The stochastic-volatility tag has no wiki summary.
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92 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 ...
4
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1answer
159 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 ...
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0answers
263 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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1answer
187 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 ...
6
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3answers
283 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 ...
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0answers
339 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..."
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5
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4answers
712 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 ...
4
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2answers
458 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 ...
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326 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+ ...
7
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1answer
174 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 ...
9
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1answer
388 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 + ...
6
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2answers
606 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?
6
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1answer
130 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 ...
1
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1answer
589 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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0answers
213 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
\begin{equation}
\sigma'=\sqrt{\frac{ln(1+\frac{\sigma}{\mu})^{2}}{t}}
...
3
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2answers
462 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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0answers
460 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 ...
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3answers
973 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?
