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APPROXIMATION OF LONG MEMORY PROCESS BY SHORT MEMORY PROCESS - with Application to Option Valuation

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dc.contributor.advisor Mullhaupt, Andrew en_US
dc.contributor.author Shao, Pengyuan en_US
dc.contributor.other Department of Applied Mathematics and Statistics en_US
dc.date.accessioned 2017-09-20T16:50:01Z
dc.date.available 2017-09-20T16:50:01Z
dc.date.issued 2013-12-01 en_US
dc.identifier.uri http://hdl.handle.net/11401/76316 en_US
dc.description 115 pgs en_US
dc.description.abstract Options on an asset which follow a long memory process are difficult to value by conventional methods, due to the existence of arbitrage opportunities. Here we show how to avoid the problem of arbitrage opportunities and value vanilla European options when underlying asset returns follow a FARIMA(<italic>p</italic>,<italic>d</italic>,<italic>q</italic>) processes with <italic>d</italic>>0 which is widely used as an model of long memory price processes. We use information distance to prove that stationary ARMA processes are dense in all FARIMA processes in the total variation distance. As a consequence, statistical tests with finite sample size fail to distinguish a FARIMA process from ARMA processes. As option values are a special case of statistical test, the well understood option values for a sufficiently close stationary ARMA process can be taken as option values for the FARIMA process, with very low probability of error. We provide Monte Carlo experiments that confirm that long memory processes are not easily distinguished from our approximate ARMA processes with finite sample sizes using a variety of well known statistical tests. We examine how long memory affects the option values and implied volatility surface. Finally we examine high frequency data for equities and spot foreign exchange rates for evidence of long memory effects. en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Applied mathematics en_US
dc.subject.other long memory process, option valuation, short memory process, statistical inference en_US
dc.title APPROXIMATION OF LONG MEMORY PROCESS BY SHORT MEMORY PROCESS - with Application to Option Valuation en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Mullhaupt, Andrew en_US
dc.contributor.committeemember Rachev, Svetlozar en_US
dc.contributor.committeemember Lindquist, Brent en_US
dc.contributor.committeemember Bishop, Christopher en_US
dc.contributor.committeemember Kim, Young Shin Aaron en_US


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