mathematical finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require ...

, fugit is the expected (or optimal) date to exercise an American- or

Bermudan option In finance, the style or family of an option is the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American (style) options. These options� ...

. It is useful for hedging purposes here; see

Greeks (finance) In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is de ...

and . The term was first introduced by Mark Garman in an article "Semper tempus fugit" published in 1989.Mark Garman in an article "Semper tempus fugit" published in 1989 by Risk Publications, and included in the book "From Black Scholes to Black Holes" pages 89-91 The

Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...

term "tempus fugit" means "time flies" and Garman suggested the name because "time flies especially when you're having fun managing your book of American options".

Details

Fugit provides an estimate of when an option would be exercised, which is then a useful indication for the maturity to use when hedging American or Bermudan products with

European option In finance, the style or family of an option is the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American (style) options. These options� ...

s.Eric Benhamou
Fugit (options)
/ref> Fugit is thus used for the hedging of

convertible bond In finance, a convertible bond or convertible note or convertible debt (or a convertible debenture if it has a maturity of greater than 10 years) is a type of bond that the holder can convert into a specified number of shares of common stock ...

s, equity linked convertible notes, and any putable or callable

exotic Exotic may refer to: Mathematics and physics * Exotic R4, a differentiable 4-manifold, homeomorphic but not diffeomorphic to the Euclidean space R4 *Exotic sphere, a differentiable ''n''-manifold, homeomorphic but not diffeomorphic to the ordinar ...

coupon notes. Although see Christopher Davenport,

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, 2003. "Convertible Bonds A Guide". and for qualifications here. Fugit is also useful in estimating "the (risk-neutral) expected life of the option" for

Employee stock options Employee stock options (ESO) is a label that refers to compensation contracts between an employer and an employee that carries some characteristics of financial options. Employee stock options are commonly viewed as an internal agreement prov ...

(note the brackets). Fugit is calculated as "the expected time to exercise of American options", and is also described as the "

risk-neutral In economics and finance, risk neutral preferences are preferences that are neither risk averse nor risk seeking. A risk neutral party's decisions are not affected by the degree of uncertainty in a set of outcomes, so a risk neutral party is indif ...

expected life of the option"

Mark Rubinstein Mark Edward Rubinstein (June 8, 1944 – May 9, 2019) was a leading financial economist and financial engineer. He was ''Paul Stephens Professor of Applied Investment Analysis'' at the Haas School of Business of the University of California, Be ...

in an article "Guiding force"; the calculation is detailed on pages 43 and 44, as well as i
Exotic Options
, a working paper by the same author. The computation requires a

binomial tree In computer science, a binomial heap is a data structure that acts as a priority queue but also allows pairs of heaps to be merged. It is important as an implementation of the mergeable heap abstract data type (also called meldable heap), wh ...

— although a Finite difference approach would also apply — where, a second quantity, additional to option price, is required at each node of the tree; see methodology aside. Note that fugit is not always a unique value.

Nassim Taleb Nassim Nicholas Taleb (; alternatively ''Nessim ''or'' Nissim''; born 12 September 1960) is a Lebanese-American essayist, mathematical statistician, former option trader, risk analyst, and aphorist whose work concerns problems of randomness, ...

proposes a "rho fudge", as a “shortcut method... to find the right duration (i.e., expected time to termination) for an American option”. Taleb terms this result “Omega” as opposed to fugit. The formula is :''Omega = Nominal Duration x (Rho2 of an American option / Rho2 of a European option).'' Here, Rho2 refers to sensitivity to dividends or the foreign interest rate, as opposed to the more usual rho which measures sensitivity to (local) interest rates; the latter is sometimes used, however. Taleb notes that this approach was widely applied, already in the 1980s, preceding Garman.Nassim Taleb
Review of ''Derivatives'' by Mark Rubinstein
/ref>

References

{{reflist Mathematical finance Options (finance)