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Bounds on European Option Prices under Stochastic Volatility
Author(s) -
Frey Rüdiger,
Sin Carlos A.
Publication year - 1999
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 - 10.1111/1467-9965.00064
Subject(s) - stochastic volatility , volatility smile , implied volatility , economics , volatility (finance) , volatility swap , econometrics , arbitrage , sabr volatility model , forward volatility , financial economics , valuation of options
In this paper we consider the range of prices consistent with no arbitrage for European options in a general stochastic volatility model. We give conditions under which the infimum and the supremum of the possible option prices are equal to the intrinsic value of the option and to the current price of the stock, respectively, and show that these conditions are satisfied in most of the stochastic volatility models from the financial literature. We also discuss properties of Black–Scholes hedging strategies in stochastic volatility models where the volatility is bounded.