# Tag Info

16

Consider the standard error, and in particular the distance between the upper and lower limits: $$\Delta = (\bar{x} + SE \cdot \alpha) - (\bar{x} - SE \cdot \alpha) = 2 \cdot SE \cdot \alpha$$ Using the formula for standard error, we can solve for sample size: n = \left(\frac{2 \cdot s \cdot ...

9

There are really a few issues here: 1) When do I turn off a model because I believe the model is invalid? This is a subjective call and depends on many things such as how strong the economic reasoning behind the model is, how crowded the space is, and how poorly the model is performing relative to backtest. With regard to the last point, as a rule of ...

9

You ought to have pre-determined "kill" switches, like a maximum allowable drawdown or time-from-high. Ideally you should get an idea of what these values would be from your backtests. When you do shutdown a model, don't just throw away the code. The strategy might not be working at the moment, but it could come back in the future. I just heard that models ...

7

The "price protection" refers to RegNMS in the US. A stock exchange that does not have the best price must route all order flow to the exchange that does. The SIP in the figure is a consolidated feed that lists the best price among all exchanges. Consider this example: a broker sends a market order to buy JNJ to NYSE where the best offer is \$86.97. ... 6 This depends a little bit on your definition of volatility arbitrage but in general what is meant is a strategy that takes advantage of the difference between implied volatility and realized volatility. Normally you receive implied variance and pay realized variance. This strategy is the classical example of picking up nickles in front of a steamroller ... 6 You can use a equity based model. Stop trading when your equity drops below your "X-day" equity moving average, and resume trading when your equity crosses above the "X day" equity moving average. You could also do this by measuring the slope of the curve, and not trading when the slope is statistically below 0. I like this method because it does not tie ... 6 An index is just an abstract concept and does not hold securities. Hence no source of revenue from lending them. A portfolio mirroring an index holds the securities and can in fact generate revenue by loaning the securities to others wanting to short the stocks. This provides a positive bias. That is often offset by a negative bias when the index ... 5 I am not sure why your question had so many upvotes because in currency markets anything else but triangular arbitrage does not exist. What is a quadrangular arb, I have never heard of it despite having traded fx among other asset classes for over ten years now. Think about it: Lets say you observe the price of EUR/USD. You can build triangular arbs by ... 5 Yes, there is a software application that you can purchase for$39.99 which stores all your tick data in a highly compressed format while still allowing maximum throughput and lowest latency data queries that I have ever seen. The package provides APIs to all languages under the sun but because they have a special sale going on it comes with the complete ...

5

I typically have several tests. Like Ralph Winters said, one calculation to use is the equity curve. I use "...equity curve slope must be greater than x1..." to continue using a model. Another test is, "...%wins must be greater than x2...". Another is, "...average %return per winning transaction must be greater than x3...". Another is "...%return per ...

5

To see the connection between put-call parity and option price you should read this highly insightful paper by Espen Gaarder Haug & Nassim Nicholas Taleb: Option traders use (very) sophisticated heuristics, never the Black– Scholes–Merton formula It shows how you can heuristically derive option pricing formulas by adapting the tails and skewness ...

5

The option is a contract that gives you the right to buy the stock in one year for 18. Today people are trading the stock for 20, so you can sell the stock short for 20 today. Selling the stock short means someone will give you 20 cash today in return for a stock IOU, where you are obligated to deliver the stock to them on a later date. So you get 20 cash ...

4

Are there any other mechanisms at play here which might explain this kind of tracking error? Dirk is right, you often lend the titles internally or not, etc. You can also write calls for your index, this is not orthodox, but it's ETF, there is no orthodoxy there... Edit : With the graph and given the outperforming is seasonnal (around May), I think we ...

4

Short answer: yes. Long answer: the challenge in trading these things, like you mentioned, is that each contract is not perfectly hedgable. This is an intentional choice made by the exchanges that list these products, so that they can provide an incentive to trading firms(locals) to provide liquidity for these new products and help boost trading volume. ...

4

Here's the relationship of rho on calls and puts. When you buy call options instead of the the underlying, you are effectively buying an indirect leveraged position in the underlying. A simple way to see this is buy re-arranging the terms of the Put-Call parity equation solving for the call price. The value of the call is equal to a synthetic position ...

4

Fatih Yilmaz, formerly of Bank of America (currently BlueGold), has a piece called "Imaginal Spreads and Pairs Trading" on exactly this topic, if you can find it (I couldn't find a copy on the public internet), originally published April 17, 2009. He writes: Academics and industry practitioners generally concentrate on time series aspects of currency ...

