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The Stock Option Problem Read chapter Read first chapter

2015 | OriginalPaper | Chapter

7. The Continuous Hedging Argument

Authors : Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

Published in: Derivative Security Pricing

Publisher: Springer Berlin Heidelberg

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Abstract

This chapter develops a continuous hedging argument for derivative security pricing. Following fairly closely the original Black and Scholes (1973) article, we make use of Ito’s lemma to derive the expression for the option value and exploit the idea of creating a hedged position by going long in one security, say the stock, and short in the other security, the option. Alternative hedging portfolios based on Merton’s approach and self financing strategy approach are also introduced.

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previous chapter Ito’s Lemma and Its Applications
next chapter The Martingale Approach
Appendix
Available only for authorised users
Footnotes
1
Nor is the strategy required to generate some cash outflow, say in the form of dividends.
 
2
In (7.36) we set τ → T, 0 → t, Q 1 → Q S , Q 2 → Q B , μ 1 → μ S, μ 2 → rB, σ 1 → σ S, σ 2 → 0.
 
3
Which here becomes \(V (u) = Q_{S}(u)S(u) + Q_{B}(u)B(u)\).
 
Literature
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–659.CrossRef
Hull, J. (2000). Options, futures and other derivatives (4th ed.). Boston: Prentice-Hall.
Samuelson, P. A. (1973). Mathematics of speculative price. SIAM Review, 15(1), 1–42.CrossRef
Thorp, E. O., & Kassouf, S. T. (1967). Beat the market. New York: Random House.
Metadata
Title
The Continuous Hedging Argument
Authors
Carl Chiarella
Xue-Zhong He
Christina Sklibosios Nikitopoulos
Copyright Year
2015
Publisher
Springer Berlin Heidelberg
Book
Derivative Security Pricing

Print ISBN: 978-3-662-45905-8

Electronic ISBN: 978-3-662-45906-5

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-662-45906-5_7