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School project about Black Scholes with stochastic volatility

In a university project I am looking at Black Scholes model with a stochastic volatility. I’m still not quite sure about my focus (I am in the beginning 'Idea phase'). I want to explain the theory ...
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22 views

wishart stochastic volatility models

Stochastic volatility models assume that volatility follow a random process.In the emerging market the volatility tend to be high. why is it that the wishart stochastic volatility model fit well the ...
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2answers
48 views

Martingale correction for Andersen scheme with Interest Rate

I have implemented martingale correction to my Andersen scheme for Heston model, as it is in the paper (page 19-22): ...
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0answers
73 views

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: ...
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3answers
272 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 ...
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1answer
37 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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1answer
58 views

Realized variance in SVJJ (Heston with jumps) model

I am working with the stochastic volatility model with jumps in both the price and volatility dynamics, ie. the risk neutral dynamics are of the form: $\mathrm{d}V_t = \kappa(\theta - V_t)\mathrm{d}t ...
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0answers
41 views

When to use SV or a GARCH model

So i have been searching for this answer for a question if there is a rule or something that would say when to use GARCH type model or use an stochastic volatility model to predict the volatility of ...
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1answer
101 views

Extrapolating SVI

In his paper Gatheral presents the following parametrization of the implied total variance $w(k,T) = \sigma_{BS}(k,T)^2T$ $$ w(k) = a + b\{\rho (k-m) + \sqrt{(k-m)^2 + \sigma^2} \}.$$ Assuming that ...
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1answer
58 views

Implied volatility as price transform

Implied volatility The way I understand it, traders often think of implied volatility as a transformed price. So in a way, the Black Scholes model is considered a 'model-free' blackbox that takes a ...
2
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2answers
78 views

Calibrating stochastic volatility model from price history (not option prices)

For stochastic volatility models like Heston, it seems like the standard approach is to calibrate the models from option prices. This seems a bit like a chicken and an egg problem -- wouldn't we ...
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1answer
29 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 ...
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1answer
47 views

Applying interest rate models for volaility rate

To what extent may the interest rate models be applied for modeling implied volatity? The story: I was checking different stochastic option pricing models for being able to replicate implied ...
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0answers
104 views

Why is it useless to model stochastic volatility when pricing Vanilla style derivatives?

With respect to the answer by user AFK in Ideas about Stochastic volatility models. I am specifically interested in interest rate options (IR Caps/Floors and Swaptions).
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53 views

Practical Delta hedging under stochastic volatility models (e.g. SABR model)

I'm currently straggling with Delta hedging under SABR model (or other stochastic volatility models). As far as I know there are numerous Delta hedging strategies theoretically and practically such as ...
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0answers
69 views

Approximate asian geometric option with Heston

I am trying to implement Theorem 1 from this Journal in RStudio. The journal says the it is possible to find a approximate price of a geometric asian option in a Heston setup this way: ...
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3answers
94 views

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 ...
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1answer
191 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 ...
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1answer
248 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 ...
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1answer
166 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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1answer
111 views

How to use calibrated Standard Stochastic Volatility?

I'm considering the standard stochastic volatility model: $$x_t = \rho x_{t-1} + \sigma \epsilon_x$$ $$y_t = \beta \exp\left[ \frac{x_t}{2} \right] \epsilon_y$$ where $y_t$ is the log-returns and ...
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1answer
91 views

A Difference between Local Vol and Stochastic Vol Models

For the purpose of this question a local vol model is a 1d SDE which specifies the price process and we have a contingent claim that depends on those prices (in general, at multiple times). e.g. ...
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2answers
71 views

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 ...
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1answer
99 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 ...
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88 views

Transition densities in the Heson 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 ...
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2answers
84 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 ...
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1answer
385 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 ...
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39 views

Stochastic Volatility in current market environment

Some price exotics with stochastic vol, some use other models such as local vol. What is the impact/advantage/disadvantage of using stochastic volatility in the current market environment? In other ...
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1answer
458 views

Covariance matrix and Cholesky decomposition

I am simulating a spread option with stochastic volatility using Monte Carlo simulation. I have the positive-definite covariance matrix $$ \rho = \left( \begin{array}{cccc} 1 & \rho_{1,2} & ...
5
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1answer
113 views

Market price of volatility risk

Reading Gatheral's The volatility surface, page 7. The model they are talking about is ...
2
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1answer
135 views

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 ...
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1answer
133 views

derivation of heston pde in gatheral

Following Gather (the volatility surface, chapter 2) we assume the following process: $$ dS_t = S_t(\mu_t dt+\sqrt{\nu_t}dZ^1_t)$$ $$ d\nu_t= -\lambda(\nu_t-\bar{\nu})dt+\eta\sqrt{\nu_t}dZ^2_t$$ ...
3
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1answer
266 views

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} ...
2
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1answer
125 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} ...
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2answers
167 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 \, ...
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2answers
257 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 ...
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1answer
154 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.
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1answer
150 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 ...
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1answer
449 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 ...
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1answer
179 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 ...
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1answer
280 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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1answer
499 views

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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178 views

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, ...
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2answers
205 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 ...
2
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0answers
38 views

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, ...
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1answer
625 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: ...
3
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1answer
187 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 ...
2
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2answers
455 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: ...
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1answer
306 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: ...
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0answers
142 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 ...