28
votes
Accepted
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 ...
- 3,836
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 ...
- 1,865
5
votes
Accepted
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 ...
- 7,702
3
votes
Accepted
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*...
- 20.5k
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 ...
- 27k
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 ...
- 7,702
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))^{...
- 234
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 ...
- 1,608
2
votes
Accepted
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 ...
- 136
1
vote
Accepted
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.
...
- 1,638
1
vote
Accepted
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 ...
- 1,788
1
vote
Accepted
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));
- 5,649
Only top scored, non community-wiki answers of a minimum length are eligible