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Valuation of Index Options. Bruce Kelvin Grace Louisiana State University and Agricultural & Mechanical College Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1995 Valuation of Index Options. Bruce Kelvin Grace Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Grace, Bruce Kelvin, "Valuation of Index Options." (1995). LSU Historical Dissertations and Theses. 6102. https://digitalcommons.lsu.edu/gradschool_disstheses/6102 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type o f computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/521-0600 VALUATION OF INDEX OPTIONS A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Interdepartmental Program in Business Administration by Bruce Kelvin Grace B.S., University of New Orleans, 1984 M.B.A., University of New Orleans, 1985 December 1995 UMI Number: 9618292 UMI Microform 9618292 Copyright 1996, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 ACKNOWLEDGEMENTS I wish to thank my dissertation committee chairman, Gary Sanger for all of his help on this dissertation. In addition, Edward Blomeyer, G. Geoffrey Booth, R. Carter Hill, Ji-Chai Lin, and Alvin Schupp provided invaluable help. My colleagues, such as David DeBoeuf and Raymond So, helped to keep my sanity. To others I might have overlooked, thanks. TABLE OF CONTENTS ACKNOWLEDGEMENTS............................................... LIST OF TABLES.............................................................. ABSTRACT....................................................................... INTRODUCTION........................................................................................................... 1 CHAPTER 1 THE VALUE OF EARLY EXERCISE IN STANDARD AND POOR’S 100 INDEX O PTIONS................................................................................................... 7 1.1 Literature Review ................................................................................... 7 1.2 Method of Analysis ............................................................................... 15 1.3 Data ........................................................................................................ 17 1.4 Econometric Models ............................................................................ 21 1.5 Empirical Results ................................................................................. 28 1.6 Chapter 1 Summary ............................................................................... 37 CHAPTER 2 MARKET EFFICIENCY AND RISK-FREE ARBITRAGE OPPORTUNITIES IN THE STANDARD AND POOR’S 100 INDEX OPTION MARKET....................................................................................... 38 2.1 Literature Review ................................................................................. 38 2.2 Method of A nalysis .............................................................................. 48 2.2.1 Synthetic Index ........................................................................ 49 2.2.2 Futures .................................................................................... 52 2.2.3 Stock Portfolios ...................................................................... 54 2.2.4 Transactions Costs ................................................................. 55 2.3 Data ....................................................................................................... 57 2.4 Tests ....................................................................................................... 59 2.4.1 American Boundaries ............................................................ 59 2.4.2 Black-Scholes Model Prices .................................................. 63 2.4.3 Black-Scholes Plus the Value of Early Exercise ............... 63 2.4.4 Binomial Option Pricing Model .......................................... 64 2.5 Chapter 2 Summary .............................................................................. 66 CHAPTER 3 PRICE DISCOVERY AND INDEX OPTIONS....................................................... 70 3.1 Literature Review ................................................................................ 70 iii 3.2 Method of A nalysis ................................................................................ 75 3.3 Data ....................................................................................................... 82 3.4 T e s ts ....................................................................................................... 83 3.5 Chapter 3 Summary............................................................................... 94 CONCLUSION............................................................................................................. 96 BIBLIOGRAPHY ........................................................................................................ 98 APPENDIX A ................................................................................................................. 103 APPENDIX B ................................................................................................................. 104 V IT A ................................................................................................................................ 105 iv LIST OF TABLES Table 1. Generalized Least Squares Estimates Using Prais-Winsten Two-step Estimators for: A = b0 + bjf(S - X) + b2g(T) + b3h(r) + £ Where Calls are in-the-money and A > 0 All Data Are Included Except Where DT > X(1 - e'rT) .......................................... 30 Table la. Generalized Least Squares Estimates Using Prais-Winsten Two-step Estimators for: A = b0 + b,f(S - X) + b2g(T) + b3h(r) + e Where Calls Are in-the-money and A > 0, All Data Are Included ....................... 31 Table lb. Generalized Least Squares Estimates Using Prais-Winsten Two-step Estimators for: A = b0 + b,f(S - X) + b2g(T) + b3h(r) + £ Where Puts Are in-the-money and A < 0 ................................................................. 31 Table 2. Random Coefficient Model Estimates of Ait = Poi, + Pii,f(Sit - Xit) + p2ilg(Tit) + P3ilh(rit) + P4iti(oit) + uit For Calls in-the-money and A > 0 All Data Are Included Except Where Dx > X(1 - e'*1) .......................................... 33 Table 2a. Random Coefficient Model Estimates of Ait = Poit + PiiASn - Xit) + P2ilg(Tit) + P3ilh(rit) + p4iti(Oil) + ujt For Calls in-the-money and A > 0, All Data Are Included ................................... 33 Table 2b. Random Coefficient Model Estimates of Ait = Poi, + Ptilf(Sit - Xu) + p2itg(Tit) + P3ith(rit) + P4iti(ait) + uit For Puts in-the-money and A < 0 ............................................................................. 34 Table 3. Hsiao Random Coefficient Model Estimates of [Abs(BS Call - Actual)]it = poit + P,j,[Abs(BS Call + A - Actual)] + uit ............... 35 Table 4. Hsiao Random Coefficient Model Estimates of [Abs(BS Put - Actual)]h = p0il + pm[Abs(BS Put + A - Actual)] + uj t .................. 36 Table 5. Average Values of Calls and the Estimated Value of Early Exercise ................................................................................................................ 36 Table 6. Average Values of Puts and the Estimated Value of Early Exercise ................................................................................................................ 37 Table 7. Final Payoffs for an Option Arbitrage With a Written Call, Purchased Put, and an Amount Borrowed Proxying for the Shorted Underlying Security .....................................................................................................
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