# 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 \...
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 ...
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 ...

### 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 ...
Accepted

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 $(v_0,\theta,\kappa)$, ...
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 ...
Accepted

### 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 ...

### 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 ...
Accepted

### 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.
Accepted

### 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 $\nu$...

### 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 ...

### Is pricing options using the volatility surface implied by the Heston model equivalent to pricing using the Heston model directly for all options?

Consider the Heston model and the Local Volatility model with local volatility built (using Dupire) from the Heston reconstructed vanilla options implied volatility. The price of any European payoff ...
Accepted

### Heston Model Integration Oscillations

I'd use FFT or similar rather than direct integration. Here is an old paper with Heston example: Option pricing using fractional FFT

### Heston ITM and OTM options pricing

There are a number of tricks. My favourite is to use the Black--Scholes price as a control. The integrals become much better behaved. You compute the difference of the Heston price from the BS price ...
Accepted

### Example of complex structured products on FX market?

Here are a few FX structured product examples: All of these can be notes or swaps, notes will pay back the notional at the end and carry no credit risk (and are normally set so that they are worth ...