Determening Exchange Rate Volatility

[chris t]

Hello
I am trying to develop a simple model which will approximate how volatile an exhange rate is and then determine how often new data should be retrieved in order to update the model. The purpose of this model is to eliminate the need to check whether a value is over or under a certain amount by hand. I am more interested in being slightly conservative so that I have to check more things by hand than not in order to avoid missing any items over the threshold.
To give an example, since CAD/USD is not a very volatile rate, new data can be acquired weekly or even monthly, but some other rates are a lot more volatile and require daily monitoring.
How would you approach this problem?
Thanks,
Chris


Here is what i have come up with so far: Although I have up to 10 years of data, I think 90 (or even 60 days) might be a more accurate predictor. Since momentum clearly plays a part in the rate from day to day, I should somehow account for the skewness of the distribution (it is obviously not normal). I am currently unsure of how to do this. I know I will need to take the absolute of the skewness because direction really does not matter in this case.
Here is some excel statistics:

Mean	1.052848
Standard Error	0.002132
Median	1.0487
Mode	1.0445
Standard Deviation	0.020116
Sample Variance	0.000405
Kurtosis	-0.14035
Skewness	0.726448
Range	0.0832
Minimum	1.0237
Maximum	1.1069
Sum	93.7035
Count	89

 

[JeffM]

You understand, I hope, that this is not really a mathematical problem at all. You are assuming that the future will mimic the past, which is true until it isn't. More technically, you are assuming that the underlying process that you are trying to approximate with a model is relatively stable over periods of unknown duration, and you want to know when that process changes so substantially that your model must be adjusted or scrapped. Engineers deal with a similar problem, but it seems to me that the assumptions behind process control do not apply to financial markets, which are designed to absorb risk from every other segment of the global economy. Look up the history of Long Range Capital Management.

There may be someone here who is knowledgeable about the mathematics of process control monitoring (I am not). If you are risking large sums of money, it probably is worthwhile to pay someone who is knowledgeable about process control monitoring and mathematical financial models to help you. This is primarily a site to help students learn math, not to design systems to monitor the assumptions behind a trading strategy. That calls for an expert, who still may turn out to be wrong.

 

[chris t]

Hi Jeff,
While I appreciate the response, you are incorrect in every assumption you made regarding my question. I am a student who is currently working at a company and the model does not relate to a trading strategy at all. It has to do with a cut off point based on local currency for prescribed reporting. The purpose is to eliminate a large portion of the workload while still keeping conservative enough so that the company does not get fined for noncompliance by missing a report.

I understand that no model will be perfect which is why I plan on including a 3 tier system for amount that obviously do not have to be reported, ones that need to, and ones that are close enough to the cutoff that warrant a manual check.

 

[JeffM]

Hi Jeff,
While I appreciate the response, you are incorrect in every assumption you made regarding my question. I am a student who is currently working at a company and the model does not relate to a trading strategy at all. It has to do with a cut off point based on local currency for prescribed reporting. The purpose is to eliminate a large portion of the workload while still keeping conservative enough so that the company does not get fined for noncompliance by missing a report.

I understand that no model will be perfect which is why I plan on including a 3 tier system for amount that obviously do not have to be reported, ones that need to, and ones that are close enough to the cutoff that warrant a manual check.

Sorry that I was off the mark. Then this looks likes a statistical control process to me. I can't help you, but maybe someone else can.

 

[zmatula]

Chris, I was a commodity trader for 12 years and I'm very familiar with this type of mid office process. First off, you need to define your sensitivity threshold (either monetary or price movement). For example, I don't want to make/lose $X before I refresh the data or I don't want the price to move by $X before i refresh the data. Also, you need to define how sure you want to be or you confidence interval. For example, I don't want to cross my threshold more than 4% of the time. From there, its just a matter of scaling your standard deviation by theta (or time) to reach your thresholds. Lets take product X for example:

Daily Stdev: $2
Threshold: $9
Confidence interval: 96% (two standard deviations)

If stdev for one period is n then stdev for n periods is s * sqrt(n) so I need to solve for 9 = (2*2) * sqrt(n) or n = 5.0625. In this case, I would update the data every 5 days. Also, as a matter of best practice, I would strongly advise you against using more than 60 days of data in calculating your stdev. Hope this helps.