Start your review of Quantitative Trading: How to Build Your Own Algorithmic Trading Business Write a review Shelves: finance This a very readable introduction to quantitative trading and is quite motivational at the same time. Ernest tells us that individual traders could set up profitable businesses thanks to the lack of restrictions that big hedge funds face. The content of the book can be classified into three sections: I. Algorithmic Trading Business: the necessary steps in setting up a trading This a very readable introduction to quantitative trading and is quite motivational at the same time. Algorithmic Trading Business: the necessary steps in setting up a trading business are: a Seeking a trading idea: sources for ideas include academic research, blogs and forums.
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Quantitative investment and trading ideas, research, and analysis. Whatever optimal parameters one found are likely to suffer from data snooping bias, and there may be nothing optimal about them in the out-of-sample period.
On the other hand, optimizing the parameters of a time series model such as a maximum likelihood fit to an autoregressive or GARCH model is more robust, since the input data are prices, not trades, and we have plenty of prices.
Fortunately, it turns out that there are clever ways to take advantage of the ease of optimizing time series models in order to optimize parameters of a trading strategy. One elegant way to optimize a trading strategy is to utilize the methods of stochastic optimal control theory - elegant, that is, if you are mathematically sophisticated and able to analytically solve the Hamilton-Jacobi-Bellman HJB equation see Cartea et al. Even then, this will only work when the underlying time series is a well-known one, such as the continuous Ornstein-Uhlenbeck OU process that underlies all mean reverting price series.
This OU process is neatly represented by a stochastic differential equation. Furthermore, the HJB equations can typically be solved exactly only if the objective function is of a simple form, such as a linear function. If your price series happens to be neatly represented by an OU process, and your objective is profit maximization which happens to be a linear function of the price series, then stochastic optimal control theory will give you the analytically optimal trading strategy: with exact entry and exit thresholds given as functions of the parameters of the OU process.
There is no more need to find such optimal thresholds by trial and error during a tedious backtest process, a process that invites overfitting to sparse number of trades. But what if you want something more sophisticated than the OU process to model your price series or require a more sophisticated objective function? What if, for example, you want to include a GARCH model to deal with time-varying volatility and optimize the Sharpe ratio instead?
In many such cases, there is no representation as a continuous stochastic differential equation, and thus there is no HJB equation to solve. Fortunately, there is still a way to optimize without overfitting. In many optimization problems, when an analytical optimal solution does not exist, one often turns to simulations. This process is much more robust than applying a backtest to the real time series, because there is only one real price series, but we can we can simulate as many price series all following the same ARMA process as we want.
That means we can simulate as many trades as we want and obtain optimal trading parameters with as high a precision as we like.
This is almost as good as an analytical solution. See flow chart below that illustrates this procedure - click to enlarge. Optimizing a trading strategy using simulated time series Here is a somewhat trivial example of this procedure. The maximum likelihood fit is done using a one-year moving window of historical prices, and the model is refitted every month. Once the sequence of monthly models are found, we can use them to predict both the log midprice at the end of the hourly bars, as well as the expected variance of log returns.
So a simple trading strategy can be tested: if the expected log return in the next bar is higher than K times the expected volatility square root of variance of log returns, buy AUDCAD and hold for one bar, and vice versa for shorts. But what is the optimal K? In fact, we simulate this 1, times, generating 1, time series, each with the same number of hourly bars in a month. Then we simply iterate through all reasonable value of K and remember which K generates the highest Sharpe ratio for each simulated time series.
We pick the K that most often results in the best Sharpe ratio among the 1, simulated time series i. That certainly makes for a simple trading strategy: just buy whenever the expected log return is positive, and vice versa for shorts. The CAGR is about 4.
Our universe of strategies is a pretty simplistic one: just buy or sell based on whether the expected return exceeds a multiple of the expected volatility. But this procedure can be extended to whatever price series model you assume, and whatever universe of strategies you can come up with.
In every case, it greatly reduces the chance of overfitting. But later on, we found that a similar procedure has already been described in a paper by Carr et al.
Ray Ng is a quantitative strategist at QTS. He received his Ph. February 24 and March 3: Algorithmic Options Strategies This online course focuses on backtesting intraday and portfolio option strategies. No pesky options pricing theories will be discussed, as the emphasis is on arbitrage trading. Posted by.
Quantitative Trading de Ernest Chan: Review
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