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OzQuant
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Joined: June 6th, 2002, 4:23 am

Options to replicate best stock in a portfolio?

May 13th, 2004, 12:28 am

A few years back, I remember reading a paper that described how to construct a strategy with options which replicated the return/performance of the best stock in a portfolio/basket/index.Say we have 10 stocks in a portfolio. The strategy involved options. Then at the end of the month (year whatever), the strategy had the same return as the best performing stock out of the ten, which ever it may be. The portfolio of 10 could have had an average return of 50 points, but stock H had 75. The strategy would then have returned 75.Does anyone know what paper I'm talking about? I don't remember names or years or titles. Complete blank. It would be greatly appreciated if someone here could shed some light on this or point me in the right direction.Thanks.
 
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grabben
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Joined: August 23rd, 2002, 12:47 pm

Options to replicate best stock in a portfolio?

May 13th, 2004, 10:52 am

Sounds like some type of Mountain range option. Himalaya? Try looking at the site below:Global Derivatives - Mountain Range Options
 
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OzQuant
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Joined: June 6th, 2002, 4:23 am

Options to replicate best stock in a portfolio?

May 14th, 2004, 1:13 am

Thanks - interesting site. What I want is the 'inverse' of the Everest option so that I get the payoff of the best performing stock and not the worst as in the Everest Option...
 
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Bull
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Joined: September 18th, 2002, 12:43 pm

Options to replicate best stock in a portfolio?

May 14th, 2004, 2:02 pm

I think what you are looking for is a best-of option. That is one of the flavours of rainbow options..
 
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Graeme
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Joined: April 25th, 2003, 5:47 pm

Options to replicate best stock in a portfolio?

May 14th, 2004, 6:51 pm

Indeed. Margrabe does it for two stocks. A paper of Rene Stulz is also important. There is a paper by a chap by the name of Herb Johnson (could be Johnston or whatever) where he claims to have the pricing formula for n assets. Uses n-variate normal cumulative function.Trouble with these princing formulae is that they are especially dependent on the Geometric Brownian motion assumption. In particular, you can't build in a skew because inter alia the price is not monotone in vol (and which vol is that?) And of course correlations are very badly behaved; the formulae are full of the usual correlations stuff. Thus, nobody will sell you an option anywhere near the theoretical price, as hedging is very difficult.