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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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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 ...
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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
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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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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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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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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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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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 ...
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0answers
54 views

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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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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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 ...
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0answers
107 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 ...
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0answers
268 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 ...
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677 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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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
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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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
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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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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0answers
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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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 ...