Type
Text
Type
Dissertation
Advisor
Mullhaupt, Andrew | Rachev, Svetlozar | Lindquist, Brent | Bishop, Christopher | Kim, Young Shin Aaron.
Date
2013-12-01
Keywords
long memory process, option valuation, short memory process, statistical inference | Applied mathematics
Department
Department of Applied Mathematics and Statistics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76316
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
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(p,d,q) processes with d>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. | 115 pages
Recommended Citation
Shao, Pengyuan, "APPROXIMATION OF LONG MEMORY PROCESS BY SHORT MEMORY PROCESS - with Application to Option Valuation" (2013). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2240.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2240