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Basic Black-Scholes: option pricing and trading

Author: Crack, Timothy Falcon Publisher: Timothy Falcon Crack, 2009.Edition: Revised 2nd ed.Language: EnglishDescription: 236 p. : Graphs ; 28 cm.ISBN: 9780970055248Type of document: BookBibliography/Index: Includes bibliographical references and index
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print HG6024 .A3 C73 2009
(Browse shelf)
001258554
Available 001258554
Total holds: 0

Includes bibliographical references and index

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Basic Black-Scholes: Options Pricing and Trading Contents Preface Tables Figures 1 Introduction to Options ix xi xiii 1 1.1 Hedging. Speculation, and Arbitrage...................................................................... 4 1.2 Forwards, Futures. and Options............................................................................... 5 1.3 Introductory Option Examples ............................................................................... 8 1.3.1 Buying a Protective Put............................................................................... 8 1.3.2 Introduction to Transactions Costs (T-Costs)........................................... 10 1.3.3 Buying a Speculative Call ......................................................................... 13 2 Mathematics, Statistics, and Finance Prerequisites 15 2.1 Logarithms and Exponentials ............................................................................... 15 2.1.1 Logarithins ................................................................................................ 15 2.1.2 Exponentials ............................................................................................. 16 2.1.3 Inverse Properties...................................................................................... 16 2.2 Normality ami Lognormality ................................................................................ 19 2.2.1 Normal Distribution .................................................................................. 19 2.2.2 Lognormal Distribution ............................................................................ 19 2.2.3 Inverse and Other Properties.................................................................... 21 2.2.4 Z-Score and Cumulative Standard Normal .............................................. 25 2.3 Expected Values ................................................................................................... 26 2.3.1 Conditional Expected Values ................................................................... 27 2.4 Rates of Return ..................................................................................................... 28 2.4.1 Statistical/Distributional Arguments ........................................................ 28 2.4.2 Continuously Compounded Returns ........................................................ 30 2.4.3 Pricing Forwards/Futures with Continuons Dividemis . . . ...................... 31 2.5 Other Prerequisites 34 2.5.1 Equilibrium versus No-Arbitrage .............................................................. 34 2.5.2 Percent ...................................................................................................... 35 2.5.3 Binomial Coefficients 35 2.5.4 Ex-Dividend Process ............................................................................... 36 3 Option Pricing Foundations 39 3.1 Factors Affecting Option Prices ........................................................................... 39 3.2 Payoffs and Payoff Diagrams ............................................................................... 40 3.3 Directionally Correct ............................................................................................ 42 3.4 Call Options: Restrictions ..................................................................................... 48 3.4.1 Demonstration and Discussion of Call Restrictions ................................ 50 3.5 Put Options: Restrictions ...................................................................................... 52 3.5.1 Demonstration and Discussion of Put Restrictions ................................. 53 3.6 Put-Call Parity ....................................................................................................... 54 3.6.1 Synthetic Instruments and Arbitrage ....................................................... 55 3.6.2 Leverage and Insurance ........................................................................... 55 3.6.3 Plotting Put-Cali Parity ............................................................................ 57 3.6.4 American-Style Put-Call Parity ............................................................... 58 3.6.5 Put-Call Parity "Regrets" Decompositions .............................................. 62 3.6.6 Put-Call Parity Intrinsic Value Decomposition ........................................ 65 4 Risk-Neutral Option Pricing 67 4.1 The Simple Answer: Traditional Methods Fail ..................................................... 67 4.2 Replication ............................................................................................................ 68 4.3 The Formula .......................................................................................................... 70 4.4 Risk-Neutral Pricing Review................................................................................. 71 4.4.1 First Method (Merton [1973]) ................................................................... 73 4.4.2 Second Method (Cox and Ross [1976]) .................................................... 75 4.4.3 Third Method (Harrison and Kreps [1979]) ............................................. 76 4.5 The Complex Answer: Non-Traditional Methods ................................................ 77 5 Numerical Option Pricing: Monte Carlo 79 5.1 Do I Need to Know This? ..................................................................................... 79 5.2 Monte Carlo Methods ........................................................................................... 79 5.3 Monte Carlo in Science ......................................................................................... 80 5.4 Monte Carlo for Options ....................................................................................... 83 5.4.1 Overview of the Method ........................................................................... 84 5.4.2 Generating Stock Price Paths .................................................................... 84 5.4.3 Monte Carlo Put Option Example ............................................................ 84 5.4.4 Variance Reduction ................................................................................... 85 5.4.5 Drift and Dividends .................................................................................. 88 6 Numerical Option Pricing: Lattice/Binomial 89 6.1 Do I Need to Know This? ..................................................................................... 89 6.2 Lattice Pricing I: One-Step Model ........................................................................ 89 6.3 Lattice Pricing II: J-Step Model ............................................................................ 