# Questions tagged [stochastic-volatility]

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### Heston model - Andersen scheme implementation

I would like to implement Andersen scheme for Heston simulation. On the following snipped is my code for generating asset path: ...
2k views

### Why is there a stong intraday-correlation between spot and vol?

Fig.1 shows an intraday scatterplot of the DAX future against its volatility index VDAX on 6-Jan-2016. The data suggest a strong negative correlation between the two. There are various models ...
103 views

### Motivation: Stochastic Interest rate model

what is a reason that someone might be interested in a stochastic-interest model such as the Chen model? Also can you provide me with a link to an easy to read motivational paper/part of a paper on ...
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### Why Jumps in Option Pricing models?

The Bates model adds a Jump process to the Underlying. I understand this may represent observed time series more realistically, but why would one care about this in option pricing? The option price ...
1k views

### Calculating 6-minute, 20-minute, 45-minute, and 3-hour volatility

I am looking to measure the volatility from the open of the market until a trade takes place and use that volatility in post-trade regressions to help explain transaction costs. A simple regression ...
3k views

### Option prices in Bates SVJ model?

In this [post] discussed the European put and call price formulas under the Heston Stochastic Volatility model. There exists an important extension of Heston model to include diffusion jumps, known ...
2k views

### Numerical example of how to calculate local vol surface from IV surface

I'm looking for an excel example (not a copy of Dupire's eqn) of how to convert an IV surface to a local vol surface. If unsuccessful I'll work through Dupire's eqn but would be helpful to look at an ...
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### Where to find pricing formulas for affine stochastic volatility jump-diffusion models?

Does anyone know a reference where I can find the pricing formulas for vanilla calls in the affine stochastic volatility jump diffusion class of models such as SVJ and SVJJ? I am looking for ...
422 views

### Validation of Bates SVJ model

I have just finished implementing the Bates model for pricing European call options. To check results, I have been looking for a validation set where I could see the Bates parameter values and ...
283 views

### Transition densities in the Heston model

Knowing the Characteristic function $\Phi_{T,t} = \mathbb{E} [ e^{i u S_T} | S_t, V_t]$ (or equivalently, the Laplace transform) of an affine process, it's possible to know the distribution of the ...
1k views

### Garch for covariance matrix?

I have seen plenty of literature about GARCH on estimation volatility. how about covariance? There are plenty of risk models depending on the covariance matrix. I guess we can assume the correlation ...
2k views

### using garch to forecast volatility but getting low persistence model

I am using a GARCH(1, 1) model to try model volatility for a certain stock. I have a GARCH function in matlab that returns the three parameters, omega, alpha & beta. I then use this parameters ...
1k views

### Heston model with Jumps

Heston model can be used to find prices of options under stochastic volatility. How do I include jumps in the model, so that I end up with a different stochastic volatility curve? References to ...
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### Asymptotic behavior of theta of vanilla call option

It is well known that the theta of call option is always negative. Also, the theta of (at the money call option) goes to infinity as the time approaches to the maturity. On the other hands, (ITM and ...
924 views

### derivation of heston pde in gatheral

Following Gather (the volatility surface, chapter 2) we assume the following process: $$dS_t = S_t(\mu_t dt+\sqrt{\nu_t}dZ^1_t)$$ $$d\nu_t= -\lambda(\nu_t-\bar{\nu})dt+\eta\sqrt{\nu_t}dZ^2_t$$ ...
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### Stochastic Volatility CIR estimation

Would anyone have a code (pref. Matlab or R) for any type of estimation (QML, GMM) not using option prices of a stochastic volatility model driven by a CIR process described below? \begin{equation} ...
504 views

### Do we need Feller condition if volatility process jumps?

It is fairly known that in affine processes, as Heston model \begin{equation} \begin{aligned} dS_t &= \mu S_t dt + \sqrt{v_t} S_t dW^{S}_{t} \\ dv_t &= k(\theta - v_t) dt + \xi \sqrt{v_t} dW^{...
546 views

