AN INTRODUCTION TO FINANCIAL OPTION VALUATION
CONTENTS OPTIONS WHAT ARE OPTIONS? WHY DO WE STUDY OPTIONS? HOW ARE OPTIONS TRADED? TYPICAL OPTION PRICES OTHER ?NANCIAL DERIVATIVES NOTES AND REFERENCES PROGRAM OF CHAPTER 1 AND WALKTHROUGH OPTION VALUATION PRELIMINARIES MOTIVATION INTEREST RATES SHORT SELLING ARBITRAGE PUT–CALL PARITY UPPER AND LOWER BOUNDS ON OPTION VALUES PROGRAM OF CHAPTER 2 AND WALKTHROUGH RANDOM VARIABLES RANDOM VARIABLES, PROBABILITY AND MEAN INDEPENDENCE VARIANCE NORMAL DISTRIBUTION CENTRAL LIMIT THEOREM PROGRAM OF CHAPTER 3 AND WALKTHROUGH COMPUTER SIMULATION PSEUDO-RANDOM NUMBERS STATISTICAL TESTS PROGRAM OF CHAPTER 4 AND WALKTHROUGH ASSET PRICE MOVEMENT EF?CIENT MARKET HYPOTHESIS ASSET PRICE DATA ASSUMPTIONS PROGRAM OF CHAPTER 5 AND WALKTHROUGH ASSET PRICE MODEL: PART I DISCRETE ASSET MODEL CONTINUOUS ASSET MODEL LOGNORMAL DISTRIBUTION FEATURES OF THE ASSET MODEL PROGRAM OF CHAPTER 6 AND WALKTHROUGH ASSET PRICE MODEL: PART II COMPUTING ASSET PATHS TIMESCALE INVARIANCE SUM-OF-SQUARE RETURNS PROGRAM OF CHAPTER 7 AND WALKTHROUGH BLACK–SCHOLES PDE AND FORMULAS SUM-OF-SQUARE INCREMENTS FOR ASSET PRICE HEDGING BLACK–SCHOLES PDE BLACK–SCHOLES FORMULAS PROGRAM OF CHAPTER 8 AND WALKTHROUGH MORE ON HEDGING DISCRETE HEDGING DELTA AT EXPIRY LARGE-SCALE TEST LONG-TERM CAPITAL MANAGEMENT NOTES PROGRAM OF CHAPTER 9 AND WALKTHROUGH 10 THE GREEKS THE GREEKS INTERPRETING THE GREEKS BLACK–SCHOLES PDE SOLUTION PROGRAM OF CHAPTER 10 AND WALKTHROUGH 11 MORE ON THE BLACK–SCHOLES FORMULAS WHERE IS µ? TIME DEPENDENCY THE BIG PICTURE CHANGE OF VARIABLES PROGRAM OF CHAPTER 11 AND WALKTHROUGH 12 RISK NEUTRALITY EXPECTED PAYOFF RISK NEUTRALITY PROGRAM OF CHAPTER 12 AND WALKTHROUGH 13 SOLVING A NONLINEAR EQUATION GENERAL PROBLEM BISECTION NEWTON FURTHER PRACTICAL ISSUES PROGRAM OF CHAPTER 13 AND WALKTHROUGH 14 IMPLIED VOLATILITY IMPLIED VOLATILITY OPTION VALUE AS A FUNCTION OF VOLATILITY BISECTION AND NEWTON IMPLIED VOLATILITY WITH REAL DATA PROGRAM OF CHAPTER 14 AND WALKTHROUGH 15 MONTE CARLO METHOD MONTE CARLO MONTE CARLO FOR OPTION VALUATION MONTE CARLO FOR GREEKS PROGRAM OF CHAPTER 15 AND WALKTHROUGH 16 BINOMIAL METHOD METHOD DERIVING THE PARAMETERS BINOMIAL METHOD IN PRACTICE PROGRAM OF CHAPTER 16 AND WALKTHROUGH 17 CASH-OR-NOTHING OPTIONS CASH-OR-NOTHING OPTIONS BLACK–SCHOLES FOR CASH-OR-NOTHING OPTIONS DELTA BEHAVIOUR RISK NEUTRALITY FOR CASH-OR-NOTHING OPTIONS PROGRAM OF CHAPTER 17 AND WALKTHROUGH 18 AMERICAN OPTIONS AMERICAN CALL AND PUT BLACK–SCHOLES FOR AMERICAN OPTIONS BINOMIAL METHOD FOR AN AMERICAN PUT OPTIMAL EXERCISE BOUNDARY MONTE CARLO FOR AN AMERICAN PUT PROGRAM OF CHAPTER 18 AND WALKTHROUGH 19 EXOTIC OPTIONS BARRIER OPTIONS LOOKBACK OPTIONS ASIAN OPTIONS BERMUDAN AND SHOUT OPTIONS MONTE CARLO AND BINOMIAL FOR EXOTICS PROGRAM OF CHAPTER 19 AND WALKTHROUGH 20 HISTORICAL VOLATILITY MONTE CARLO-TYPE ESTIMATES ACCURACY OF THE SAMPLE VARIANCE ESTIMATE MAXIMUM LIKELIHOOD ESTIMATE OTHER VOLATILITY ESTIMATES EXAMPLE WITH REAL DATA PROGRAM OF CHAPTER 20 AND WALKTHROUGH 21 MONTE CARLO PART II: VARIANCE REDUCTION BY ANTITHETIC VARIATES DEPENDENCE ANTITHETIC VARIATES: UNIFORM EXAMPLE ANALYSIS OF THE UNIFORM CASE NORMAL CASE MULTIVARIATE CASE ANTITHETIC VARIATES IN OPTION VALUATION 21 10 PROGRAM OF CHAPTER 21 AND WALKTHROUGH 22 MONTE CARLO PART III: VARIANCE REDUCTION BY CONTROL VARIATES CONTROL VARIATES CONTROL VARIATES IN OPTION VALUATION PROGRAM OF CHAPTER 22 AND WALKTHROUGH 23 FINITE DIFFERENCE METHODS FINITE DIFFERENCE OPERATORS HEAT EQUATION DISCRETIZATION FTCS AND BTCS LOCAL ACCURACY VON NEUMANN STABILITY AND CONVERGENCE CRANK–NICOLSON 23 10 PROGRAM OF CHAPTER 23 AND WALKTHROUGH 24 FINITE DIFFERENCE METHODS FOR THE BLACK–SCHOLES PDE FTCS, BTCS AND CRANK–NICOLSON FOR BLACK–SCHOLES DOWN-AND-OUT CALL EXAMPLE BINOMIAL METHOD AS ?NITE DIFFERENCES PROGRAM OF CHAPTER 24 AND WALKTHROUGH THREE MONTHS FROM NOW AFTER THOSE THREE MONTHS HAVE ELAPSED, YOU WOULD THEN TAKE ONE OF TWO ACTIONS: (A) IF THE ACTUAL VALUE OF 100 IBM SHARES TURNS OUT TO BE MORE THAN $1000 YOU WOULD EXER- CISE YOUR RIGHT TO BUY THE SHARES FROM PROFESSOR SMART – BECAUSE YOU COULD IMMEDIATELY SELL THEM FOR A PRO?T