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9

There is certainly much more to quantitative finance than technical analysis, and a previous question does a decent job of outlining the different areas, as does the wikipedia on "quantitative analyst". Even for what wikipedia terms an "algorithmic trading quant" or what Mark Joshi terms a "statistical arbitrage quant", technical analysis is just one tool ...


6

C++ Think in C++ can be a starting point. This is free. And, you might study Beginning Visual C++ 2010 by Ivan Horton Quantitative finance and C++ (if you are derivatives-oriented) You might find Mark Joshi as well as Daniel Duffy's writings of (great) interest. It is easy to find the references of both their books on a website such as Amazon. You can ...


5

Hi Quantitative Finance has in my opinion two main streams. The first is about of valuation of some derivative contracts in a consistent way. This is a theory and once paradigms accepted it is coherent, it can considered as science at the same level as economy can pretend to this kind of terminology. The second is about making (or trying to) prediction(s) ...


4

I found these nice lecture note by Karl Sigman on the web. On page three you see if $X\sim N(\mu,\sigma)$ then the moment generating function (mgf) of $X$ is given by $$M_X(s) = E(exp(sX)) = \exp( \mu s + \sigma^2 s^2 /2)$$ Thus for Brownian motion with drift $X_t$ you get $$ M_{X_t}(s) = E(exp(s X_t)) = \exp( \mu t s + \sigma^2 s^2 t /2). $$ Finally for ...


4

One approach would be to rescale these metrics so that they are approximately normally distributed with unit variance under the null hypothesis that the stock's price is an unbiased geometric random walk (equivalently that the log returns are zero mean). This rescaling is effectively going to 'downweight' the statistics with a large amount of variance. Once ...


4

Quant in trading creates system that can be backtested, has a certain risk valuation. It is more like playing chess when you need to calculate multistep strategy. Let say certain instrument moves 1% a day. Our goal is to create strategy for one year (250 step strategy). If we use stock + options we get 50 or more entries a day into our system for analysis. ...


3

I don't know what $\mu$ stands for in the model so let me just recall the standard Black-Scholes formalism. It's likely that everything can be extended with minor modifications to the model you're interested in. The price of the vanilla call option with a strike $K$ is equal to the expectation of the discounted pay-off $$C_K=\mathbb E(e^{-rT}(S_T-K)_+),$$ ...


3

A multi-alpha trading model ranks each asset according to the individual signals. For example, if I have two metrics and three stocks, I could just create this reverse-sorted table: Rank| PNL W2L ----| --------- 3 | AAPL AAPL 2 | MSFT YHOO 1 | YHOO MSFT Because this ranking/sorting method is non-parametric, I can just average each metric's rank by ...


3

One that I found via google that seems promising (for beginners though) is. Numerical methods in finance and Economics


3

Options, Futures, and Other Derivatives Analysis of Financial Time Series Inside the Black Box: The Simple Truth About Quantitative Trading Trading and Exchanges: Market Microstructure for Practitioners


3

Question 2 has a straight forward solution using a differential equation approach: $\mathbb{P}(\tau^\mu_a<\infty)=1$ The following link (pp. 21 f.) explains it nicely (and is also very detailed) - could not write it much better. If you were to google "brownian motion linear boundary" you will get additional results. Also if you are generally interested ...


3

We have, $$ h(x) = x^\beta(x-K)^+ = x^\beta (x - K) \, \mathbf{1}_{[x>K]}$$ Thus we get, $$ h(x) = x^{\beta+1}\mathbf{1}_{[x>K]} - K\,x^{\beta}\mathbf{1}_{[x>K]}$$ now $x \in [x>K]$ if and only if $ x \in [x^{\beta}>K^{\beta}]$ Therefore, $$ h(x) = x^{\beta+1}\mathbf{1}_{[x^{\beta + 1}>K^{\beta + 1}]} - ...


3

A hurst exponent, H, between 0 to 0.5 is said to correspond to a mean reverting process (anti-persistent), H=0.5 corresponds to Geometric Brownian Motion (Random Walk), while H >= 0.5 corresponds to a process which is trending (persistent). The hurst exponent is limited to a value between 0 to 1, as it corresponds to a fractal dimension between 1 and 2 ...


3

If you have a fairly good model of regime separation (of course requiring a good quantitative measure of regime state classifications -- momentum and reverting) and predictive likelihood (using something like a markov state transition matrix)-- one could weight contributions corresponding to next state probabilities. Of course, you will rarely get a ...


2

A detailed description of the Hurst Exponent can be found here. A further (rather short search of Google) turned up this site claiming to provide an Excel Workbook with, among other things, Hurst Exponent estimation.


2

Momentum and mean reversion are labels to describe the behavior of a stock relative to the time period under consideration. That means same stock can be a momentum stock at one point in time and mean reverting stock at different point in time. Similarly at same time, a stock can be both a momentum stock and mean reverting stock depending on which time frame ...


2

I like the following book (though have only very briefly skimmed it): Optimization methods in finance


2

This may be too basic a book for what you're hungering for. In preparation for the Financial Engineering actuarial exam, I'm studying from Derivative Markets by McDonald. It's very technical, but gives a great introduction to the mathematics behind pricing options and even goes into depth on Brownian motion. Check it out here: http://amzn.to/g3QOES.



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