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14
votes
0answers
646 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
votes
1answer
233 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
votes
1answer
614 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
votes
2answers
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?
6
votes
1answer
182 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
vote
1answer
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?
7
votes
0answers
284 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
votes
2answers
620 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 ...
22
votes
0answers
634 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 ...
16
votes
4answers
3k 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?