Fugit
In mathematical finance, fugit is the expected (or optimal) date to exercise an American- or Bermudan option. It is useful for hedging purposes here; see Greeks (finance) and Optimal stopping § Option trading. The term was first introduced by Mark Garman in an article "Semper tempus fugit" published in 1989.[3] The Latin term "tempus fugit" means "time flies"[4] and Garman suggested the name because "time flies especially when you're having fun managing your book of American options".
Calculation of fugit:
For Fugit — where n is the number of time-steps in the tree; t is the time to option expiry; and i is the current time-step — the calculation is as follows:[1]; see also [2] (1) set the fugit of all nodes at the end of the tree equal to i = n (2) work backwards recursively:
(3) the number calculated 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. |