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2 votes

When calculating VIX, how to deal with the problem of asymmetry of put and call data?

I have dealt with this problem in my research, here are my findings and takeaways: Not enough options are a problem: Jiang and Tian (2007) showed that an insufficient range of strikes leads to a ...
Martin Georg Haas's user avatar
2 votes
Accepted

Vanna Volga Price of an Up and In Put

I do not think you should (can) use the opposite probability (going from p touch to p no touch) because there exists a so called In-out parity: $$European \ vanilla\ option = European\ KI + European\ ...
AKdemy's user avatar
  • 9,014
2 votes
Accepted

Typical values Heston parameters for FX options

Since no one answered yet I'll provide a few numbers from Bloomberg's OVML as mentioned in a comment. The following logic is used by Bloomberg: The Heston model parameters are calibrated to at-the-...
AKdemy's user avatar
  • 9,014
2 votes
Accepted

Value of the logcontract $Q^T(t,S)$ with payoff $Q(T,S)=-2lnS_T$

In the Black-Scholes model, risk-neutral the dynamics of $S_t$ are given by $$ dS_t = (r-q)S_t dt + \sigma S_t dW_t. $$ Using Itô's lemma, we can find the dynamics of the log-process $$ d\log S_t = \...
Achrbot's user avatar
  • 373
1 vote

Heston model characteristic function

To answer your comment about (A7), it is a typo. It should read as: $$\boldsymbol{-\frac{1}{2}\phi^2} + \rho\sigma\phi i D + \boldsymbol{\frac{1}{2}\sigma^2D^2}+u_j\phi i-b_jD+\frac{\partial D}{\...
javier quintanilla's user avatar
1 vote

A book that has exercises which closely resembles the content of Lorenzo's Stochastic Volatility Modeling book?

You can check Sebastien Bossu's book "Advanced Equity Derivatives" Not going as deeply as Lorenzo's book but it contains lot of exercises which make it richer
StochasticMan's user avatar
1 vote

Calibrating the Heston with the Levenberg-Marquardt algorithm

The situation is a little more complicated than expected. We use this notation for the damped least squares equation $$ [J^{T}J + \lambda I_{d}] \Delta \theta = -\nabla f(\theta) $$ where $\theta$ is ...
SimoPape's user avatar
1 vote
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Characteristic Function for Wishart Heston Model

I have solved the problem myself. In summary, one has to evaluate the complex matrix for each argument of the Fourier/Laplace transform $u_1, \dots, u_{1000}$. This cannot be done with MatLab's ...
SimoPape's user avatar
1 vote

Volatility Mismatch in SABR Calibration

Let's assume you can calibrate just as well using $\beta = 1$. Then you'd have $$ dF = \alpha \sqrt F dW $$ and $$ dF = \tilde\alpha F dW = (\tilde\alpha \sqrt F) \sqrt F dW $$ So you can make the ...
Frido's user avatar
  • 1,906
1 vote

Time-shifted power law in path dependent volatility

The time-shifted power-law kernels $K_1 (t)$ and $K_2 (t)$ assign a weight to past returns and squared returns, respectively. Each kernel is a function of the following parameters: lag parameter $\tau&...
alexbougias's user avatar
  • 1,426
1 vote

Reference request about stochastic volatility model

In my opinion, the best book on this area is Lorenzo Bergomi's "Stochastic Volatility Models" which covers the local volatility models, stochastic volatility models and local stochastic ...
Lost1's user avatar
  • 1,023

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