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What is Fugit?

Fugit, from Latin time passes, is the time that an investor estimates that it remains until it is no longer advantageous to exercise a option sooner or the likelihood that an American-style option will be exercised before it expires.

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

Key points to remember:

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

Understanding Fugit

Fugit is a term used in options trading, borrowed from Latin. Specifically, it comes from a verse in the epic poem Georgina which was written by the Roman poet Virgil: “but in the meantime, irreparable time flees.” In English, it means: “but it escapes in the meantime” or “the irretrievable time escapes”. It refers to the early exercise feature granted to holders of American-style options (and which is absent from European-style options).

Unless an option is at the bottom of the money, it generally should not be exercised early because it leads to a loss of intrinsic value. It would be more profitable to keep the option instead of transforming it into long Where short position in the underlying title. Some investors find it beneficial to exercise calls early when they are in the money just before a ex-dividend date, or deep in the money puts that have nearly 100 delta.

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

Special Considerations

Fugit calculations are also used with Bermudian options, contracts that can only be exercised on predetermined dates, often one day a month. The concept is also used to determine if and when to use the functionality to convert debt to equity for Convertible links.

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

Calculate Fugit

The calculation of the fugit of an option is as follows: where not is the number of time steps in the binomial tree; you is the time remaining until the option expires, 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, going back: if the option is to be exercised at a particular node, set the fugit at that node equal to its period; or, if the option is not to be exercised at a particular node, set the fugit to the expected risk-neutral fugit in the next period. The value thus obtained 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.

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