Revisited Multi-moment Approximate Option
Bertrand Maillet and
FMG Discussion Papers from Financial Markets Group
After the seminal paper of Jarrow and Rudd (1982), several authors have proposed to use different statistical series expansion to price options when the risk-neutral density is asymmetric and leptokurtic. Amongst them, one can distinguish the Gram-Charlier Type A series expansion (Corrado and Su, 1996-b and 1997-b), the log-normal Gram-Charlier series expansion (Jarrow and Rudd, 1982) and the Edgeworth series expansion (Rubinstein, 1998). The purpose of this paper is to compare these different multi-moment approximate option pricing models. We first re-call the link between the risk-neutral density and moments in a general statistical series expansion framework under the martingale hypothesis. We then derive analytical formulae for several four-moment approximate option pricing models, namely, the Jarrow and Rudd (1982), Corrado and Su (1996-b and 1997-b) and Rubinstein (1998) models. We investigate in particular the conditions that ensure the respect of the martingale re-striction (see Longsta ., 1995) and consequently revisit the approximate option pricing models under study. We also get for these models the analytical expressions of implied probability densities, implied volatility smile functions and several hedging parameters of interest.
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed
Downloads: (external link)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:fmg:fmgdps:dp430
Access Statistics for this paper
More papers in FMG Discussion Papers from Financial Markets Group
Series data maintained by The FMG Administration ().