# Tag Info

### Pricing VIX Futures

Heston - Change of measure Consider the following Heston dynamics written under the real world measure $\Bbb{P}$ \begin{gather} \frac{dS_t}{S_t} = \mu_t dt + \sqrt{v_t} dW_S^{\Bbb{P}}(t),\ S(0) = S_0 \...
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### Difference between GARCH and Heston Volatility model

Heston gives an expression for the characteristic function, from which option prices can be computed. Therefore it can be calibrated (statically) on a set of vanilla option prices with different ...
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### Delta of an option under Heston model

Bad news: Your calculation is not quite correct As you say, the initial price of a European call option is $$C(S_0;K,T)= S_0e^{-qT}\Pi_1-Ke^{-rT}\Pi_2. \tag{\star}$$ However, the exercise ...
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### Book/ Articles recommendation for Volatility models

I have also currently started to learn about the subject. This is some of the material I have encountered: Many people recommend the book "The Volatility Surface: A Practitioner's Guide" by ...

### Option Pricing Model Calibration In Practice

The typical approach is: you only use option data from the last day. Furthermore, you only include those points that are liquid enough. One approach to this is to weigh the modelling error of an ...
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### Heston Model Integration Oscillations

There has been a huge amount of work on this. Generally a Fourier transform approach is used. First, be careful to use the form of the characteristic function that does not wind about zero in order ...
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### Interpretation and intuition behind the Put-Call symmetry under the Heston Model

This is a consequence of transforming a Put on $S_T$ with strike $K$ into a Call on $(K S_0)/S_T$ with strike $S_0$ under the stock measure. The new set of parameters $r_p$, $q_p$, $\kappa_p$, ... etc ...
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### Most accurate Fourier transform method for extreme OTM options

I'll give it a start and stick with Fourier methods. The approaches from Carr and Madan (1999) and Fang and Oosterlee (2009) are indeed known to be inaccurate for highly OTM options. I'd suggest to ...
• 13.8k
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### Quadratic exponential method (by Andersen) in Heston model

There is a qualitative shift in the shape of the density. When V is small it is monotone decaying. When V is large it looks more like a Gaussian. Another reason he uses two schemes is that he wants ...
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The Feller condition applies without modification. That is under the assumption that $v$ is square-root process with poisson-arrival jumps (as you wrote), and assuming the jump distribution is ...