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Hang Seng Index Options in Particular, Are Then Investigated TRADESfG m OPTIONS - AN nvJ-DEPTH ANALYSIS by FU YIU-HANG 傅耀衡 MBA PROJECT REPORT Presented to The Graduate School In Partial Fulfilment ofthe Requirements for the Degree of MASTER OF BUS_SS ADMnvTISTRATION TWO-YEAR MBA PROGRAMME THE CHnSHESE UNIVERSITY OF HONG KONG May 1999 The Chinese University ofHong Kong holds the copyright ofthis project. Any person(s) intending to use a part or whole ofthe materials in the project in a proposed publication must seek copyright release from the Dean ofthe Graduate School. ^^\ € i 1 服 ^ )d • -- 一-一—‘ ‘ I. ：、/i, .., j....•‘、-.":,、，-、/ / 〜•、/•；•( APPROVAL Name: Fu Yiu-Hang Degree: Master ofBusiness Administration Title ofProject: Trading in Options - An In-depth Analysis 知(]LL^ (Prof。Raymond Chiang, Date Approved: C/f^jyJ ii ABSTRACT Aspects of options are analyzed in detail in this paper. The ideas of options, the properties, and various factors affecting the prices are studied. The information has its importance in valuation, arbitrage and applications such as mimic portfolio and create synthetic instrument. Black-Scholes option pricing model is analyzed thoroughly. First, the assumptions of the model are investigated critically. The test on the normality of the rate of retum on Hang Seng Index shows that the distribution of the rate of retum on Hang Seng Index is not exactly a normal distribution. Detail investigations also show that the variance of the rate of retum on Hang Seng Index is not a constant. It changes over time. Moreover, it tends to increase as the index level falls. Nevertheless, the assumptions are good approximations. Volatility is an important variable of the model. An investigation of the predictability of implied volatility versus historical volatility shows that implied volatility has better forecasting power about future volatility. When compared with market prices, clearly the Black-Scholes model has bias. This can be due to its assumptions in building the model. Volatility smile and volatility term structure is the result. Practitioners construct volatility matrices handle the different volatility figures. Other sophisticated option pricing models are analyzed, but none is definitely superior to the Black-Scholes model. The new parameters introduced may create problems about whether the new parameters can be estimated with sufficient accuracy. Practically, the Black-Scholes model is adequate and useful for most applications. The sensitivities of option prices with the factors are also analyzed and then applied to trading strategies. Numerous strategies, with their properties are explored。Moreover, analyses on the profit potential and risk of the strategies are conducted。The monthly transactions generated the maximum profits and losses in the past two years of the main strategies are investigated. The sensitivities ofthe portfolios with the factors are also computed to show the effective way to use those strategies. The results show that each strategy has its strengths and weaknesses. Traders should apply strategies most suitable to their expectations and their degrees ofrisk aversion. In sum, the studies, tests and investigations in the paper provide useful results and insights for researchers and practitioners。 iii TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS iii LIST OF TABLES vi LIST OF EXfflBITS vii PREFACE viii ACKNOWLEDGMENTS . , . • . , .. x Chapter I. ESTTRODUCTION . „. 1 What is an Option? . , 。,. • . 。.. 。. ., „. 1 Options Market .。..。....。..奢,,.,,„ ..,. ..., . , 2 Uses of Options ....。.。。.，，。。，... .,, .。，，, , , 2 Value of Options。。。，..。’。。，。.. ,。..,, . , , „。。，.，，.。,。。，•，..,,.. 3 Index Options 4 Hang Seng Index Options。.。.，。，. .。。. .。.。,。.，. , 4 II. BASIC PROPERTffiS OF OPTIONS 5 Assumptions •. 。。.. 。。。。。。。。。。。。。。。. 。。。。。。。。。. ，. , ,。.。。.。。.。，。。，.。.，。。5 Notation . • , , 。 . • . , , 。 . „ . 。 。 . • . 。 , , • . 。 . , 5 Option Prices at Expiration 6 Call Option Prices at Expiration。。。。。。。。。。。。。。。。。。。，。。，。。 . 6 Put Option Prices at Expiration。。。，。，。。，，。。。。。。.。，。’ . .，. 6 Upper Bounds for Option Prices。。。•, 。,。，。。，。’ 6 Upper Bounds for Call Option Prices . .。。. .。，. , •。。。，.。，6 Upper Bounds for Put Option Prices。。。。，。。。。。..。。。。，,.。.，。。. .. , ..。，, 6 Lower Bounds for European Option Prices。。。. , , . 7 Lower Bounds for European Call Option Prices 7 Lower Bounds for European Put Option Prices .。，. , , . , . 8 Put-Call Parity , . .。.. ,。.。..。。。。.。, . 。。, „ .。. , 8 iv III. FACTORS AFFECTmG OPTION PRICES 10 Price ofUnderlying Instrument 10 Exercise Price of the Option 10 Volatility of the Price ofUnderlying Instrument 11 Time to Expiration . •. 11 Risk-free Rate 11 Dividends 12 W。OPTION PRICnslG MODEL 13 Assumptions , , • 13 The Price ofUnderlying Instrument Follows a Lognormal Distribution 13 The Variance of the Rate of Retum of Underlying Instrument is a Constant . 