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?"
Just fit a normal distribution around the fwd, et voila... You will just need the sigma (volatility) and the actual fwd.
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.
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.
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?
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.