## What Is Fugit?

Fugit, from the latin *tempus fugit, *is the amount of time that an investor believes is left until it would no longer be beneficial to exercise an option early, or the likelihood that an American-style option will be exercised before it expires.

The fugit concept was named and created by the economist Mark Garman, a Berkeley professor who studied the optimal time for exercising an American option priced using binomial trees.

### Key Takeaways:

- Fugit is time remaining for an American option until it is no longer beneficial for early exercise.
- Fugit can also be interpreted as the probability that such an option's exercise feature will be used prior to expiration.
- The concept was formalized by Mark Garman, a Berkeley economist, using binomial tree models to identify the optimal conditions for early exercise.
- Fugit calculations are also used for timing Bermudian options and convertible bonds.

## Understanding Fugit

Fugit is a term used in options trading, borrowed from Latin. Specifically, it originates from a verse in the epic poem *Georgica,* which was written by the Roman poet Virgil: "*sed fugit interea fugit irreparabile tempus.*" In English, this means: “but it flees meanwhile" or "irretrievable time flees." It refers to the early exercise feature given to holders of American-style options (and which is absent from European-style options).

Unless an option is deep in the money, it should usually not be exercised early because this causes a loss of inherent value. It would be more cost-effective to keep the option instead of converting it into a long or short position in the underlying security. Some investors find it profitable to exercise call options early when they are in the money right before an ex-dividend date, or deep in the money puts that have close to a 100 delta.

Given an option that is a potential candidate for early exercise, the holder of the option will compute its fugit to see if it should indeed be exercised or not. Fugit is computed as the expected time remaining to exercise an American option, or alternatively, as the risk-neutral expected life of an option during which it can still be effectively hedged. The computation usually requires a binomial tree model and may not always arrive at one unique value.

## Special Considerations

Fugit calculations are also used with Bermudian options, contracts that can only be exercised on predetermined dates, often on one day each month. The concept is also used for determining if and when to utilize the feature to convert debt to equity for convertible bonds.

Nassim Taleb, options trader and the author of the book *The Black Swan: The Impact of the Highly Improbable*, proposes an alternative to the fugit calculation, which he calls a "rho fudge," or the option's *Omega *= *Nominal Duration x (Rho2 of an American option / Rho2 of a European option). *Note that Taleb employs different uses of the words rho (traditionally related to interest rate sensitivity) and omega (traditionally related to price sensitivity and also known as the lambda). Here the omega is akin to fugit, and the rho2 is an option's price sensitivity to dividend payments.

### Calculating Fugit

The calculation for an option's fugit is as follows: where *n* is the number of time-steps in the binomial tree; *t* is the time remaining to the option's expiration, and *i* is the current time-step in the binomial tree.

First, set the fugit value of each of the nodes at the end of the binomial tree equal to *i = n. *Then, working backward: if the option should be exercised at a particular node, set the fugit at that node equal to its period; or else if the option should not be exercised at a particular node, set the fugit to the risk-neutral expected fugit over the next period. The value arrived at in this fashion at the beginning of the first period (i = 0) is the current fugit. Finally, to annualize the fugit, multiply the resulting value by* t / n*.