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Contingent Claims and Market Completeness in a Stochastic Volatility Model
Author(s) -
Romano Marc,
Touzi Nizar
Publication year - 1997
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.00038
Subject(s) - convexity , economics , volatility (finance) , arbitrage , econometrics , completeness (order theory) , financial economics , market price , volatility smile , stochastic volatility , implied volatility , mathematical economics , microeconomics , mathematics , mathematical analysis
In an incomplete market framework, contingent claims are of particular interest since they improve the market efficiency. This paper addresses the problem of market completeness when trading in contingent claims is allowed. We extend recent results by Bajeux and Rochet (1996) in a stochastic volatility model to the case where the asset price and its volatility variations are correlated. We also relate the ability of a given contingent claim to complete the market to the convexity of its price function in the current asset price. This allows us to state our results for general contingent claims by examining the convexity of their “admissible arbitrage prices.”