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Preface xi
Acknowledgements xiii
Introduction 1
Conventional Options, Forwards and Greeks 3
Call and Put Options and Forwards 3
Pricing Calls and Puts 6
Implied Volatility 8
Determining the Strike of the Forward 8
Pricing of Stock Options Including Dividends 9
Pricing Options in Terms of the Forward 10
Put-Call Parity 11
Delta 12
Dynamic Hedging 14
Gamma 14
Vega 16
Theta 18
Higher Order Derivatives Like Vanna and Vomma 19
Options' Interest Rate Exposure in Terms of Financing the Delta Hedge 21
Profit on Gamma and Relation to Theta 23
Delta Cash and Gamma Cash 25
Example: Delta and Gamma Cash 26
Skew 27
Reasons for Higher Realised Volatility in Falling Markets 27
Skew Through Time: 'The Term Structure of Skew' 28
Skew and its Effect on Delta 29
Skew in FX versus Skew in Equity: 'Smile versus Downward Sloping' 32
Pricing Options Using the Skew Curve 34
Simple Option Strategies 35
Call Spread 35
Put Spread 37
Collar 39
Straddle 40
Strangle 42
Monte Carlo Processes 45
Monte Carlo Process Principle 45
Binomial Tree versus Monte Carlo Process 46
Binomial Tree Example 46
The Workings of the Monte Carlo Process 48
Chooser Option 49
Pricing Example: Simple Chooser Option 49
Rationale Behind Chooser Option Strategies 51
Digital Options 53
Choosing the Strikes 55
The Call Spread as Proxy for the Digital 55
Width of the Call Spread versus Gearing 55
Barrier Options 57
Down-and-In Put Option 58
Delta Change over the Barrier for a Down-and-In Put Option 58
Factors Influencing the Magnitude of the Barrier Shift 60
Delta Impact of a Barrier Shift 63
Situations to Buy Shares in Case of a Barrier Breach of a Long Down-and-In Put 63
Up-and-Out Call 63
Up-and-Out Call Option with Rebate 64
Vega Exposure Up-and-Out Call Option 64
Up-and-Out Put 65
Barrier Parity 65
Barrier at Maturity Only 65
Skew and Barrier Options 66
Double Barriers 68
Forward Starting Options 71
Forward Starting and Regular Options Compared 71
Hedging the Skew Delta of the Forward Start Option 72
The Forward Start Option and the Skew Term Structure 73
Analytically Short Skew but Dynamically No Skew Exposure 74
Forward Starting Greeks 75
Ladder Options 77
Example: Ladder Option 77
Pricing the Ladder Option 78
Lookback Options 79
Pricing and Gamma Profile of Fixed Strike Lookback Options 79
Pricing and Risk of a Floating Strike Lookback Option 80
Cliquets 83
The Ratchet Option 83
Risks of a Ratchet Option 85
Reverse Convertibles 87
Example: Knock-in Reverse Convertible 87
Pricing the Knock-in Reverse Convertible 89
Market Conditions for Most Attractive Coupon 89
Hedging the Reverse Convertible 90
Autocallables 93
Example: Autocallable Reverse Convertible 93
Pricing the Autocallable 95
Autocallable Pricing without Conditional Coupon 97
Interest/Equity Correlation within the Autocallable 98
Callable and Puttable Reverse Convertibles 99
Pricing the Callable Reverse Convertible 99
Pricing the Puttable Reverse Convertible 102
Asian Options 105
Pricing the Geometric Asian Out Option 105
Pricing the Arithmetic Asian Out Option 107
Delta Hedging the Arithmetic Asian Out Option 109
Vega, Gamma and Theta of the Arithmetic Asian Out Option 110
Delta Hedging the Asian in Option 110
Asian in Forward 112
Pricing the Asian in Forward 114
Asian in Forward with Optional Early Termination 116
Quanto Options 119
Pricing and Correlation Risk of the Option 119
Hedging FX Exposure on the Quanto Option 122
Composite Options 125
An Example of the Composite Option 125
Hedging FX Exposure on the Composite Option 126
Outperformance Options 129
Example of an Outperformance Option 129
Outperformance Option Described as a Composite Option 130
Correlation Position of the Outperformance Option 131
Hedging of Outperformance Options 132
Best of and Worst of Options 135
Correlation Risk for the Best of Option 135
Correlation Risk for the Worst of Option 137
Hybrids 138
Variance Swaps 139
Variance Swap Payoff Example 140
Replicating the Variance Swap with Options 140
Greeks of the Variance Swap 142
Mystery of Gamma Without Delta 144
Realised Variance Volatility versus Standard Deviation 145
Event Risk of a Variance Swap versus a Single Option 146
Relation Between Vega Exposure and Variance Notional 147
Skew Delta 147
Vega Convexity 148
Dispersion 151
Pricing Basket Options 151
Basket Volatility Derived From its Constituents 152
Trading Dispersion 153
Quoting Dispersion in Terms of Correlation 153
Dispersion Means Trading a Combination of Volatility and Correlation 153
Ratio'd Vega Dispersion 155
Skew Delta Position Embedded in Dispersion 156
Engineering Financial Structures 157
Capital Guaranteed Products 157
Attractive Market Conditions for Capital Guaranteed Products 158
Exposure Products for the Cautions Equity Investor 160
Leveraged Products for the Risk Seeking Investor 163
Variance of a Composite Option and Outperformance Option 167
Replicating the Variance Swap 169
Bibliography 175
Index 177
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