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Combinatorial Implications of Nonlinear Uncertain Volatility Models
 

Summary: Combinatorial Implications of
Nonlinear Uncertain Volatility Models:
the Case of Barrier Options
Marco Avellaneda
New York University
Robert Buff
New York University
August 15, 1998
Abstract
Extensions to the Black-Scholes model have been suggested recently
that permit to calculate worst-case prices for a portfolio of vanilla options
or for exotic options when no a priori distribution for the forward volatility
is known. The Uncertain Volatility Model (UVM) by Avellaneda and
ParŽas finds a one-sided worst-case volatility scenario for the buy resp. sell
side within a specified volatility range. A key feature of this approach is
the possibility of hedging with options: risk cancellation leads to super-
resp. sub-additive portfolio values. This nonlinear behavior causes the
combinatorial complexity of the pricing problem to increase significantly
in the case of barrier options. In this paper, we show that for a portfolio
P of n barrier options and any number of vanilla options, the number of

  

Source: Avellaneda, Marco - Department of Mathematics, Courant Institute of Mathematical Sciences, New York University

 

Collections: Mathematics