2007
DOI: 10.1016/j.jspi.2006.06.023
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Higher order asymptotic option valuation for non-Gaussian dependent returns

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Cited by 5 publications
(5 citation statements)
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“…Rubinstein (1998) grafts an implied binomial tree onto an Edgeworth density expansion. Tamaki and Tanaguchi (2006) link the Edgeworth density expansion approach to time series moment estimates. Jurczenko, Maillet, and Negrea (2002a, 2000b, 2004 provide a broad overview of the Edgeworth/Gram-Charlier density expansion approach to option valuation along with several key extensions.…”
mentioning
confidence: 99%
“…Rubinstein (1998) grafts an implied binomial tree onto an Edgeworth density expansion. Tamaki and Tanaguchi (2006) link the Edgeworth density expansion approach to time series moment estimates. Jurczenko, Maillet, and Negrea (2002a, 2000b, 2004 provide a broad overview of the Edgeworth/Gram-Charlier density expansion approach to option valuation along with several key extensions.…”
mentioning
confidence: 99%
“…It is clear that if the underlying stock price process deviates much from a semimartingale, there may not be an equivalent martingale measure, based on which an analytical pricing formula can be deduced by applying martingale argument (see Refs 26,27). Yet if such a deviation is not too substantial, the usual expectation of discounted terminal contingent claim under the ‘risk neutral measure’ can still serve as a proxy of the fair price of the contingent claim (see Refs 28–30). To this end, let { P t : t ≥ 0} be the price process, under the ‘risk neutral measure’, of the underlying stock at the trading time t , so that its terminal price P T at the maturity date T is given by: where X j is the j th period log return, T 0 is the present time, r is the risk‐free interest rate, τ = T − T 0 , N = τ/ Δ is the number of unit time intervals each of length Δ.…”
Section: Edgeworth Expansionmentioning
confidence: 99%
“…In financial literature, a significant number of empirical studies shows that these X j 's are not necessarily independent, for example, X j may follow an ARCH or GARCH process. Under certain technical conditions (see (A1) to (A3) in Tamaki and Taniguchi30), even for dependent process X j , by applying similar argument leading to (6), we can also derive an Edgeworth expansion of the density g ( z ) of \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$Z \triangleq \left( 2\pi N f_{X,2} \right)^{-\frac{1}{2}} \sum_{j=1}^N X_j$\end{document}: where f X,k is the k th order cumulant spectral density evaluated at frequency 0: and c X,k ( u 1 , …,u k −1 ) is the k th order joint cumulant, and By substituting this Edgeworth expansion in place of the ‘risk‐neutral density’ in the expectation of discounted terminal contingent claim, say for the European call option, we come up with an approximate option ‘price’ C (see Ref 30 for further details): where for any integer k > 0. Note that G 0 is just the ordinary Black–Scholes formula for a vanilla European call, and the rest of the other terms are asymptotic adjustments for skewness and kurtosis.…”
Section: Edgeworth Expansionmentioning
confidence: 99%
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“…In this paper, we extend the discretized Vasicek model following the approach of Tamaki and Taniguchi (2007). The short rate model is expressed as follows:…”
Section: The Short Rate Models and Assumptionsmentioning
confidence: 99%