93 6.3.1 Choosing u and d--and Deducing n* ....................................................... 93 6.3.2 Binomial Valuation Example .................................................................... 95 6.4 Lattice Pricing III: American Options ................................................................. 99 6.5 Adjusting for Dividends ...................................................................................... 99 7 Partial Differential Equations 103 7.1 Do I Need to Know This? .................................................................................. 103 7.2 PDEs 101 ........................................................................................................... 103 7.3 Where Do Financial PDEs Come From? ........................................................... 104 7.4 Transforming the PDE ....................................................................................... 104 7.5 PDE Solution by Finite Differences .................................................................. 106 7.6 PDE Interpretation: Greeks 101 ........................................................................ 107 8 Analytical Option Pricing: Black-Scholes 111 8.1 Black-Scholes Assumptions .............................................................................. 111 8.1.1 A Note on Concavity and Geometric Averages ..................................... 115 8.2 Black-Scholes Derivation ................................................................................... 116 8.3 Black-Scholes Interpretations and Intuition ....................................................... 120 8.3.1 Interpretation I: Recipe for Replication .................................................. 120 8.3.2 Interpretation II: DCF, Cost/Benefit ...................................................... 121 8.3.3 Interpretation III: Binomial Limit .......................................................... 124 8.3.4 Interpretation IV: Stock-Numeraire ....................................................... 126 8.3.5 Interpretation V: Digital (Binary) Options.............................................. 130 8.3.6 Interpretation VI: Conditional Payoffs ................................................... 130 8.3.7 Interpretation VII: PDE Solution ............................................................ 135 8.3.8 Interpretation VIII: See figure 3.3 .......................................................... 136 8.4 Approximations to Black-Scholes ...................................................................... 136 8.4.1 Louis Jean Baptiste Alphonse Bachelier (1900) .................................... 137 8.5 Immediate Extensions ......................................................................................... 139 8.5.1 Index: Merton (1973) .............................................................................. 139 8.5.2 Futures: Black (1976b) ........................................................................... 140 8.5.3 FX: Garman and Kohlhagen (1983) and Grabbe (1983) . . .................... 140 8.6 Application: The Adequation Formula for FX Option Parity . . . ...................... 141 8.7 Black-Scholes Implementation ........................................................................... 142 8.7.1 Method I: Estimate Historical o- ............................................................ 145 8.7.2 Method II: Infer Market Forecast o- ....................................................... 146 8.8 Synthetic Options: Greeks 102 ........................................................................... 147 8.8.1 Delta Hedging ......................................................................................... 149 8.8.2 Delta-Gamma (and Theta) Hedging ....................................................... 149 9 Beyond Black-Scholes 153 9.1 American-Style Options ..................................................................................... 153 9.1.1 Approximate Analytical Pricing ............................................................. 154 9.1.2 Exact Analytical Pricing ......................................................................... 155 9.2 Some New Formulae ........................................................................................... 158 9.2.1 Arithmetic Brownian Motion ................................................................. 158 9.2.2 Power Option I: Crack (1997) ................................................................ 163 9.2.3 Power Option II: Crack (1997. 2008) .................................................... 164 9.2.4 Forward on an At-the-Money Option: Crack-Maines (Crack [1997]) 165 9.3 Summary of Option Pricing Methods I: Plain Vanilla versus Exotic Options............................................................... 166 9.4 Otter Data-Generating Processes....................................................................... 166 9.4.1 ·ump Risk. Replication, and Risk-Neutral Pricing ................................ 166 9.4.2 Stochastic V >la t ility........................................................................... 169 9.5 Summary of Option Pricing Methods II: Discret e versus Continuons Models .............................................................. 170 10 Trading 171 10.1 Institutional Details.......................................................................................... 172 10.1.1 Options Specifications.......................................................................... 172 10.1.2 Exchanges, Regulatory Bodies. and Securities ................................... 174 10.1.3 Brokers ................................................................................................. 177 10.1.4 T-Costs ................................................................................................. 178 10.2 Black-Scholes Assumptions and Violations ........................................................................................................ 182 10.3 The Spreadsheet Tools ..................................................................................... 183 10.4 Trading Experiences and Lessons ................................................................... 187 10.4.1 Stylized Facts....................................................................................... 189 10.4.2 Information Sources 193 10.4.3 Other Trading Tips and Tools 194 10.4.4 Orders ami Executions 197 10.4.5 Market Views ami Opinions 198 10.4.6 The Deathly Slow Crawl 198 10.5 Trading Tools: Greeks 103 .............................................................................. 199 10.6 Spread Positions and Other Strategies 199 A HP Source Code A.1 HP17B/HP19B Black-Scindes.......................................................................... A.2 HP12C Black-Scholes....................................................................................... A.3 HP17B/HP19B Binomial Pricing ..................................................................... A.4 An HP17B/HP19B Warning ............................................................................. References for Further Research Abbreviations, Acronyms, and Symbols Alphabets and Numerical Equivalences Index 203 203 206 209 210 211 217 218 219

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