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Опубликовано в Forex diversification is | Октябрь 2, 2012

FOREX Market Currency Pair Temperature In a physical system the intensity of the Brownian motion of a particle can be taken as the average square of its. Human trading activities have since time immemorial generated great controversies. Just as market trades happen because there can never be a consensus by those. Brownian motion is the string that ties institutional financial risk models, markets and algos together because it allows them to predict the.
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It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. We assume this satisfies. We may rewrite 9. Why would it make sense to model exchange rates as in 9. Why would exchange rates be compounding? Wouldn't that result in every increasing or decreasing exchange rates? You are right that for long horizons this may be a strange model for FX dynamics.

However, it doesn't always result in the FX rate tending to zero or infinity. For constant parameters the GBM has the well known solution. This gives the zero mean arithmetic Brownian motion which also does not tend to anything:. Whichever distribution is chosen, is must be able to cope with the Argentine peso, which has had multiple redenominations.

Whichever distribution is chosen, is must be able to cope with the US dollar, which has gone from being worth a handful of pesos moneda nacional to being worth about a quadrillion. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Start collaborating and sharing organizational knowledge. Create a free Team Why Teams? Learn more. Why would exchange rates follow a geometric brownian motion?

Ask Question. Asked 6 months ago. Some are highly intelligent with PhDs in mathematics and are employed by big Wall Street firms. These are the guys who always win and we always lose. These people are known as Quants and they look at technical analysis with derision.

Quants use sophisticated mathematical models to predict market movements. Most of their models are probabilistic and make heavy use of stochastic calculus. Brownian motion is a random process that was first used in pricing stock options. Share it with friends:.

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It was just the result of the molecular nature of matter. A one dimensional random walker is one that is as likely to take a step forward as backward, say X axis, at any given time. A bidimentional random walker does the same in X or Y see illustration.

The stock prices change slightly on every transaction, a buy will increase its value a sell will decrease it. Subject to thousands of buy and sell transactions stock prices should show a one-dimensional Brownian movement. It presented a stochastic analysis of the stock and option markets. C urrency rates should behave very much as a pollen particle in water too.

An interesting property of the Brownian motion is its spectrum. This is called the Fourier series. The concept can be further extended to non periodic functions, allowing the period to go to infinite, and this would be the Fourier integral. Instead of a sequence of amplitudes for each multiple frequency you deal with a function of the frequency, this function is called spectrum. Signal representation in the frequency space is the common language in information transmission, modulation and noise.

Graphic equalizers, included even in the home audio equipment or PC audio program, have brought the concept from the science community to the household. Present in any useful signal is noise. These are unwanted signals, random in nature, from different physical origins. The spectrum of noise relates to its origin:. Thermal noise is approximately white , meaning that the power spectral density is equal throughout the frequency spectrum. It occurs in almost all electronic devices , and results from a variety of effects, such as impurities in a conductive channel, generation and recombination noise in a transistor due to base current, and so on.

The probability density of finding a random walker at position x after a time t follows the Gaussian law. An analytical expression for the above figure with rates in pips and t in minutes from an initial time t 0 :. Motion of pollen particles can be said to have two components, one random in nature described above, but if the liquid has a flow in some direction, then a drift motion is superimposed to the Brownian.

The FOREX market presents both types of motion, a higher frequency random component and a slower drift motions caused by news affecting the rates. Random motion is bad for the speculation business; there is no way to average a profit on a perfectly random market.

Only drift motion can render profits. Market randomness is not constant in time and neither is drift motion. During news events, drift movements are big and it is during events that profits can be made, But there are cleaner events in which automatic algorithms work the best and there are dirty ones, with a lot of randomness, that can drive the cleverest algorithm into losing.

The random velocity is the difference of the total velocity minus the average or drift velocity. The true sense to a drift velocity would be the average velocity of a big number of particles at given time that would indicate that the whole body of liquid and suspended particles is moving as a whole. But, since the random velocity must average in time to zero, the average of the velocity of a single particle in time is also equal to the drift velocity.

Finding the mass for each currency pair would allow having a common reference for temperature. If we took the EUR mass as 1, then:. Values for the currency pair masses could also be defined so as to make the average currency temperatures match the room temperature in the Kelvin scale or even fancier, to the Celsius or Fahrenheit.

Since the square root of the variance is the standard deviation, such a temperature definition gives an idea of how intense the random motion is in pips. A news event affecting the value of the US dollar can be detected when its rates to the rest of the main currencies change consistently. In other words, when the rate movements happen to correlate. See Appendix A on Event Trigger calculation. A numerical expression of this correlation is the average of difference to its EMA Exponential Moving Average over all the main currencies.

The problem with this approach is that the significant currencies to consider are not that many, actually only 6 pairs can be used. An average over such a small sample is not immune against random motion and prone to render false positives. More precisely: pondered by the probability of the observed rate velocity not being due to the Brownian nature of the motion. Here are 5 things you need to know about Geometric Brownian Motion.

Brownian Motion is in truth a physics concept that was ported over to finance; check out the wiki definition below. Brownian Motion: the erratic random movement of microscopic particles in a fluid, as a result of continuous bombardment from molecules of the surrounding medium. A financial quantity refers to the value of an asset e. Sure, we all know stock prices fluctuate over time, but how do you actually describe that movement precisely, and in a way that is consistent to everyone?

Equivalently, the log of the quantity is Normal. Finally, another way to think of it is: if the modelled quantity follows GBM, the log of the quantity follows BM. That is, at the end of a certain time period e. The above is how a typical Log-normal distribution looks like. Key things to note are the variable x cannot take negative values and it has a long tail to the right i.

The limitation of positive-only values of the Log-Normal distribution has forced some changes in interest rate modelling, in order to cater to negative interest rates.

Asked 2 years, 6 months ago. Modified 2 years, 6 months ago. Viewed 5k times. Quant Job Interview. Question: Why is Brownian motion useful in finance? Improve this question. Idonknow Idonknow 8 8 silver badges 20 20 bronze badges. Therefore, BW can be a reasonable process to use for modelling changes in log prices.

In fact, the whole black scholes framework is based on that assumption. Add a comment. Sorted by: Reset to default. Highest score default Date modified newest first Date created oldest first. Improve this answer. Kevin Kevin A word of warning as you have a pure math background. All these modells make assumptions that various quantities are Gaussian normally distributed. Real life data is not. Whether the models are still useful or not is exactly the question they should want to hire a pure math PhD for.

Alex C Alex C 9, 1 1 gold badge 19 19 silver badges 32 32 bronze badges. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Featured on Meta. Announcing the arrival of Valued Associate Dalmarus.

Testing new traffic management tool. Custom Quantitative Finance design and logo - Information gathering. Finally, another way to think of it is: if the modelled quantity follows GBM, the log of the quantity follows BM. That is, at the end of a certain time period e.

The above is how a typical Log-normal distribution looks like. Key things to note are the variable x cannot take negative values and it has a long tail to the right i. The limitation of positive-only values of the Log-Normal distribution has forced some changes in interest rate modelling, in order to cater to negative interest rates. In the classic Black-Scholes option pricing model, one of the fundamental assumptions is the stock price follows GBM.

It is not immediately clear what the significance of stock prices following GBM is. When we take log, however, the intuition becomes clearer. Saying that a stock price follows GBM i. Returns following a Normal distribution is much more intuitive. Most of the time, returns are around the average return value.