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September 11th, 2018, 11:00 pm
Topic: Correlation & Volatility - what returns period to use ?
Replies: 4
Views: 360

### Re: Correlation & Volatility - what returns period to use ?

In the absence of any real autoregressive effects, if you sum the direct and lagged covariance, you end up with an (almost) unbiased estimate of the covariance between then two processes.  Then just divide by the 1-day standard deviations.  My estimate is that roughly 75-80% of the dependence is in ...
July 6th, 2018, 11:32 pm
Forum: Off Topic
Topic: Spewers of bullshit
Replies: 59
Views: 938

### Re: Spewers of bullshit

... (More generally, a problem (caused by a misplaced sense of egaliterianism) is that you are not allowed to attack people's ideas because they take it personally. Tyranny of the majority)  Please attack responsibly. The word 'attack' aligns this with the personality conflicts that seem to dominat...
June 7th, 2018, 11:10 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 777
Views: 48254

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

I am reasonably familiar with Kloeden+Platen, and thought I was simply repeating Exercise 5.2.7 (first edition) or, since you're going beyond first order, what happens in section 10.4/10.5.
Maybe not.
June 7th, 2018, 12:11 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 777
Views: 48254

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

... $X(t)=X(t_0) + \mu X(t_0)^{\beta} \int_{t_0}^t ds + \sigma X(t_0)^{\gamma} \int_{t_0}^t dz(s)$ $+\mu \sigma \beta X(t_0)^{\beta + \gamma -1} \int_{t_0}^t \int_{t_0}^s dz(v) ds$ ... Everything else aside, I get that you can introduce standard normal drivers to represent the distribution...
May 25th, 2018, 11:08 am
Forum: Student Forum
Topic: Options replication
Replies: 12
Views: 704

It becomes messy with two times already, and perhaps not really what you are after in hindsight... briefly: Writing $H$ as the bivariate copula function for the joint distribution of the asset at $T_1$ and $T_2$, the value of an option with payoff $g(S(T_1),S(T_2))$ is ($f_1(S)... May 25th, 2018, 12:10 am Forum: Student Forum Topic: Options replication Replies: 12 Views: 704 ### Re: Options replication Interesting. There are probably some Frechet copulas in there somewhere in disguise... May 24th, 2018, 12:06 pm Forum: Student Forum Topic: Options replication Replies: 12 Views: 704 ### Re: Options replication I looked at something similar to your first form a while ago... One thing I tried at was to introduce the bivariate density function (for S(T1) and S(T2)) and write it in terms of marginals and a copula function -- which I was quite happy to assume was normal with correlation given by the time over... April 4th, 2018, 11:38 am Forum: Technical Forum Topic: Breakthrough in the theory of stochastic differential equations and their simulation Replies: 777 Views: 48254 ### Re: Breakthrough in the theory of stochastic differential equations and their simulation 99.9% May 7th, 2017, 7:45 pm Forum: Technical Forum Topic: Breakthrough in the theory of stochastic differential equations and their simulation Replies: 777 Views: 48254 ### Re: Breakthrough in the theory of stochastic differential equations and their simulation It might be quite simple: the constants 2.5/sqrt(2 Pi) is nearly equal to one, so perhaps you have rounded something somewhere. If you set this equal to one, get rid of the sigma on the left and assume that dz is a driftless Wiener process with volatility sigma, then you're fine I think. May 7th, 2017, 2:44 pm Forum: Technical Forum Topic: Breakthrough in the theory of stochastic differential equations and their simulation Replies: 777 Views: 48254 ### Re: Breakthrough in the theory of stochastic differential equations and their simulation I thought the logic was fairly clear: one of the results that you provided (that presumably resulted from the development in your `definitive answers' post) appears to be in conflict with known results. If I can convince you (somehow) that this is the case, then you might have to go back and revisi... May 7th, 2017, 1:23 pm Forum: Technical Forum Topic: Breakthrough in the theory of stochastic differential equations and their simulation Replies: 777 Views: 48254 ### Re: Breakthrough in the theory of stochastic differential equations and their simulation The validity of your proof I will leave you(/others?) to investigate, I merely point out that: 1. the left side is proportional to sigma, your right side is not. 2. There is a well-known result that your result does not agree with. For me that is sufficient to conclude that your result is either inc... May 6th, 2017, 8:14 pm Forum: Technical Forum Topic: Breakthrough in the theory of stochastic differential equations and their simulation Replies: 777 Views: 48254 ### Re: Breakthrough in the theory of stochastic differential equations and their simulation ... the fact that the left side is linear in sigma and the right has mysteriously picked up sigma^2 terms should be enough to conclude something. :) May 6th, 2017, 2:23 pm Forum: Technical Forum Topic: Breakthrough in the theory of stochastic differential equations and their simulation Replies: 777 Views: 48254 ### Re: Breakthrough in the theory of stochastic differential equations and their simulation ... We give another general simulation expansion as$\int _0^t z(s)\text{$\sigma$dz}(s)=\frac{2.5}{\sqrt{2\text{Pi}}}z(0)\sigma \sqrt{t}N(0,1) +.5\frac{2.5}{\sqrt{2\text{Pi}}}\sigma ^2t\text{  }N(0,1)^2-.5\sigma ^2t[\$]The above simulation for the stochastic integral is valid for any length of tim...
March 16th, 2017, 11:31 am
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 777
Views: 48254

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

When I wrote my post and made comparison with multistep numerical methods, I was trying to say that you can use the method even if you do not take enough series terms for the solution to converge(totally analytic solution will take enough terms and just one step). Sometimes, you might have just a f...
March 13th, 2017, 9:32 pm
Forum: Technical Forum
Topic: Breakthrough in the theory of stochastic differential equations and their simulation
Replies: 777
Views: 48254

### Re: Breakthrough in the theory of stochastic differential equations and their simulation

Interesting.  So if I understand you correctly, you realize that your series solution need not converge, and are essentially suggesting a multi-step method using your series approach within each step.  I'd be pretty surprised if something like that hadn't already been considered, although i have to ...

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