Binary Option Greeks
Binary option Greeks are the letters of the Greek alphabet that are used to represent the sensitivity, generally of the options price, to a change in one of the inputs.
Who needs binary options greeks? The pricing of options is one thing but once a position has been opened options risk analysis needs to be generated, especially so if the position is likely to be closed prior to expiry.
Who cares? But here’s a new take on an old story. Aristotle, in his Politics, described how Thales of Miletus was able to forecast bumper olive harvests and negotiated options contracts with the local olive press owners. If the following year produced a bumper harvest then Thales exercised his options on the olive presses; alternatively he abandoned the options if the harvest was not a bumper.
Aristotle was born in 384BC, Thales died in 546BC, 162 years earlier: since we are looking at a period two thousand years prior to DropBox maybe Aristotle has instead been the raconteur of the most creative trading fantasy of all time. Maybe Thales couldn’t forecast olive harvests; maybe he was just the first ever options trader who figured out that Olive Press implied volatility was simply too low……………….
The binary option Greeks covered are:
|Binary Options Greeks||Below Strike||Above Strike|
|Binary Call Option Delta||+ve||+ve|
|Binary Put Option Delta||-ve||-ve|
|Binary Call Option Gamma||-ve||+ve|
|Binary Put Option Gamma||+ve||-ve|
|Binary Call Option Theta||+ve||-ve|
|Binary Put Option Theta||-ve||+ve|
|Binary Call Option Vega||+ve||-ve|
|Binary Put Option Vega||-ve||+ve|
Other Greeks do exist but have little weight compared to the above’s delta, gamma, theta and vega. In 15 years of options market-making in the pits and subsequently in front of (soul-destroying) screens these were the Greeks that concerned me, with Greeks such as Rho (Rho measures the option price change with respect to a change in interest rates) having little bearing, even less so nowadays with global interest rates being so low.
The price of an option is sensitive to a directional price move in the underlying asset, the change in time to expiry plus changes in the implied volatility of the asset price. Other sensitivity analysis could involve changes in interest rates, changes in the dividend/asset yield and for two-asset binary options, changes in the correlation of the two asset’s prices.