# Two-Asset Binary Options

30th September, 2010 - Posted by in Binary Options Strategies

#### An Introduction to Two-Asset Binary Options

Two-asset binary options consist of binary structures with two underlying instruments.

Two-asset binary options present a challenge in that having the extra variable, asset 2, also involves a further extra variable, the correlation coefficient of the two asset’s prices*. This requires a far more complex study of the sensitivity analyses in that, for example, each strategy has two deltas, two gammas etc.. The approach in this sector has been to hold the asset 2 price static while the delta of asset 1 is illustrated and analysed, but this also requires a static Rho. So the reader will find an abundance of three dimensional graphics on the following pages although, unfortunately, three dimensions are insufficient.

Two-Asset Binary Options StrategiesStrikesPayoutSettles
Correlation CoefficientN/AN/AN/A
Double Binary Options20:100Only at Expiry
Double Tunnel Options40:100Only at Expiry
Pyramid OptionsVariableOnly at Expiry

The first two-asset binary options to be considered are binary spreads (both call & put) and binary eachway spreads (also both call & put). Of all the two-asset binary options, binary spread call options and binary spread put options are the easiest to grasp as they only have one strike price.  The simplicity of the binary spread options makes them obvious candidates for retail traders who are already conducting futures spread trading. Binary eachway spreads have two strikes but this concept, too, is relatively easy to understand.

Double binary options require greater consideration as there are now at least two strikes. Double binary calls, double binary puts, binary call/puts and binary put/calls enable traders to speculate on the individual performance of two assets independently of each other. A binary call/put or binary put/call could well be the ideal limited risk instrument when trading the reverse yield spread for example.

Finally, the last of the two-asset binary options consist of cubes, eachway cubes and the pyramid which require the buyer to correctly assess the price ranges that two asset’s prices will be within at the expiry of the option. Yet again the absolute price of the asset is the focus unlike the relative performance of the binary spread. The author’s experience in trading short-term interest rate (conventional) options would suggest to him that these strategies would be highly popular in the STIR market.

The additional variables in the above strategies increase the risk to the market-maker both in pricing and the subsequent risk management; consequently a sufficiently wide bid/ask spread would be required in order to compensate for the extra risk load.

* This correlation coefficient is the variable rho, which in itself can cause a problem for the first differential of an option with respect to the interest rate is also sometimes referred to as rho. But since the variables interest rate and yield of the asset have been studiously avoided within the section Binary Options Strategies the usage of the term rho will be constrained to the correlation coefficient.