-neutral measure in a Heston model?

To clarify, I'm quite familiar with the risk-neutral pricing framework, and I know one can efficiently Monte-Carlo a Heston model via the non-central $\chi^2$ distribution approach. But so far we're ...
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1answer
184 views

Good references on Heston Model?

I am looking for good bibliographic references on Heston Model and Stochastic volatility models in general. Does anyone know any good introductory/intermediate references on this topic?
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ATM strike Heston model

I'm thinking about the heston model. price of the asset $S^1=(S_t^1)_{t \leq T}$ fullfills the differential equation $dS_t^1=S_t^1(\mu dt + \sqrt{V_t} dB_t^1)$ the stochastic volatility is given by ...
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164 views

Heston model computations

In the Heston model the dynamics of a single-asset $S$ are given by: $dS_t = rS_tdt+S_t \sqrt{V_t}dW^S$ where $W^s$ is a brownian-motion $W^S$ and the square root variance process $V$ is given by ...
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1answer
275 views

Options on realized volatility / variance

If I'd like to price options on variance/volatility in the Heston model. Is MC simulation and/or finite difference the only way to do it? Or is there an analytical expression for the probability ...
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1answer
468 views

Intuition for the Effect of Vol of Vol in Heston Model on Volatility Surface

I was hoping someone could describe the economic/mathematical intuition behind the effect that the vol of vol parameter has on the volatility surface, in particular the slope to maturity. Take for ...
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239 views

Forward implied vol vs Instantaneous vol

In the Discrete Stochastic Implied Volatility Model which is from the standard Heston Model, the model shows the evolution of forward implied volatilities with time. I thought forward implied ...
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105 views

Equivalent martingale measure in time changed Levy models

I am investigating time changed Levy models. As far as I have seen, these models are usually directly described under the risk neutral measure $\mathbb{Q}$. However, I'm interested in first modelling ...
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1answer
256 views

Hybrid Heston-Hull White Model

I am wondering if anyone could recommend a few good papers on hybrid heston-hull white models, in particular with respect to the approximation of model European options for calibration. Literature on ...
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98 views

Pricing a Path-Dependent Option with Heston

I want to price a path-dependent option (let's say for example an arithmetic average Asian option) under a Heston model. In a Black-Scholes setup, I use forward volatilities to do so. I want to apply ...
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1answer
165 views

How to do QE scheme for n correlated assets?

I'm trying to simulate correlated assets under Heston model. I coded the QE scheme for a single asset but i dont understand the next step: How should i set the correlation matrix given my n-asset ...
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482 views

Robust and free Heston pricing software

For a PhD research paper, I need to calibrate Heston. So far, I use Dale Roberts R-Code: https://github.com/daleroberts/heston/blob/master/heston.r for computing prices from which I invert IV ...
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56 views

Positive Heston model theta

Under the Heston model, is there a concrete example where the theta $\frac{\partial C}{\partial t}>0$ where $C$ is the price of a European call?
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184 views

Monte Carlo simulation error estimation

How does one estimate the error of a Monte Carlo simulation, for example, of the price of a European call under the Heston model with a given step size and number of paths?
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206 views

Multi-Asset Heston Model

How does one best define the correlation structure in a Multivariate Heston Setup? (i.e. Correlations between the Wiener processes of the Stocks / their Variance Processes)
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Calibrating Heston paremeters based on market data for Implied Vol for Call options

Several questions have been asked in here regarding calibration in Heston yet I have not found what I have been looking for, so I will ask: I am looking at a Heston model: $$dS_t=\lambda \sqrt{v_t}...
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1answer
375 views

Jim Gatheral's assertion on ATM implied volatility vs. square root variance

In Jim Gatheral's book The Volatility Surface Section Dependence on Skew and Curvature on page 138, he asserts that We know that the implied volatility of an at-the-money forward option in the ...
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1answer
336 views

Interpretation and intuition behind the Put-Call symmetry under the Heston Model

I am currently working on a report regarding the put-call symmetry relations under the Heston model. I did all the math and managed to prove the relations using PDE approach. However, I wish to have a ...
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243 views

Quasi Monte Carlo method and Heston model

I want to run a quasi monte carlo simulation for Heston model in matlab. Obviously there exists a lot of literature regarding the theoretical aspects of the topic, for example by Baldeaux and Roberts, ...