4

While triangular arbitrages exists, they are a rare, short lived, and shallow. In several academic datasets they are very rarely seen, mainly for two reasons, market efficiency aside: (1) the time resolution of the data is not tick by tick but aggregated at some level (for example at 1 second intervals), (2) the dataset doesn't include all available quotes ...

4

Interesting question! I don't think you will get very far just using mid prices, though...any sufficiently sensitive test will flag nearly every situation as an arbitrage since $A_\text{mid}+B_\text{mid} \neq (A+B)_\text{mid}$ in most cases. Instead, what about viewing each price set as a dimension in $n$-dimensional space? The arbitrages occur if the ...

4

Not sure why Python is recommended when you clearly ask for a .Net solution (well you may look at IronPython but I do not recommend it given there are much better options, see below), aside the fact that Python is horribly slow even when performing non-mission-critical data analysis and research. Even C# easily runs circles around most python scripts, given ...

4

The intuitive reason is that an arbitrary payoff in $L^0_+$ can always throw away wealth to be in $L^\infty_+$. Strange economically, but it's a common trick whenever a duality argument is going to be used. A bit more formally: Since $L^\infty_+ \subset L^0_+$, it's clear that Condition $1$ implies Condition $2$. If Condition $1$ doesn't hold, take a ...

4

I can offer you two explanations, one more economical, and the other mathematical. The one based on economics is based on no arbitrage (and probably what you're looking for): You are aware of the "Second" FTAP, which says roughly, that there is precisely one equivalent true/local/$\sigma$ martingale measure if and only if the market is complete, i.e. all ...

3

In my mind, there are two questions here: 1) How does DB make money given a zero expense ratio? This is covered by Dirk and Lliane. Basically, DB gets cheap funding and stock loan fees in return for paying marketing / index / hedging costs. The ETF investor gets zero expense ratio in return for taking DB credit risk. 2) Why does it look like the etf ...

3

The main problem is that you cannot achieve Libor in the markets. So the old-fashioned method of discounting at Libor doesn't work any more. As an example, if you compound up the 3m Libor with today's price on a 3x6 FRA, you won't get 6m Libor. Traditionally, that would mean arbitrage, but these days it's just a fact of life. You cannot achieve 3m Libor for ...

3

I think that you are missing one key condition on the call prices that I would say is standard, namely that the call prices should be bounded below by an "intrinsic" value. Specifically, we would expect $C(K) \ge (S-e^{-rT}K)_+$, and this can easily be seen to yield a static arbitrage if violated. This condition (in a slightly different form) can be found ...

3

The original Nelson Siegel paper describes a parsimonious model of the term structure using only four or three (if $\lambda_t$ is fixed). Filipovic (1999) proves that this model can never be used in a arbitrage free context, paraphrasing the abstract: We introduce the class of consistent state space processes, which have the property to provide an ...

3

Disclaimer: I know nothing about FX trading, other than that I've heard something to the effect of "The first rule of FX trading is that you do not trade FX. The second rule..." you know how it goes. I'm not into macroeconomics, but I get the impression that the benchmark for FX models is a random walk. That is to say that the fundamentals have nothing to ...

2

I would also note that you need to watch out for correlations between data points. (EG ,if you have a data point proving this works for oil company x. Another data point for oil company y may not actually count as separate.) If you are looking at 5 day holding periods, why not just grab all the EOD data that you can as well.EOD data is obviously not ...

2

The main reason that rho term is positive is that we are using arbitrage-free pricing theory. In particular, regardless of model, the value of a forward contract (for an asset paying no dividends) is $$F_T = S_0 e^{rT}$$ Therefore, in whatever option pricing model you choose, the center of its forward distribution for the asset price $S_T$ at time ...

2

This is probably not a good question for Q.SE—despite its application in your strategy, you're (perhaps unaware) asking a general math question: the difference between the ratio of means and the mean of ratios. There are numerous results online that distinguish the difference, but I assume the terminology wasn't apparent to you at the time. I've come ...

2

The price of payoff is convex if for every $0\le\lambda\le 1$: $V(\lambda K_1 + (1-\lambda)K_3 )\le \lambda V(K_1) + (1-\lambda)V(K3)$ , where $V(K)$ is the price of an option with strike $K$. We want that $\lambda K_1 + (1-\lambda)K_3 = K_2$. Solving it for $\lambda$ we get $\lambda=0.5$. Substituting $\lambda$ back to our inequality, we see that the ...

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