Option pricing where the underlying assets follow a Gram/Charlier density of arbitrary order

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dc.contributor.author Schlogl, E
dc.date.accessioned 2014-04-03T01:53:34Z
dc.date.issued 2013-01
dc.identifier.citation Journal of Economic Dynamics and Control, 2013, 37 (3), pp. 611 - 632
dc.identifier.issn 0165-1889
dc.identifier.other C1 en_US
dc.identifier.uri http://hdl.handle.net/10453/23442
dc.description.abstract If a probability distribution is sufficiently close to a normal distribution, its density can be approximated by a Gram/Charlier Series A expansion. In option pricing, this has been used to fit risk-neutral asset price distributions to the implied volatility smile, ensuring an arbitrage-free interpolation of implied volatilities across exercise prices. However, the existing literature is restricted to truncating the series expansion after the fourth moment. This paper presents an option pricing formula in terms of the full (untruncated) series and discusses a fitting algorithm, which ensures that a series truncated at a moment of arbitrary order represents a valid probability density. While it is well known that valid densities resulting from truncated Gram/Charlier Series A expansions do not always have sufficient flexibility to fit all market-observed option prices perfectly, this paper demonstrates that option pricing in a model based on these densities is as tractable as the (far less flexible) original model of Black and Scholes (1973), allowing non-trivial higher moments such as skewness, excess kurtosis and so on to be incorporated into the pricing of exotic options: Generalising the Gram/Charlier Series A approach to the multiperiod, multivariate case, a model calibrated to standard option prices is developed, in which a large class of exotic payoffs can be priced in closed form. Furthermore, this approach, when applied to a foreign exchange option market involving several currencies, can be used to ensure that the volatility smiles for options on the cross exchange rate are constructed in a consistent, arbitrage-free manner
dc.publisher Elsevier Inc
dc.relation.isbasedon 10.1016/j.jedc.2012.10.001
dc.title Option pricing where the underlying assets follow a Gram/Charlier density of arbitrary order
dc.type Journal Article
dc.parent Journal of Economic Dynamics and Control
dc.journal.volume 3
dc.journal.volume 37
dc.journal.number 3 en_US
dc.publocation Amsterdam, Netherlands en_US
dc.identifier.startpage 611 en_US
dc.identifier.endpage 632 en_US
dc.cauo.name BUS.Finance en_US
dc.conference Verified OK en_US
dc.for 1502 Banking, Finance and Investment
dc.for 1402 Applied Economics
dc.for 1401 Economic Theory
dc.personcode 990337
dc.percentage 34 en_US
dc.classification.name Economic Theory en_US
dc.classification.type FOR-08 en_US
dc.edition en_US
dc.custom en_US
dc.date.activity en_US
dc.location.activity en_US
dc.description.keywords Hermite expansion; Semi-nonparametric estimation; Risk-neutral density; Option-implied distribution; Exotic option; Currency option en_US
dc.description.keywords Hermite expansion
dc.description.keywords Semi-nonparametric estimation
dc.description.keywords Risk-neutral density
dc.description.keywords Option-implied distribution
dc.description.keywords Exotic option
dc.description.keywords Currency option
pubs.embargo.period Not known
pubs.organisational-group /University of Technology Sydney
pubs.organisational-group /University of Technology Sydney/Faculty of Business
pubs.organisational-group /University of Technology Sydney/Faculty of Business/Finance
pubs.organisational-group /University of Technology Sydney/Strength - Quantitative Finance
utslib.copyright.status Closed Access
utslib.copyright.date 2015-04-15 12:17:09.805752+10
utslib.collection.history Finance (ID: 371)
utslib.collection.history Closed (ID: 3)

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