Long Memory Options: Valuation

Sutthisit Jamdee and Cornelis Los
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Sutthisit Jamdee: Kent State University

Finance from University Library of Munich, Germany

Abstract: This paper graphically demonstrates the significant impact of the observed financial market persistence, i.e., long term memory or dependence, on European option valuation. Many empirical researchers have observed non-Fickian degrees of persistence or long memory in the financial markets different from the Fickian neutral independence (i.i.d.) of the returns innovations assumption of Black-Scholes' geometric Brownian motion assumption. Moreover, Elliott and van der Hoek (2003) have now also provided a theoretical framework for incorporating these findings in the Black-Scholes risk-neutral valuation framework. This paper provides the first graphical demonstration why and how such long term memory phenomena change European option values and provides thereby a basis for informed long term memory arbitrage. Risk-neutral valuation is equivalent to valuation by real world probabilities. By using a mono-fractional Brownian motion, it is easy to incorporate the various degrees of persistence into the binomial and Black-Scholes pricing formulas. Long memory options are of considerable importance in Corporate remuneration packages, since warrants are written on a company's own shares for long expiration periods. Therefore, we recommend that for a proper valuation of such warrants, the degrees of persistence of the companies' share markets are measured and properly incorporated in the warrant valuation.

Keywords: Options; Long Memory; Persistence; Hurst Exponent; Executive Remuneration (search for similar items in EconPapers)
JEL-codes: C14 G14 G15 G33 (search for similar items in EconPapers)
Date: 2004-09-18
New Economics Papers: this item is included in nep-fin
Note: Type of Document - pdf. Jamdee, Sutthisit and Los, Cornelis A., 'Long Memory Options: Valuation' (September 9, 2004).
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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpfi:0409049

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