Arbitrage bounds for prices of weighted variance swaps
File(s)DAVIS-OBLOJ-RAVAL.PDF (307.68 KB)
Accepted version
Author(s)
Davis, MHA
Obloj, J
Raval, V
Type
Journal Article
Abstract
We develop robust pricing and hedging of a weighted variance swap when market prices for a finite number of co--maturing put options are given. We assume the given prices do not admit arbitrage and deduce no-arbitrage bounds on the weighted variance swap along with super- and sub- replicating strategies which enforce them. We find that market quotes for variance swaps are surprisingly close to the model-free lower bounds we determine. We solve the problem by transforming it into an analogous question for a European option with a convex payoff. The lower bound becomes a problem in semi-infinite linear programming which we solve in detail. The upper bound is explicit. We work in a model-independent and probability-free setup. In particular we use and extend F\"ollmer's pathwise stochastic calculus. Appropriate notions of arbitrage and admissibility are introduced. This allows us to establish the usual hedging relation between the variance swap and the 'log contract' and similar connections for weighted variance swaps. Our results take form of a FTAP: we show that the absence of (weak) arbitrage is equivalent to the existence of a classical model which reproduces the observed prices via risk-neutral expectations of discounted payoffs.
Date Issued
2013-02-07
Online Publication Date
2013-02-07
2016-11-16T15:30:35Z
Date Acceptance
2012-09-01
ISSN
0960-1627
Publisher
Wiley
Start Page
821
End Page
854
Journal / Book Title
Mathematical Finance
Volume
24
Issue
4
Copyright Statement
© 2013 Wiley Periodicals, Inc. This is the accepted version of the following article: Davis, M., Obłój, J. and Raval, V. (2014), ARBITRAGE BOUNDS FOR PRICES OF WEIGHTED VARIANCE SWAPS. Mathematical Finance, 24: 821–854., which has been published in final form at https://dx.doi.org/10.1111/mafi.12021
Source Database
web-of-science
Identifier
http://onlinelibrary.wiley.com/doi/10.1111/mafi.12021/abstract
Subjects
Social Sciences
Science & Technology
Physical Sciences
Business, Finance
Economics
Mathematics, Interdisciplinary Applications
Social Sciences, Mathematical Methods
Business & Economics
Mathematics
Mathematical Methods In Social Sciences
weighted variance swap
weak arbitrage
arbitrage conditions
model-independent bounds
pathwise Ito calculus
semi-infinite linear programming
fundamental theorem of asset pricing
model error
PROBABILITIES
OPTIONS
Finance
0102 Applied Mathematics
1502 Banking, Finance And Investment
Publication Status
Published