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Unbounded Volatility in the Uncertain Volatility Model

Matthieu Leblanc 1 Claude Martini 1
1 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
Abstract : We work in the Uncertain Volatility Model setting of Avellaneda, Levy, Paras [1] and Lyons [1O]¸ (cf. also [11]. We first look at European options in a market with no interest rate and focus on the extreme case where the volatility has a lower bound but no upper bound. We show that the smallest riskless selling price of the claim is the Black-Scholes price (at volatility given by the lower bound) of an option with payoff the smallest concave function above the initial payoff. We next extend our results to the case with interest rate.
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Submitted on : Wednesday, May 24, 2006 - 10:18:36 AM
Last modification on : Thursday, February 3, 2022 - 11:14:06 AM
Long-term archiving on: : Thursday, March 24, 2011 - 12:02:03 PM


  • HAL Id : inria-00072571, version 1



Matthieu Leblanc, Claude Martini. Unbounded Volatility in the Uncertain Volatility Model. [Research Report] RR-4065, INRIA. 2000. ⟨inria-00072571⟩



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