Contents

**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 Option’s Interest Rate Exposure in Terms of Financing the Delta Hedge

**3 Profit on Gamma and Relation to Theta**

**4 Delta Cash and Gamma Cash**

4.1 Example Delta and Gamma Cash

**5 Skew**

5.1 Reasons for Higher Realised Volatility in Falling Markets

5.2 Skew Through Time: ‘The Term Structure of Skew’

5.3 Skew and Its Effect on Delta

5.4 Skew in FX versus Skew in Equity: ‘Smile versus Downward Sloping’

5.5 Pricing Options Using the Skew Curve

**6 Simple Option Strategies**

6.1 Call Spread

6.2 Put Spread

6.3 Collar

6.4 Straddle

6.5 Strangle

**7 Monte Carlo Processes**

7.1 Monte Carlo Process Principle

7.2 Binomial Tree versus Monte Carlo Process

7.3 Binomial Tree Example

7.4 The Workings of the Monte Carlo Process

**8 Chooser Option**

8.1 Pricing Example Simple Chooser Option

8.2 Rationale Behind Chooser Option Strategies

**9 Digital Options**

9.1 Choosing the Strikes

9.2 The Call Spread as Proxy for the Digital

9.3 Width of the Call Spread versus Gearing

**10 Barrier Options**

10.1 Down-and-In Put Option

10.2 Delta Change over the Barrier for a Down-and-In Put Option

10.3 Factors Influencing the Magnitude of the Barrier Shift

10.4 Delta Impact of a Barrier Shift

10.5 Situations to Buy Shares in Case of a Barrier Breach of a Long Down-and-In Put

10.6 Up-and-Out Call

10.7 Up-and-Out Call Option with Rebate

10.8 Vega Exposure Up-and-Out Call Option

10.9 Up-and-Out Put

10.10 Barrier Parity

10.11 Barrier at Maturity Only

10.12 Skew and Barrier Options

10.13 Double Barriers

**11 Forward Starting Options**

11.1 Forward Starting and Regular Option Compared

11.2 Hedging the Skew Delta of the Forward Start Option

11.3 The Forward Start Option and the Skew Term Structure

11.4 Analytically Short Skew but Dynamically No Skew Exposure

11.5 Forward Starting Greeks

**12 Ladder Options**

12.1 Example Ladder Option

12.2 Pricing the Ladder Option

**13 Lookback Options**

13.1 Pricing and Gamma Profile of Fixed Strike Lookback Options

13.2 Pricing and Risk of a Floating Strike Lookback Option

**14 Cliquets**

14.1 The Ratchet Option

14.2 Risks of a Ratchet Option

**15 Reverse Convertibles**

15.1 Example Knock-in Reverse Convertible

15.2 Pricing the Knock-in Reverse Convertible

15.3 Market Conditions for Most Attractive Coupon

15.4 Hedging the Reverse Convertible

**16 Autocallables**

16.1 Example Autocallable Reverse Convertible

16.2 Pricing the Autocallable

16.3 Autocallable Pricing without Conditional Coupon

16.4 Interest/Equity Correlation within the Autocallable

**17 Callable and Puttable Reverse Convertible**

17.1 Pricing the Callable Reverse Convertible

17.2 Pricing the Puttable Reverse Convertible

**18 Asian Options**

18.1 Pricing the Geometric Asian Out Option

18.2 Pricing the Arithmetic Asian Out Option

18.3 Delta Hedging the Arithmetic Asian Out Option

18.4 Vega, Gamma and Theta of the Arithmetic Asian Out Option

18.5 Delta Hedging the Asian in Option

18.6 Asian in Forward

18.7 Pricing the Asian in Forward

18.8 Asian in Forward with Optional Early Termination

**19 Quanto Options**

19.1 Pricing and Correlation Risk of the Option

19.2 Hedging FX Exposure on the Quanto Option

**20 Composite Options**

20.1 An Example of the Composite Option

20.2 Hedging FX Exposure on the Composite Option

**21 Outperformance Options**

21.1 Example of an Outperformance Option

21.2 Outperformance Option Described as a Composite Option

21.3 Correlation Position of the Outperformance Option

21.4 Hedging of Outperformance Options

**22 Best of andWorst of Options**

22.1 Correlation Risk for the Best of Option

22.2 Correlation Risk for the Worst of Option

22.3 Hybrids

**23 Variance Swaps**

23.1 Variance Swap Payoff Example

23.2 Replicating the Variance Swap with Options

23.3 Greeks of the Variance Swap

23.4 Mystery of Gamma Without Delta

23.5 Realised Variance Volatility versus Standard Deviation

23.6 Event Risk of a Variance Swap versus a Single Option

23.7 Relation Between Vega Exposure and Variance Notional

23.8 Skew Delta

23.9 Vega Convexity

**24 Dispersion**

24.1 Pricing Basket Options

24.2 Basket Volatility Derived From Its Constituents

24.3 Trading Dispersion

24.4 Quoting Dispersion in Terms of Correlation

24.5 Dispersion Means Trading a Combination of Volatility and Correlation

24.6 Ratio’d Vega Dispersion

24.7 Skew Delta Position Embedded in Dispersion

**25 Engineering Financial Structures**

25.1 Capital Guaranteed Products

25.2 Attractive Market Conditions for Capital Guaranteed Products

25.3 Exposure Products for the Cautious Equity Investor

25.4 Leveraged Products for the Risk Seeking Investor

**Appendix A Variance of a Composite Option and Outperformance Option**

**Appendix B Replicating the Variance Swap**

**References**

**Index**