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Volatility. Practical Options Theory. Wiley Finance

  • ID: 4449344
  • Book
  • October 2018
  • 208 Pages
  • John Wiley and Sons Ltd
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Gain a deep, intuitive and technical understanding of practical options theory

The main challenges in successful options trading are conceptual, not mathematical.  Volatility: Practical Options Theory provides financial professionals, academics, students and others with an intuitive as well as technical understanding of both the basic and advanced ideas in options theory to a level that facilitates practical options trading.  The approach taken in this book will prove particularly valuable to options traders and other practitioners tasked with making pricing and risk management decisions in an environment where time constraints mean that simplicity and intuition are of greater value than mathematical formalism.

The most important areas of options theory, namely implied volatility, delta hedging, time value and the so–called options greeks are explored based on intuitive economic arguments alone before turning to formal models such as the seminal Black–Scholes–Merton model.  The reader will understand how the model free approach and mathematical models are related to each other, their underlying theoretical assumptions and their implications to level that facilitates practical implementation.

There are several excellent mathematical descriptions of options theory, but few focus on a translational approach to convert the theory into practice. This book emphasizes the translational aspect, while first building an intuitive, technical understanding that allows market makers, portfolio managers, investment managers, risk managers, and other traders to work more effectively within and beyond the bounds of everyday practice.

  • Gain a deeper understanding of the assumptions underlying options theory
  • Translate theoretical ideas into practice
  • Develop a more accurate intuition for better time–constrained decision making

This book allows its readers to gain more than a superficial understanding of the mechanisms at work in options markets. Volatility gives its readers the edge by providing a true bedrock foundation upon which practical knowledge becomes stronger.

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1 Volatility and Options 1

1.1 What is an Option?      1

1.2 Options are bets on Volatility     3

1.3 Option Premiums and Breakevens     5

1.3.1 Understanding Option Premiums   6

1.3.2 Relation between Premium and Breakeven  7

1.4 Strike Conventions      8

1.5 What is Volatility? 9

1.5.1 Implied Volatility, simplied     9

1.5.2 Probabilities and Breakevens     13

1.5.3 Implied Volatility and Realised Volatility   13

1.5.4 Realised Volatility, srealised    14

1.6 Trader s Summary 17

2 Understanding OptionsWithout a Model    19

2.1 Vanilla Options  19

2.1.1 Option Payoffs      20

2.2 Making Assumptions     21

2.3 Understanding Vt with Economic Assumptions    21

2.4 Delta and Delta Hedging     23

2.5 The Value Function      24

2.6 Defining Delta 25

2.7 Understanding Delta      26

2.8 Delta as the Probability of an In–The–Money Expiry   29

2.9 Applying Delta as the Probability of an ITM Expiry in Practical Trading  33

2.10 Constructing Vt  34

2.10.1 Jensen s Inequality 35

2.10.2 Trading Intuition Behind Jensen s Inequality   36

2.10.3 American Options     37

2.10.4 Gradient of Vt     37

2.10.5 Drawing Vt      37

2.11 Option Deltas 39

2.12 A Note on Forwards      39

2.13 Put–Call Parity 41

2.14 Trader s Summary 43

3 The Basic Greeks: Theta 45

3.1 Theta, q  46

3.1.1 Overnight Theta for an ATM option    47

3.1.2 Dependence of q(St ; t;si) on St    48

3.1.3 Dependence of q(St ; t;si) on t    56

3.2 Trader s Summary 60

4 The Basic Greeks: Gamma      61

4.1 Gamma, G  62

4.2 Gamma and Time Decay     63

4.3 Traders Gamma, Gtrader      64

4.4 Gamma–Time Decay Trade–offs In More Detail   64

4.5 PnL Explain  66

4.5.1 Example: Gamma, Time Decay and PnL Explain for a 1 week Option      66

4.6 Delta Hedging and PnL Variance     69

4.7 Transaction Costs 71

4.8 Daily PnL Explain 71

4.9 The Gamma Profile      73

4.9.1 Gamma and Spot     73

4.9.2 Gamma and Implied Volatility    74

4.9.3 Gamma and Time     75

4.9.4 Total Gamma.     76

4.10 Trader s Summary 76

5 The Basic Greeks: Vega      79

5.1 Vega  80

5.2 Understanding Vega via the PDF     81

5.3 Understanding Vega via Gamma Trading   81

5.4 Vega of an ATMS Option across Tenors    82

5.5 Vega and Spot 82

5.6 Dependence of Vega on Implied Volatility    85

5.7 Vega Profiles Applied in Practical Options Trading   85

5.8 Vega and PnL Explain     87

5.9 Trader s Summary 87

6 Implied Volatility and Term Structure    89

6.1 Implied Volatility, simplied     90

6.2 Term Structure 94

6.3 Flat Vega and Weighted Vega Greeks     94

6.3.1 Flat Vega 94

6.3.2 Weighted Vega      95

6.3.3 Beta Weighted Vega      97

6.4 Forward Volatility, Forward Variance and Term Volatility  97

6.4.1 Calculating Implied Forward Volatility    99

6.5 Building a Term Structure Model using Daily Forward Volatility 100

6.6 Setting Base Volatility Using a 3 Parameter GARCH Model 102

6.6.1 Applying the 3 Parameter Model   104

6.6.2 Limitations of GARCH    105

6.6.3 Risk Management Using the 3 Parameter Model   106

6.6.4 Empirical GARCH estimation    106

6.7 Volatility Carry and Forward Volatility Agreements   107

6.7.1 Volatility Carry in the GARCH model   108

6.7.2 Common Pitfalls in Volatility Carry Trading   108

6.8 Trader s Summary 109

7 Vanna, Risk Reversal and Skewness     111

7.1 Risk Reversal 112

7.2 Skewness 114

7.3 Delta Space  116

7.4 Smile in Delta Space      117

7.5 Smile Vega  119

7.5.1 Smile Vega Notionals     121

7.6 Smile Delta  122

7.6.1 Considerations Relating to Smile Delta    123

7.7 Trader s Summary 124

8 Volgamma, Butterfly and Kurtosis    125

8.1 The Butterfly Strategy     126

8.2 Volgamma and Butterfly      127

8.3 Kurtosis  128

8.4 Smile  129

8.5 Butterflies and Smile Vega     130

8.6 Trader s Summary 131

9 Black–Scholes–Merton Model     133

9.1 The Log–normal Diffusion Model     133

9.2 The BSM Partial Differential Equation (PDE)   134

9.3 Feynman–Kac. 137

9.4 Risk Neutral Probabilities     138

9.5 Probability of Exceeding the Breakeven in the BSM model  139

9.6 Trader s Summary 139

10 The Black–Scholes Greeks     141

10.1 Spot Delta, Dual Delta and Forward Delta    141

10.1.1 Spot Delta 141

10.1.2 The ATM Strike and the Delta Neutral Straddle  143

10.1.3 Dual Delta 144

10.1.4 Forward Delta     144

10.2 Theta  145

10.3 Gamma  147

10.4 Vega  147

10.5 Vanna   148

10.6 Volgamma  148

10.7 Trader s Summary 148

11 Predictability and Mean Reversion    149

11.1 The Past and the Future      149

11.2 Empirical Analysis      150

A Probability   155

A.1 Probability Density Functions (PDFs)    155

A.1.1 Discrete Random Variables and PMFs   155

A.1.2 Continuous Random Variables and PDFs   156

A.1.3 Normal and Lognormal Distributions   157

B Calculus  161

Glossary   163

References  167

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Adam S. Iqbal
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