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Factorization of European and American option prices under complete and incomplete markets

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  • Ibáñez, Alfredo

Abstract

In a standard option-pricing model, with continuous-trading and diffusion processes, this paper shows that the price of one European-style option can be factorized into two intuitive components: One robust, X0, which is priced by arbitrage, and a second, [Pi]0, which depends on a risk orthogonal to the traded securities. This result implies the following: (1) In an incomplete market, these parts represent the price of a hedging portfolio, which is unique, and a premium, which depends only on the risk premiums associated with the residual risk, respectively. (2) In a complete market, it allows factoring the contribution of the different sources of risk to the final option price. For example, in a stochastic volatility model, we can quantify the impact on the option price of volatility risk relative to market risk, [Pi]0 and X0, respectively. Hence, certain misspricings in option markets can be directly related to the premium, [Pi]0. (3) Moreover, these results extend to American securities, which have a third component - an additional early-exercise premium.

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  • Ibáñez, Alfredo, 2008. "Factorization of European and American option prices under complete and incomplete markets," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 311-325, February.
    • Handle: RePEc:eee:jbfina:v:32:y:2008:i:2:p:311-325
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    1. Chung, San-Lin & Hung, Mao-Wei & Wang, Jr-Yan, 2010. "Tight bounds on American option prices," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 77-89, January.

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