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 Dec 13 comment George Soros models @PatrickBurns That is a really great hypothesis! However, a thorough explanation of the hypothesis would include a discussion of the role of changing fundamentals as the core driver of this phenomenon. Dec 12 comment Stock Price Behavior and GARCH This is the Euler-Marayama discretization. There are better ones (such as Milstein). Dec 12 comment Do markets typically fall fast, and rise slowly For this interested in @PatrickBurns comment about people following the crowd, you may be interested in the herding literature which finds that this does in fact happen to some non-trivial extent in most countries. Dec 12 comment Estimating two normal random numbers with one equation Maybe this will help. If we have that $\langle W_1,W_2\rangle = \rho t$ then we can write that $dW_2(t) = \rho dW_1(t) + \sqrt{1-\rho^2}dW_1^\perp (t)$, where $dW_1^\perp(t)$ is a perpendicular brownian motion. Dec 10 comment GJR-GARCH Model In R rugarch really is fantastic. Dec 7 comment Taking into account the correlation in Barrier options on a Basket I think that $\langle dW_t^{i},dW_{t}^{j}\rangle=\rho_{ij}dt$ Dec 7 comment Who cares about autocorrelation? Of course publications gloss over this, as it's considered general knowledge among the readership of the paper. Dec 7 comment Using rolling returns in a multivariate linear regression? Have a look at the several serial correlation robust bootstrap estimators. Dec 7 comment Modeling interest rates with correlation What short rate model is this that multiplies $r$ with drift and $r$ with diffusion? What probability measure is this specified under? Dec 6 comment Why are regressors squared and not ^1.5 or ^2.2 or ^2.5? Very nice response. Could you address my reply to @pat in the comments section? Then I will accept the answer. Dec 5 comment What concepts are the most dangerous ones in quantitative finance work? Could you please elaborate on what you mean by "vanishes". There is no consensus (yet) in the contagion literature as to whether correlations are stable or increase during crises. When accounting for the bias in correlation coefficients caused by increased return variance during crises, Forbes & Rigobon (2002) show that correlations are stable during crises. Some recent evidence shows that correlations tend to increase during crises. But I've never seen any evidence that it vanishes. EDIT:Actually this is just for index level.Perhaps with other asset classes or constituent level you're right. Dec 5 comment What is Ito's lemma used for in quantitative finance? This is a fantastic solution! My lecture slides apply Ito's to $e^{aX(t) + bt}$ to get the answer and it takes about 30 lines of working! Dec 5 comment What advanced statistical techniques are quant researchers using? Can you please give some more concrete examples? (curious) Dec 5 comment Why are regressors squared and not ^1.5 or ^2.2 or ^2.5? @pat I'm talking about strictly positive regressors. For example, the $Age$ variable in actuarial studies. Also, even if the regressor (call it $X_t$) can assume negative values we could just do something like $|X_t|^{1.95}$ to construct a regressor that's almost the same thing as $X_t^2$. Dec 4 comment Why are regressors squared and not ^1.5 or ^2.2 or ^2.5? @John What are these extra variables? Dec 4 comment Why are regressors squared and not ^1.5 or ^2.2 or ^2.5? @John I don't understand. Do you mean that it's like this because $2$ looks prettier than $x\in[1.5,2.5]$? Surely parsimonious should be defined statistically instead of based on how pretty something looks from a qualitative perspective. Dec 3 comment How to improve the Black-Scholes framework? Do you have a source for this definition of returns? (where they actually use to word "returns") Dec 2 comment How to improve the Black-Scholes framework? I agree that $\frac{S(T)}{S(t)} = e^{(r-\sigma^2)(T-t)+\sigma(W(T)-W(t))}$ is lognormal, but I thought that the most common meaning of "stock returns" in finance is $ln \frac{S(T)}{S(t)}$. Dec 2 comment How to improve the Black-Scholes framework? Prices, not returns, are assumed to be lognormal. Nov 23 comment Pricing forward contract on a stock I am increasing in confidence that this is correct because I get the same answer when I work with measure $P^*$ associated with taking the growth optimal portfolio as the numeraire.