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Option pricing and perfect hedging on correlated stocks

✍ Scribed by Josep Perelló; Jaume Masoliver

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
509 KB
Volume
330
Category
Article
ISSN
0378-4371

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✦ Synopsis

We develop a theory for option pricing with perfect hedging in an ine cient market model where the underlying price variations are autocorrelated over a time ¿ 0. This is accomplished by assuming that the underlying noise in the system is derived by an Ornstein-Uhlenbeck, rather than from a Wiener process. With a modiÿed portfolio consisting in calls, secondary calls and bonds we achieve a riskless strategy which results in a closed and exact expression for the European call price which is always lower than Black-Scholes price. We obtain the same price and a modiÿed delta hedging if we start from an e ective one-dimensional market model. We compare these strategies and study the sensitivity of the call price to several parameters where the correlation e ects are also observed.

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