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tw
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Posts: 1176
Joined: May 10th, 2002, 3:30 pm

possible arbitrages?

December 4th, 2010, 11:20 am

Here's an issue that's been puzzling me.Suppose you have two tradeable assets, prices A and B.If there's a market in vanilla options in A and B and also in the spread option max(A-B,0) obviously there's a possibility if the spread option gets too cheap relative to the spread of the two vanilla options.Now suppose there are the two vanilla option markets on A and B and now a market on options on the ratio max(A/B-K,0).Are there any (non-trivial) arbitrage portfolios?One possibility might be the dispersion-like portfolio between a compo option and B0*max(A/B-A0/B0,0) +(A0/B0)*max(B-B0,0) - max(A-A0,0) However in the event that effective exchange rate, A/B becomes linearly related to B, the porfolio becomes short an option on a quadratic asset. but long options on linear assets.However there most be come combination that overcomes this..
 
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prodiptag
Posts: 124
Joined: September 12th, 2008, 4:41 pm

possible arbitrages?

December 4th, 2010, 3:35 pm

have a feeling you are talking about FX here. I vaguely remember I was curious about this too a long while back ... and what dawned on me is this -> suppsed A = eur/usd, b = gbp/usd, so a/b is eur/gbp, so max(a-b,0) depends on eur/usd vol, gbp/usd vol and their correlations, and max(a/b - k,0) depends on eur/gbp vol. Now my maths is rusty, so I can't prove it, but I don't see why eur/gbp vol would be specified completely by eur/usd vol, gbp/usd vol and there correlation, and if it is not, then I don't think there is any arbitrage. open to be enlightened!!
 
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tw
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Posts: 1176
Joined: May 10th, 2002, 3:30 pm

possible arbitrages?

December 8th, 2010, 7:59 am

It was commodities dual listed in different currencies. We've seen some very high FX vols and some very low commodity vols recently.QuoteOriginally posted by: prodiptaghave a feeling you are talking about FX here. I vaguely remember I was curious about this too a long while back ... and what dawned on me is this -> suppsed A = eur/usd, b = gbp/usd, so a/b is eur/gbp, so max(a-b,0) depends on eur/usd vol, gbp/usd vol and their correlations, and max(a/b - k,0) depends on eur/gbp vol. Now my maths is rusty, so I can't prove it, but I don't see why eur/gbp vol would be specified completely by eur/usd vol, gbp/usd vol and there correlation, and if it is not, then I don't think there is any arbitrage. open to be enlightened!!
 
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tagoma
Posts: 18849
Joined: February 21st, 2010, 12:58 pm

possible arbitrages?

December 8th, 2010, 8:16 am

hello tw. which commodities are you refering to ?agriculturals ? cpo chicago and malaysia ?