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28 votes
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Why dynamics of local volatility is wrong?

A general model (with continuous paths) can be written $$ \frac{dS_t}{S_t} = r_t dt + \sigma_t dW_t^S $$ where the short rate $r_t$ and spot volatility $\sigma_t$ are stochastic processes. In the ...
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7 votes

Why dynamics of local volatility is wrong?

Here "dynamics" means the assumed future behaviour of the spot process, namely that it follows the SDE $$ dS/S = r dt + \sigma_{loc}(S,t) dW_t .$$ There are various ways to see that these dynamics ...
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5 votes
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Do you have a good application example of Approximate Dynamic Programming?

I totally missed the coining of the term "Approximate Dynamic Programming" as did some others. Also, in my thesis I focused on specific issues (return predictability and mean variance optimality) so ...
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3 votes
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Dynamics of LIBOR foward rate under T-forward measure

We assume that, under the risk-neutral measure $Q$, \begin{align*} dP(t, T) = P(t, T)(r_t + \sigma(t, T)dW_t), \end{align*} where $\{W_t, \, t \ge 0\}$ is a standard Brownian motion. Then \begin{align*...
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3 votes

Non-linear Dynamical Systems and Quantitave Finance

This book might be what you are looking for: Theory of Financial Risk and Derivative Pricing. From Statistical Physics to Risk Management by J.-P. Bouchaud and M. Potters As one reviewer from amazon ...
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3 votes

Are there stocks dynamic that cannot be represented by Generalized Black Scholes model?

KeSchn and I pointed out in the comments that this it is not possible to represent all stock dynamics using the Generalized Black Scholes model. For example, there can be jumps at random moments and ...
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3 votes

Trading 3 stocks X Y Z where X cointegrated to Y, Y to Z, but no other cointegration is available

Assuming we are talking about Pearson correlation, then we may apply the triangle inequality. Let $\rho(X,Y)$ denote the correlation between $X$ and $Y$. Then, $(1-\rho(X,Z))^{1/2}\le (1-\rho(X,Y))^{...
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2 votes

Dynamical Behavior of Hurst Exponent

Hurst exponents are most often used in identifying trends in time series. It's been quite a while, but I read this book years ago and this sort of thing is addressed therein (albeit, in a somewhat ...
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2 votes
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How to (efficiently) calculate the maximum possible return of a perfect "crystal ball" investment strategy?

To me, that smelled like dynamic programming too. After implementing a dynamic programming solution according to http://www.cs.rpi.edu/~magdon/courses/cf/notes/optimal.pdf and other sources from the ...
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1 vote
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Why is this utility function not picking up its penalty?

The problem was a missing $W_t$ in the equation for correlation. I've updated the above code and did a rerun. We have now the following allocation which is much closer to the Infanger paper. ...
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1 vote
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How to estimate an Engle's asymmetric DCC model in R?

The "rmgarch" package in R requires specifying univariate GARCH models before a DCC (or asymmetric DCC, aDCC) can be fitted. The workaround is to specify models that essentially "do nothing", e.g. a ...
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1 vote
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Simulate from time-dependent copula in MatLab using COPULARND

You can use a for-loop on your correlation series. for i=1:2000 simulation=copularnd('t',rho(i),NU,N));
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