### arbitrage in Heston model

Really struggling in this question: Consider a market with two assets $(B,S)$ whose price dynamics satisfy \begin{equation} dB_t = B_t r dt \end{equation} \begin{equation} \quad \quad \quad \quad \, ...
816 views

### Does it make sense to use upward and downward volatility in option pricing?

Historically stocks have a higher likelihood to increase in price than to fall in price. As such would it make sense to split a stocks volatility measurement into upward and downward components? For ...
192 views

### Help with integrating stochastic calculus expression from yield curve model

I am very rusty on stochastic calculus, and I am having trouble integrating the following simple term from a yield curve model: $$z(t)=\int_0^t\exp(-k(t-s))dW(s)$$ Any suggestions appreciated.
379 views

### Filtering out AR(1) effects before using stochastic volatility model

I wonder if I first filter out AR(1) (autoregressive model with lag 1) effects from univariate time series and then fit stochastic volatility model does above procedure introduce any bias at first or ...
2k views

### Black Scholes - how to calculate delta with a vol skew

I am trying to calculate the delta of an option at different strike prices where the underlying has a pronounced implied volatility skew in order to correctly hedge an options strategy. Researching ...
515 views

### Implied volatility and pricing of vanilla options

As far as I understood, implied volatility (IV) is a lucky parametrization of the vanilla option's price. That is, instead of deciding how much the call worth now, you can decide on its IV and put ...
803 views

### Quadratic exponential method (by Andersen) in Heston model

I am having trouble understanding the reasons that led Andersen to define his QE scheme to efficiently simulate Heston Stochastic volatility model (you may check the celebrated scheme here). The ...
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### SABR calibration: simple explanation and implementation

I would like to learn more about the SABR model and ho it is used in modeling smiles in equity, FX and rates markets. How would you explain the process and its implementation in simple steps? Any web ...
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### For which instruments performs SABR/LMM better than LMM?

For which class of instruments the SABR/LIBOR Market Model does perform better than the classical LIBOR Market Model? The LIBOR Market Model The LIBOR Market Model — also known as Brace, Gatarek, ...
438 views

### Option Prices under the Heston Stochastic Volatility Model

I was wondering if anyone has come across a more straightforward derivation of the semi-closed form solution for the price of a european call under the Heston model than the one proposed by Heston (...
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### what kind of test for volatility and where find the data

I am working on a model for stochastic volatility. In short, the model try to capture that the volatility goes up suddenly after a shock (war, policy, financial events, etc) and then goes down slowly, ...
2k views

### Estimate rolling stochastic volatility forecast using stochvol in R

I want to use the R package stochvol to fit a SV model to a DAX training set and use the output to estimate a rolling one-step-ahead forecast: ...
363 views

### Fitting stochastic variance distributions to index return data

I want to calculate option prices based on a realistic distribution of the underlying. The underlying is a liquid index such as Eurostoxx50. I think of two aproaches, both of them incorporate ...
1k views

### SVCJ (SVJJ) Duffie et. al Model implementation in Matlab

I'm attempting to implement aforementioned SVCJ model by Duffie et al in MATLAB. so far without success. It's supposed to price vanilla (european) calls . parameters provided, the expected price is: ~...
942 views

### Getting the next price of a GBM (Geometric Brownian Motion)

I am writing a program that creates realizations of a GBM. Starting from an initial price, I get the following price with this formula: ...
182 views

### 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 ...
930 views

### SABR model inconsistent with Black Swaption Pricing

I am confused on the following: When we price swaption, the market convention is to use Black's Model which assumes forward swap rate is following Black's model under the Q(t) measure. When we tries ...
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### Recalibrating SABR parameters for Swaption ATM volatility

I understand that the ATM volatility of Swaption moves quite frequently and the SABR will need to be recalibrated. Which parameter should I recalibrate? Is there any financial meanings why we only ...
I have a friend in the industry who said they are interested in the model I gave in the title. Whether they use it, idk. $dS_t= S_t(rdt+ \sigma_t dW_t)$ And $\sigma_t$ is the exponential of an OU ...