17 The Risk-free Rate is a Constant 19 No Dividends are Paid 20 There are No Transaction Costs and Taxes 20 The Black-Scholes Option Pricing Model 21 Notation 。, 。. • 。... „ . 21 The Formulas .. 21 The Variables .... 22 Properties of the Black-Scholes Formulas 22 Implied Volatility。，„。。。，。，。。。。.。，.。。，。，.。，. ,, . 23 Bias of the Black-Scholes Option Pricing Model 26 Other Option Pricing Models 27 V. SENSIXrVITIES OF OPTION PRICE TO ITS FACTORS。。，. •。，。。。，，.，,.。. 29 Delta .. 。。. 。.... „ •, 。,. 。。。.. 。。. „ • . , 。. 。, 。 。 。 „,. 。 . • 29 Vega ...。..。..。..。。。.。.。。.。。.. 。,, .。.,。.,. .。. ,。, 。. 。 . 。. 。. ... „, „ , 30 Theta , • .. , „。,。. 。. 。. 。。. ..., 。,.. • 31 Rho .... .。.... .. •.. .. „。。,. .。。. ., ..,. .,, 。. ., ...。.. 32 Gamma • . 。 . 。 „ 。 . 。 , • „. 。 . „., 。 . • . 。 。 。 。 ,, . 33 Managing the Change in the Value ofOption , . .。, .，，. 34 Sensitivities ofPortfolio Value to the Factors。。。。。.，•，。。.，。，，。，，, ,。，’，，，，。34 V VI. TRADD^G STRATEGIES OF OPTIONS 35 Methodology 35 Limitations 36 Basic Strategies 37 Long Call 37 Short Call 39 Long Put 40 Short Put 42 Spread Strategies 43 Money Spread 43 Ratio Spread 46 Box Spread 46 Butterfly Spread 46 Condor 49 Calendar Spread 49 Diagonal Spread 52 Combination Strategies 52 Straddle 52 Strap 54 Strip 54 Strangle . , . .. , . • . 。 54 Selecting Trading Strategies Intelligently . ..。，•,。. 56 VII。 CONCLUSIONS。’。...,,。.。.. • ,. .. 57 APPENDICES . ,. 。 • , . , , „ . 。 . 0 。 。.. ., „ „ „ „ 0 。„ 0 „ 。 0 。 0 0 0 . „ „ „ 。 60 BIBLIOGRAPHY . „ . ,。.。. .,, „ „ 。. „ . 。. „ „ „ . „ „ „ ^ „ , „ 。^ „ „ „ ^, , . 。 , ^ 66 vi LIST OF TABLES TABLE 1 SUMMARY OF THE EFFECT OF THE FACTORS ON EUROPEAN OPTION PRICES 12 TABLE 2 FREQUENCY OF THE RATE OF RETURN 14 TABLE 3 EXPECTED FREQUENCY OF THE RATE OF RETURN 15 TABLE 4 DIFFERENCE Es[ EXPECTED AND ACTUAL FREQUENCY 16 TABLE 5 STANDARD DEVL\TION OF THE DAD^Y RATE OF RETURN ACROSS TIME 18 TABLE 6 STANDARD DEVD^TION OF THE DAILY RATE OF RETURN ACROSS JNDEX LEVEL ..... .。,.,. „. .. .. .. 19 TABLE 7 PREDICTABILITY OF IMPLIED VOLATILITY VERSUS fflSTORICAL VOLATILITY . 25 TABLE 8 RETURN PROFILE OF LONG CALL STRATEGY。• 38 TABLE 9 RETURN PROFILE OF SHORT CALL STRATEGY . 40 TABLE 10 RETURN PROFILE OF LONG PUT STRATEGY 41 TABLE 11 RETURN PROFILE OF SHORT PUT STRATEGY , 42 vii LIST OF EXHIBITS EXfflBIT 1 DISTRIBUTION OF DAILY RATE OF RETURN ON HANG SENG n^DEX 17 EXfflBIT 2 VOLATILITY SMILE FOR HANG SENG ESfDEX OPTIONS • . • . 26 viii PREFACE Derivatives have been developing at a rapid pace. Today, futures，options and swaps are common in every aspect of daily life. Options are special. They have unique characteristics that enable them to be applied in many useful ways. They can also be used as a building block of other financial instrument. In this paper, options and their applications are analyzed in depth. Many properties of options are applicable to many kinds of options. So the coverage of different options is intended to be as board as possible. However, characteristics of options of different kinds may be different in some respects. In case there are differences, Hang Seng Index options would be our benchmark. A benchmark is used to avoid unnecessary conftision in the different characteristics of the wide diverse kinds of options. Index options are chosen because index options are among the most heavily traded options in the world. In particular, Hang Seng Index options are the most popular options in the secondary options market ofHong Kong. In the first chapter, the basic ideas of options are studied. Options market is also investigated. The uses of options are numerous, and they will be explained. Moreover, the value of options is introduced, which is an important topic though out the paper. Index options and Hang Seng Index options in particular, are then investigated. These concepts are vital for further analysis. Chapter two discusses the fundamental properties of options。The value of options at expiration, and the upper bounds and lower bounds of option prices are determined. After that, the put-call parity is derived and its uses explained。These characteristics form the basis of more complicated relationships. In chapter three, the factors affecting option prices are identified. In addition, their effects on option prices are inferred. The approach is to first understand how the factors influence option ix prices at an intuitive level. Then a more rigorous approach will be involved in chapter four, which investigates option pricing in the form of mathematical modeling. In that chapter, option pricing model is analyzed thoroughly. First, assumptions necessary for building the option pricing model are considered and tested for validity. Specifically, a test of normality of rate of retum of Hang Seng Index is conducted. Next，investigations
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