Exotic Options Trading

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1 Exotic Options Trading Frans de Weert John Wiley & Sons, Ltd

2 Preface Acknowledgements 1 Introduction 2 Conventional Options, Forwards and Greeks 2.1 Call and Put Options and Forwards 2.2 Pricing Calls and Puts 2.3 Implied Volatility 2.4 Determining the Strike of the Forward 2.5 Pricing of Stock Options Including Dividends 2.6 Pricing Options in Terms of the Forward 2.7 Put-Call Parity 2.8 Delta 2.9 Dynamic Hedging 2.10 Gamma 2.11 Vega 2.12 Theta 2.13 Higher Order Derivatives Like Vanna and Vomma 2.14 Options' Interest Rate Exposure in Terms of Financing the Delta Hedge xi xiii Profit on Gamma and Relation to Theta 23 4 Delta Cash and Gamma Cash Example: Delta and Gamma Cash 26

3 vi Contents Skew Reasons for Higher Realised Volatility in Falling Markets Skew Through Time: 'The Term Structure of Skew' Skew and its Effect on Delta Skew in FX versus Skew in Equity: 'Smile versus Downward Sloping' Pricing Options Using the Skew Curve 34 6 Simple Option Strategies 6.1 Call Spread 6.2 Put Spread 6.3 Collar 6.4 Straddle 6.5 Strangle Monte Carlo Processes Monte Carlo Process Principle Binomial Tree versus Monte Carlo Process Binomial Tree Example The Workings of the Monte Carlo Process 48 8 Chooser Option Pricing Example: Simple Chooser Option Rationale Behind Chooser Option Strategies 51 9 Digital Options Choosing the Strikes The Call Spread as Proxy for the Digital Width of the Call Spread versus Gearing Barrier Options Down-and-In Put Option Delta Change over the Barrier for a Down-and-In Put Option Factors Influencing the Magnitude of the Barrier Shift Delta Impact of a Barrier Shift Situations to Buy Shares in Case of a Barrier Breach of a Long Down-and-In Put 63

4 10.6 Up-and-Out Call Up-and-Out Call Option with Rebate Vega Exposure Up-and-Out Call Option Up-and-Out Put Barrier Parity Barrier at Maturity Only Skew and Barrier Options Double Barriers Forward Starting Options Forward Starting and Regular Options Compared Hedging the Skew Delta of the Forward Start Option The Forward Start Option and the Skew Term Structure Analytically Short Skew but Dynamically No Skew Exposure Forward Starting Greeks, Ladder Options Example: Ladder Option Pricing the Ladder Option Lookback Options Pricing and Gamma Profile of Fixed Strike Lookback Options Pricing and Risk of a Floating Strike Lookback Option Cliquets The Ratchet Option Risks of a Ratchet Option Reverse Convertibles Example: Knock-in Reverse Convertible Pricing the Knock-in Reverse Convertible Market Conditions for Most Attractive Coupon Hedging the Reverse Convertible Autocallables Example: Autocallable Reverse Convertible 93

5 16.2 Pricing the Autocallable Autocallable Pricing without Conditional Coupon Interest/Equity Correlation within the Autocallable Callable and Puttable Reverse Convertibles Pricing the Callable Reverse Convertible Pricing the Puttable Reverse Convertible Asian Options Pricing the Geometric Asian Out Option Pricing the Arithmetic Asian Out Option Delta Hedging the Arithmetic Asian Out Option Vega, Gamma and Theta of the Arithmetic Asian Out Option Delta Hedging the Asian in Option Asian in Forward Pricing the Asian in Forward Asian in Forward with Optional Early Termination Quanto Options Pricing and Correlation Risk of the Option Hedging FX Exposure on the Quanto Option Composite Options An Example of the Composite Option Hedging FX Exposure on the Composite Option Outperformance Options Example of an Outperformance Option Outperformance Option Described as a Composite Option Correlation Position of the Outperformance Option Hedging of Outperformance Options Best of and Worst of Options Correlation Risk for the Best of Option Correlation Risk for the Worst of Option Hybrids 138

6 23 Variance Swaps Variance Swap Payoff Example Replicating the Variance Swap with Options Greeks of the Variance Swap Mystery of Gamma Without Delta Realised Variance Volatility versus Standard Deviation Event Risk of a Variance Swap versus a Single Option Relation Between Vega Exposure and Variance Notional Skew Delta Vega Convexity Dispersion Pricing Basket Options Basket Volatility Derived From-its Constituents Trading Dispersion Quoting Dispersion in Terms of Correlation Dispersion Means Trading a Combination of Volatility and Correlation Ratio'd Vega Dispersion Skew Delta Position Embedded in Dispersion Engineering Financial Structures Capital Guaranteed Products Attractive Market Conditions for Capital Guaranteed Products Exposure Products for the Cautious Equity Investor Leveraged Products for the Risk Seeking Investor 163 Appendix A Variance of a Composite Option and Outperformance Option 167 Appendix B Replicating the Variance Swap 169 Bibliography 175 Index 177

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