# Tag Info

Accepted

### 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 ...
• 4,267

### 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 \...
• 14.3k
Accepted

### 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 ...
• 14.9k
Accepted

### Modeling Call Price w.r.t. Strike w Models that Capture Vol Smile

The way that I understand your question is that you are looking to fit the market prices of European plain vanilla options of a single maturity and then back out the corresponding implied probability ...
• 5,821
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• 14.3k
Accepted

### Intuition for the Effect of Vol of Vol in Heston Model on Volatility Surface

Maybe it would help you to think of it the following way. The strike $\sigma^2(T)$ of a fresh-start variance swap of maturity $T$ in the Heston model only depends on parameters $(v_0,\theta,\kappa)$, ...
• 14.3k
Accepted

### 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 ...
• 14.9k
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### Boundary conditions Heston's stochastic volatility model

You can't really derive or prove boundary conditions. You impose them and try to economically motivate them. Let's consider a European-style call option and go through the boundary conditions step by ...
• 14.9k

### Introductory material for getting started with local and stochastic volatility modelling

You may find A Short Note on Volatility Models an interesting summary providing bird's-eye overview of general ideas in volatility modeling. I would highly recommend SABR and SABR LIBOR Market Models ...
• 636

### Option Pricing Model Calibration In Practice

I know two papers explaining how to calibrate this kind of models, and one of them explain the impact of the quality of the fit on a pricing model: Aït-Sahalia, Y. (2002, January). Maximum likelihood ...
• 11k
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### parameters in Heston model and their impact on volatility smile

Intuition: You can think of the vol smile as a reflection of the risk neutral distribution (compared to the Black Scholes Gaussian density). A fat tailed distribution creates the smile: fat tail -> ...
• 4,267
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### About the Feller Condition in Heston Calibration

You should not use the Feller condition as a constraint. In many cases its violation will be required for a good fit to the market data.
• 1,875
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### Analytical Solution for Heston Model

This equation is unrelated to the Heston model. It is simply the value of a European call under the a constant coefficient geometric Brownian motion, i.e. the Black and Scholes (1973) model. Here $\nu$...
• 5,821

### Terminal Variance in the Heston Model

From the equations of the model it is clear that $v_t$ is the instantaneous variance of the log-returns, not the terminal annualised variance of the log-asset price. Put differently, you are you ...
• 14.3k