Greek letters : THETA

Theta gives an indication of the value of the option, all else being equal, based on its life. It is calculated by deriving the Premium function of the option by its maturity « t ».

When buying an option (call or put), the Theta is always negative (except for exceptions such as Put Very-Deep-In-The-Money). Indeed, the more time passes, the less the option is likely to increase in value. Theta will therefore have a negative effect for the buyer and a positive effect for the seller of options.

As we can see, Theta decreases exponentially with the passage of time. In general, Theta is expressed in currency (Dollar or Euro) and is daily. The negative Theta of the option buyer will therefore be the daily loss in value of the portfolio due to the passage of time: it will be greater in absolute value as we approach expiration. This theta is, like the Gamma curve,
maximum for an ATMF option and much lower at the wings. Finally, volatility also has an impact on Theta. The higher the volatility, the higher the Theta of the option will also be in absolute value. This sensitivity can be calculated by the Greek
letter « Veta » obtained by deriving the Theta from the volatility. The buyer of options pays, at the time of the transaction, for an option that sometimes has an intrinsic value, but above all and undeniably has a time value. The higher the Theta of the
option, the more it will increase the time value and thus the purchase price of the option (which is why the Warrants have a high price). This Theta decreases from day to day and faster and faster until it reaches a null value at the expiration of the option. The shorter the option is purchased, the less Theta it will contain – and therefore its price will be lower – but the higher the daily loss of Theta will be. When buying long options, the contained Theta will be much stronger (and therefore it will be more expensive), but the daily loss of Theta will be less pronounced (because Theta’s loss only accelerates as it approaches expiration).

Written on 15/12/2020


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