# Tagged Questions

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622 views

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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 ...
1answer
185 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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329 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? ...
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176 views

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

It is fairly known that in affine processes, as Heston model \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^{...
2answers
189 views

### arbitrage in Heston model

Really struggling in this question: Consider a market with two assets $(B,S)$ whose price dynamics satisfy $$dB_t = B_t r dt$$ \quad \quad \quad \quad \, ...
2answers
318 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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162 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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177 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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625 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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207 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 ...
1answer
341 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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730 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 ...
0answers
222 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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241 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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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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921 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: ...
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216 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 ...
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582 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: ~...
1answer
394 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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147 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 ...
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546 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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115 views

### 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 ...
3answers
248 views

### Stochastic volatility model with exponential OU volatility

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 ...
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296 views

### For pricing, what types of Exotic Options are suitable using Local Volatility Model / Stochastic Volatility Model?

I understand that Stochastic Vol Models should be used when Exotic Option payoff is Volatility dependent (such as Variance Swaps and Volatility Swaps). Stochastic Vol Models should also be used when ...
3answers
5k views

### relation between asset's and equity volatilities - merton model

In terms of Merton credit risk model need to find the initial value of counterparty's assets and the volatility of the assets. Both value are not directly observable thus we have to approximate them ...
2answers
376 views

### how to calculate more efficient volatility figure than historical volatility?

can we use alpha value to calculate option price instead of historical volatility. And if we can please explain how. I am doing my MMS in Finance and this for a project i am doing. the project is ...
4answers
733 views

### How to prove that markets are incomplete under the Stochastic Volatility model?

Has anyone ever formally proved that Markets are incomplete under the stochastic volatility model? I know that if there are more random sources than traded assets, then the market is incomplete but ...
2answers
326 views

### Obtaining a consistent covariance matrix for stochastic volatility processes

What is the condition for underlying stochastic volatility processes to give a consistent covariance matrix? I read in Hull that in order to have a consistent covariance matrix, volatility parameters ...
1answer
1k views

### Can the Heston model be shown to reduce to the original Black Scholes model if appropriate parameters are chosen?

Summary For Heston model parameters that render the variance process constant, the solution should revert to plain Black-Scholes. Closed from solutions to the Heston model don't seem to do this, even ...
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304 views

### Why does the price of a derivative not depend on the derivative with which you hedge volatility risk?

I'm trying to derive the valuation equation under a general stochastic volatility model. What one can read in the literature is the following reasoning: One considers a replicating self-financing ...
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368 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 ...
0answers
726 views

### Using volatility cycles to switch between trend following & range bound trading? [closed]

"...a low volatility environment is usually a good environment for trend following strategies; see Jez Liberty’s state of trend following report here..." http://quantumfinancier.wordpress.com/2010/...
4answers
2k views

### Stock Price Behavior and GARCH

In my (limited) understanding, the behavior of a stock price can be modeled using Geometric Brownian Motion (GBM). According to the Hull book I'm currently reading, the discrete-time version of this ...
2answers
659 views

### SKEW and VIX relations?

My question is about the CBOE published index VIX and SKEW. To start with, I consider working on the variance dynamics. I calibrate the market data (such as VIX and VIX futures) into the Heston model....
0answers
812 views

### Law of an integrated CIR Process as sum of Independent Random Variables

It is known (see for example Joshi-Chan "Fast and Accureate Long Stepping Simulation of the Heston SV Model" available at SSRN) that for a CIR process defined as : dY_t= \kappa(\theta -Y_t)dt+ \...
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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 ...
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684 views

### Can VIX be interpreted as a proxy for instantaneous volatility?

BJO06 (Table 2) estimate the following Cox-Ingersoll-Ross model for market variance, $\sigma^2_t$: \$\mathrm{d}\sigma^2_t = (\alpha_0 + \alpha_1\sigma^2_t)\mathrm{d}t + \sqrt{\beta_1}\sigma_t\mathrm{d}...
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2k views

### Why is the SABR volatility model not good at pricing a constant maturity swap (CMS)?

I have heard that the SABR volatility model was not good at pricing a constant maturity swap (CMS). How is that?
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191 views

### What tradeoff is there to using an accurate estimate with a large confidence interval?

I am working on calibrating a Heston model from simulated historical stock data. After obtaining an accurate estimate of the model parameters I found very large 95% confidence intervals for these ...
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1k views

### How is mean reversion implied by different valuations of Bermudan swaptions?

Someone told me that mean reversion can be implied by the different valuations of bermudan swaptions when using different methods for volatility calibration. Does anyone know what this means?
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311 views

### Transformation of Volatility - BS

I have recently seen a paper about the Boeing approach that replaces the "normal" Stdev in the BS formula with the Stdev \sigma'=\sqrt{\frac{ln(1+\frac{\sigma}{\mu})^{2}}{t}} \end{...
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655 views

### on “recovering probability distributions from option prices” - how to subtract influence of stochastic volatility?

This is based on a 1995 paper by Rubinstein/Jackwerth by the above title where the authors produces a distribution of stock prices inferred from option prices. But their approach only produces a joint ...
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702 views

### How to show that this weak scheme is a cubature scheme?

Weak schemes, such as Ninomiya-Victoir or Ninomiya-Ninomiya, are typically used for discretization of stochastic volatility models such as the Heston Model. Can anyone familiar with Cubature on ...
4answers
4k views

### Local Volatility vs. Stochastic Volatility

Are there any empirical observations or practices when to prefer Local Volatility Model for pricing over Stochastic Model or vice versa?