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On the relation between option and stock prices: a convex optimization approach

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The idea of investigating the relation of option and stock prices just based on the no-arbitrage assumption, but without assuming any model for the underlying price dynamics has a long history in the financial economics literature. The authors introduce convex, and in particular semidefinite, optimization methods, duality and complexity theory to shed new light to this relation. For this single stock problem, given moments of the prices of the undrlying assets, they show that they can find best possible bounds on option prices with egeneral payoff fundtions efficiently, ither algorithmically (solving a semidefinite optimization problem) or in closed form. Conversely, given observable option prices, they provide best possible bounds on moments of the prices of the underlying assets, as well as on the prices of other options on the same aset by solving linear optimization problems. for options that are affected by multiple stocks either directly (the payoff of the option depends on multiple stocks) or indirectly (they have information on correlations between stock proces), they find non-optimal bounds using convex optimization methods. However, they show that it is NP-hard to find best possible bounds in multiple dimensions. They extend their results to incorporate transactions costs.

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en

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application/pdf

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http://flora.insead.edu/fichiersti_wp/inseadwp2000/2000-29.pdf

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Copyright INSEAD. All rights reserved