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ppauper
Posts: 69496
Joined: November 15th, 2001, 1:29 pm

### Bermudan Options

mj: thanks

ppauper
Posts: 69496
Joined: November 15th, 2001, 1:29 pm

### Re: Bermudan Options

does anyone have a copy of this paper?
A Series Solution for Bermudan Options
Ingmar Evers
A Series Solution for Bermudan Options
Applied Mathematical Finance
Volume 12, 2005 - Issue 4
Pages 337-349

outrun
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: Bermudan Options

Have you tried the illegal scihub service?

Edit: just checked, they have it if you paste the DOI

ppauper
Posts: 69496
Joined: November 15th, 2001, 1:29 pm

### Re: Bermudan Options

thanks, I wasn't aware of the existence of scihub

ppauper
Posts: 69496
Joined: November 15th, 2001, 1:29 pm

### Re: Bermudan Options

Out of curiosity, we're always told that American options are like a melting/solidification problem  because of the free boundary (although I think cuch pointed out that water gets mushy so not the melting/solidification of water)

Is there an analogous physical problem for Bermudan options?

Alan
Posts: 9572
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Re: Bermudan Options

Out of curiosity, we're always told that American options are like a melting/solidification problem  because of the free boundary (although I think cuch pointed out that water gets mushy so not the melting/solidification of water)

Is there an analogous physical problem for Bermudan options?
Interesting question. Just speculating -- perhaps if one posited a one-dimensional water-ice interface in which the diffusion coefficient of the water cycled from 0 to D>0 repeatedly, one might get something analogous. So, nothing happens when the diffusion is zero, but then melting proceeds normally when the diffusion is D>0. (Maybe $D(t)$ needs to be periodic with delta function spikes??). I know it sounds quite artificial, but then a one-dimensional water-ice interface (the standard solvable Stefan problem) is also arguably artificial/toy problem.

In my last book, I asked and answered somewhat of a reverse question: is there an exact financial interpretation/analog of the standard 1D Stefan problem? American-style Black-Scholes puts are a rough analog but not an exact map. (Proof: the std Stefan problem is exactly solvable and the American put problem is not; plus the two free boundaries are well-known to be different). Anyway, I was able to come up with a financial analog that, IMO, wasn't too much of a stretch. It's all in Chapter 9: 'Back to basics: update on the discrete dividend problem'.

ppauper
Posts: 69496
Joined: November 15th, 2001, 1:29 pm

### Re: Bermudan Options

ok, so it looks like there's no naturally analogous physical problem but it may be possible to create something that's horribly contrived

Alan
Posts: 9572
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Re: Bermudan Options

Yeah, in fact thinking some more, I don't think setting D=0 in-between exercise dates is analogous to Bermudans at all. So, not even sure there is a horribly contrived answer!

Since the most basic Bermudan exercise policy is simply European exercise, maybe the place to start is: what is a physical analog of that one?