How do I price OANDA box options?

External question — Quantitative Finance Stack Exchange Author: user59 Original post: https://quant.stackexchange.com/questions/114 License: CC BY-SA 3.0 — https://creativecommons.org/licenses/by-sa/3.0/ Adaptation: HTML converted to plain text; contact email addresses removed. How do I price OANDA box options without using their slow and machine-unfriendly user interface?: http://fxtrade.oanda.com (free demo account) sells "box options": If you already know what a box option is (or visit http://fxtrade.oanda.com/trade-forex/fxtrade/box-options or signup for a free demo account), you can skip the rest of this section. A box option is a highly flexible binary option where you choose a FOREX currency pair, a price range and a time range. You win if the FOREX currency pair hits the price range sometime during the time range. Here's how a box option looks on a chart on OANDA's user interface: And the same box option in a form: In the above example, you're betting that USDCAD will trade between 0.98758 and 0.99674 sometime between 1455 and 2000 GMT. Note that USDCAD does not have remain in this range the entire time: if USDCAD plunged to 0.98000 before 1455 but then rebounded to 0.98760 at 1900 (or any time between 1455 and 2000), you still win. $1000, the purchase price, is the most you can lose. If you win, OANDA will pay back $1005.48 for a profit of $5.48 . This isn't much, because it's fairly likely that you'll win. You can also buy an option betting the exact opposite: that USDCAD won't trade between 0.98758 and 0.99674 any time between 1455 and 2000 (in other words, USDCAD remains below 0.98758 from 1455 to 2000, or remains above 0.99674 from 1455 to 2000). For the opposite option, OANDA pays a little better: since it's unlikely that USDCAD won't hit that range between 1455 and 2000. I'm trying to figure how OANDA prices these options: I'm trying to optimize certain values, so I need quotes for every price range and every time range. It's infeasible to do this using their standard interface. Additionally, it's hard to record values from this user interface into a file. The prices obviously relate in some way to the probability of hitting the time/price range. I know how to calculate these probabilities ( https://github.com/barrycarter/bcapps/blob/master/box-option-value.m ), but can't find a correlation between the probabilities and OANDA's price. OANDA obviously includes a "safety factor" and "commission" in their quotes. If a box option is 50% likely to win, they won't return $2000 to your $1000 dollars, since that would mean no profit for them. When the "hit" and "miss" prices are identical (roughly meaning they feel the box option has 50% chance of success), they seem to pay out about $1400 on a $1000 bet (meaning a $400 profit). That's just a rough observation though. This might be more of a project, but I'm looking for help, tips how to get started, brilliant insights, etc. I realize OANDA charges a large "commission" on these options, but still think they can be useful in some cases.