FX volatility / measuring frequency distributions

D

d0rian

Hope my Q is not too elementary for this forum: I'd like to know how to convert the USD:CAD currency rate/volatility to a frequency-distribution chart that shows the likelihood (given the current currency-pair volatility) that the CAD will be trading at various levels at X future date.

To put it in specific terms, the current FX rate is $1 CAD = $0.7603 USD. What I'd like to do is quantify the likelihood of the CAD trading at various levels on, say, October 21st, 2016.
  • How do I do that?
  • What are the inputs required (only volatility and future date)?
  • And assuming I can produce the appropriate frequency distribution chart, what's the formula for solving for a specific FX rate? For instance, how would I solve the straightforward(?) Q of "what is the likelihood that the CAD trades at $0.78 or higher on Oct 21st?"
 
Here is a Snapshot over 5 years (FXC). The bell curve fits well the Daily returns. There are multiple ways to achieve what you wanna do. I'd run a Monte Carlo simulation over X days forward by randomly picking and reconstructing different paths, from Y days backward (Historical Data) according to the daily variations (Let it be Points or %). From there if you know the outcomes and their frequency then you can calculate the likelihood. Or morph the PDF into a CDF.

image.gif
 
Last edited:
As long as there isn't too much skew, you the delta of the currency options are a at least a first order approximation of the percentage chance that the security will trade above/below the strike price on the day the option expires. Alternately looking at the mid on binary options, if you can find any that go out more than a few days, gives you the same thing. If all you're looking for is the data you can just pull it off a few bucket shop binary operators and average, they've usually got the probabilities close to right and are close to one another in pricing, just with a big spread (hence the mid) and you may or may not see your money back if you were to ever actually trade with them.
 
Apophenia said:
Here is a Snapshot over 5 years (FXC). The bell curve fits well the Daily returns. There are multiple ways to achieve what you wanna do. I'd run a Monte Carlo simulation over X days forward by randomly picking and reconstructing different paths, from Y days backward (Historical Data) according to the daily variations (Let it be Points or %). From there if you know the outcomes and their frequency then you can calculate the likelihood. Or morph the PDF into a CDF.

View attachment 166604
More...
Martinghoul said:
Just fit a normal distribution around the fwd, et voila... You will just need the sigma (volatility) and the actual fwd.
More...

Thanks, all for the replies -- I should admit, though, that I'm pretty lost as to just what you mean in places (I'm a relative noob with currencies). I know what volatility is, and I know how to run Monte Carlo sims...what's the "fwd", though? Is there software (or a free web resource) that can help me with this process as it relates to the CAD/USD FX rate?
 
d0rian said:
Thanks, all for the replies -- I should admit, though, that I'm pretty lost as to just what you mean in places (I'm a relative noob with currencies). I know what volatility is, and I know how to run Monte Carlo sims...what's the "fwd", though? Is there software (or a free web resource) that can help me with this process as it relates to the CAD/USD FX rate?
More...
Fwd simply means Forward. Which are nothing more than Futures (6C or FXC). I know Interative Broker has a nice tool called Probability Lab -> Browse for 6C or FXC options -> Select the expiration -> You got your implied probability distribution.

You could also do it with Python, Mathematica, Matlab ... Even Excel maybe ?
But in these case you need to download the appropriate End Of Day data. From there you either analytically estimate the parameters of the bell curve or run monte carlos.
 
You must log in or register to reply here.
Back
Top