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audetto
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Joined: March 12th, 2002, 4:08 pm

Hedging Worst Of Digital Options

November 20th, 2003, 10:33 am

Does anybody have an idea about hedging worst of digital options?These are options that pay 1 if all the indexes have a positive performance on the reference period.I think one could price them using a copula and getting marginal probability from prices of single index digital options on the same strike and expiry date.Then comes the hedge. One could hedge using the same single index digitals (and coputing hedge ratios as the first derivatives of the copula), but I don't think digital market is liquid enough...Any idea about that?ciao
 
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exotiq
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Joined: October 13th, 2003, 3:45 pm

Hedging Worst Of Digital Options

November 25th, 2003, 5:31 pm

From what I understand, the position of shorting the digital worst of and going long the same number of index options essentially leave you with a spread position on the correlation of the underlying basket, in the sense that the payoff is related to an average vs. an extreme.I might try to avoid copulas by simply having a model of this spread based on an assumed process for stochastic correlation=> spread value.Consider dynamic and static hedges of this with digital index option, listed index options, or index futures. When the correlation is very high, you will be holding more position to generate a likely payoff, and as correlation decreases, you will hold less and less asset until a negative correlation just about guarantees zero payoff.HTH...