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Topic Title: Fugit
Created On Tue Jan 06, 09 02:16 PM

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dnxaque
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Tue Jan 06, 09 02:16 PM

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Does anyone know how to calculate the fugit of American options?

daveangel
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Tue Jan 06, 09 02:22 PM

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the concept of fugit was invented by Mark Garman ... if I remember correctly in a tree you start at the terminal values with a fugit equal to the maturity of the option. Roll back the tree and at any time step where the early exercise is greater than the continuation then the fugit is set to that time.

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dnxaque
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Tue Jan 06, 09 02:33 PM

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Tks Dave,

I know the definition of fugit (average exercise time)...Could I do the same things by using a PDE?. I means I rollback my PDE as you do for the tree. I wonder if the way you do can explain the word "average" in fugit's definition?

daveangel
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Tue Jan 06, 09 02:52 PM

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i think you can use the same approach in a PDE framework.

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dnxaque
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Tue Jan 06, 09 03:00 PM

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This means fugit depens on the number of time step????

daveangel
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Wed Jan 07, 09 09:19 AM

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no more than the accuracy of the solution

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riskyrisk
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Tue Jan 27, 09 03:22 PM

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During the workback through the tree doesnt the Fugit have to be weighted with the probability of hitting that node?
Can anyone point me to a link on specifics?
Thanks!
Risky

kalkin
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Thu Jan 29, 09 04:03 PM

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there isn't much information about fugit, is an arcane subject, I did a little work a while back on an excel and vba, but I found it more a math curiosity that a real applicable trading tool. There is an addin that actually calculates fugit, Ill check some back ups see if I found that spreadsheet

http://www.mbrm.com/htmls/pricelist.html

Dont remember if fincad has it

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Vegawizard
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Thu Jan 29, 09 04:25 PM

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I do not think Fugit is arcane at all, but in fact very useful, esp in dissecting american synthetics

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ppauper
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Fri Jan 30, 09 02:23 PM

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Quote
Originally posted by: daveangel
the concept of fugit was invented by Mark Garman ... if I remember correctly in a tree you start at the terminal values with a fugit equal to the maturity of the option. Roll back the tree and at any time step where the early exercise is greater than the continuation then the fugit is set to that time.

don't have the original Garman article at hand,
but eric benhamou calls it the "risk neutral expected time " to exercise an american and he suggests a methodology for PDEs similar to that for binomial trees

kalkin
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Fri Jan 30, 09 02:48 PM

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Quote
Originally posted by: Vegawizard
I do not think Fugit is arcane at all, but in fact very useful, esp in dissecting american synthetics

I didn't explain myself, for arcane I meant that there isn't a popular topic with lots of info over the internet. But I keep my view that it wasn't of much use trading / hedging, nor conclusions could be take on the value of the fugit that would help in my line of work. I would be delighted to see an example of how useful could be

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jfuqua
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Fri Jan 30, 09 05:59 PM

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In a trading firm it can be very important for knowing what your real expected 'Expire' date will be. Also for the Greeks and risk reporting.

robnavin
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Fri Jan 30, 09 07:43 PM

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Even though FUGIT is not expected time to exercise, (you need the risk premium in the drift to get this), nevertheless, as expected time to exercise could be useful, it has some value!

1) how to do FUGIT, (a little more precisely!): start with your standard Black-Scholes pricing algorithm, which solves the Black-Scholes-Merton Equation (the equation solved by the Black-Scholes formula for calls/puts). Then drop the discounting term (ie, -r$ * C). The result is a backward Kolmogorov Equation that all risk neutral expectation values solve. You can modify your weights at each node to reflect this change easily, just multiply the weights by the inverse of one time step discounting. Then, use the exercise boundary from your run of your normal pricing model, and "price" a "derivative" that has the value of "time" along this boundary. Alternatively, you can keep the same weights (ie use your normal pricing algorithm) and grow the boundary time by the inverse of the discount factor to that time.

2) Try another alternative, T = -rho / (C- delta*S). C = deriv price, S = underlying price, rho = d C/ d r$, and delta = d C/ d S. This has very similar properties (it is not the same) to FUGIT, but it is 0.0 deep ITM for an American, and it is time to Expiration way OTM, and smooth in between, and works for a lot of different types of derivs. It is easier to calc (you don't need to run another tree model to get it, assuming you calc rho and delta already). It is a generalization of the idea of duration. It is the maturity of a zero coupon bond that also has the same PV as the net long cash in the theoretically hedged derivative position, and the same rho.

kalkin
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Fri Jan 30, 09 08:48 PM

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Quote
Originally posted by: robnavin
Even though FUGIT is not expected time to exercise, (you need the risk premium in the drift to get this), nevertheless, as expected time to exercise could be useful, it has some value!

1) how to do FUGIT, (a little more precisely!): start with your standard Black-Scholes pricing algorithm, which solves the Black-Scholes-Merton Equation (the equation solved by the Black-Scholes formula for calls/puts). Then drop the discounting term (ie, -r$ * C). The result is a backward Kolmogorov Equation that all risk neutral expectation values solve. You can modify your weights at each node to reflect this change easily, just multiply the weights by the inverse of one time step discounting. Then, use the exercise boundary from your run of your normal pricing model, and "price" a "derivative" that has the value of "time" along this boundary. Alternatively, you can keep the same weights (ie use your normal pricing algorithm) and grow the boundary time by the inverse of the discount factor to that time.

2) Try another alternative, T = -rho / (C- delta*S). C = deriv price, S = underlying price, rho = d C/ d r$, and delta = d C/ d S. This has very similar properties (it is not the same) to FUGIT, but it is 0.0 deep ITM for an American, and it is time to Expiration way OTM, and smooth in between, and works for a lot of different types of derivs. It is easier to calc (you don't need to run another tree model to get it, assuming you calc rho and delta already). It is a generalization of the idea of duration. It is the maturity of a zero coupon bond that also has the same PV as the net long cash in the theoretically hedged derivative position, and the same rho.

Since it was fastest ( and curiosity always gets the best of me) I just included the quick number 2 on my model, I got 0,0006 for all options on a chain from a stock TS (the ticker if someone is interested), how would you interpret this since I have the same value for a call that has a 96% probability of exercise and other that has only 2%, expiration in feb.

Either way I'm into it now, Ill check the fugit over the weekend and compare it with both suggestions

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www.youtube.com/lordbinder

Paul
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Thu Feb 05, 09 10:40 AM

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It can also be useful with barriers, having some idea of when/if barrier will be triggered. But, yes, remember that you need to put the real drift in there otherwise it's just the risk-neutral time and therefore not so relevant.

P

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