A Trader’s Guide to Options:
Volume 1 –
Products, Pricing, Structuring
Table of Contents
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Table of Contents  CHAPTER Listing
0 Foreword and Highlights for the TG2 Series
1 Foreword and Highlights for TG2 Options Vol 1 and Caveat
PART I – Options Basics and Trading Foundation
2 First and Foremost: Trading is a Business
3 The Payout Formula, Contracts, and the Deliverable
4 Basic Options Structures, PayOut Profiles, and Usage
PART II – Pricing, Valuation, & Risk Machinery
6 Basic Non Contingent Derivatives Review
7 Valuation Under Uncertainty – Part 1: Market Models
8 Valuation Under Uncertainty – Part 2: Options Models
9 Options Risk – Part 1: Types of Risk and Risk Measurement
11 Valuation Under Uncertainty – Part 3: (Some) More Reality
12 A Little Finance and Present Value Theory for Options
13 Exercise Style: European, Bermudian, and American
14 Option Types and Asset Classes 1: Market Convention “Spot”
15 Option Types and Asset Classes 2: Market Convention “Listed/Futures”
16 Option Types and Asset Classes 3: Exotics & Hybrids/Correlation Products
17 Quotations, Contracts & Confirms, Clearing, and Much Minutia
18 (Partial) BSM Formulas Summary
19 Introduction to Quantitative Methods for Options
20 Volatility
21 ProfitatRisk (PaR): Optimal RiskAdjusted P&L
PART III – Introduction to Position Keeping and Strategies
22 Introduction to Trading & Position Keeping Strategies
Appendices
References
Subject Index
Table of Contents  DETAILED Listing
0 Foreword and Highlights for the TG2 Series
0.1 Why the TG2 Series of Books?
0.2 What is, and is not, important, and who is this for anyway?
0.2.1 Who is this Series for?
0.2.2 Pedagogical Issues
0.2.3 Notation, Grammar, Spelling
0.2.4 About Accompanying Software, and Commercial Software
0.2.5 About these books and relationship to ARTSchool
0.3 Future Direction & Road Map for the Series
0.4 About the Authors
0.4.1 Invitation for Contribution 1 Foreword and Highlights for TG2 Options Vol 1 and Caveat
1.1 Caveat: “Perspective”
1.2 Part I: Business and Options Fundamentals
1.3 Part II: Options Valuation & Risk, and Reality Impact
1.4 Part III: The Most Important Element of Trading: Position Keeping/Strategy
1.5 Caveat: No Book Can Make You Into A Trader
1.6 Caveat: If You Have Other TG2 Books PART I – Options Basic and Trading Foundation 2 First and Foremost: Trading is a Business
2.1 Where is the Greed/Economic Need?
2.2 Know Your Business
2.2.1 Businesses Objectives/Parameter (Performance, Risk, and Resources)
2.2.2 Risk/Return Profile
2.2.3 Risk/Return Profiles vs. Risk Preference
2.2.4 Trading/Operating Models
2.2.5 Trading/Operating Model Abuses
2.2.6 Know Your Contract(s)/Market (Simple ≠ Unimportant)
2.3 A Little Big Picture of Options Markets 3 The Payout Formula, Contracts, and the Deliverable
3.1 Spot vs. Forward vs. Basket Contracts – What is a Derivative?
3.2 Contingent vs. NonContingent Instruments Basics
3.3 The PayOut Formula, Deliverable, and Settlement
3.4 Options vs. Contingent Derivatives: Hedging vs. Provisioning
3.5 The RiskNeutral/ArbitrageFree Framework Demands Liquidity
4 Basic Options Structures, PayOut Profiles, and Usage
4.1 NonContingent Derivatives: Futures, Forwards, and (most) Underlyings
4.2 Puts, Calls, and PutCall Parity
4.3 PayOut vs. Value
4.4 Is it a Bet, Insurance, or a Hedge (or All)?
4.5 Two Basic Factors of Valuation: Volatility and Time
4.6 Time Decay (Theta) vs. Market Direction (Delta/Gamma) and MultiDimensional Risk
4.7 Shaping the Risk/Return Profile
4.8 Combos, Simple, and Not So Simple Structures
4.8.1 Covered Calls and Puts
4.8.2 Put, Call (Ratio) Spreads (limited bets)
4.8.3 Straddles, Strangles, and Butterflies (big vol or no vol?)
4.8.4 Collars
4.8.5 Calendar Trades: Diagonals, Curves, and Correlation
4.9 Exercise Style
4.9.1 European
4.9.2 American
4.9.3 Bermudian
4.9.4 Serial Options (Caps, Floors, etc)
4.10 Exotics and Hybrids
4.10.1 Exotics: The "Usual Suspects"
4.10.2 UpSide Participation Options
4.10.3 Accrual Notes/Fairway Bonds
4.10.4 Callable, Putable, Extendable, Retractable, etc
4.10.5 Credit Derivatives and Credit Protected Structures
4.10.6 Convertible Bonds
4.11 Uses vs. Structures vs. (a little) Reality
4.11.1 EndUsers and Hedging
4.11.2 Price Directional
4.11.3 Vol Directional
4.11.4 Hungry for Yield
4.11.5 Replication vs. Arbitrage
4.11.6 Hedging and Delivery
4.11.7 Getting Out Of Options Positions
4.11.8 Path Dependence (always)
4.12 Options Markets and Asset Classes
4.12.1 Options Markets
4.12.2 Equity Options
4.12.3 FX Options
4.12.4 Commodity Options
4.12.5 Interest Rate Options
4.12.6 MultiAsset Options (Correlation Products)
4.13 The Story So Far
PART II – Pricing, Valuation, & Risk Machinery
5 Valuation Overview: Market Models vs. Options Models
5.1 Market Models (trends and wobbles)
5.2 Options Models (are synthetic delivery models)
6 Basic Non Contingent Derivatives Review
6.1 CashandCarry vs. RiskNeutrality (the “pure” market maker)
6.2 Is CashandCarry Really RiskNeutral? (often not)
6.3 (Classical) Arbitrage
6.4 ArbitrageFree Forward Prices (“fair value”?)
6.5 Fair Value Reality for Options Trading (“42”?)
6.6 ArbitrageFree Forward Prices (fair value) vs. Actual Forward Prices
7 Valuation Under Uncertainty – Part 1: Market Models
7.1 Overview of Underlying Issues
7.1.1 Mathematical Modelling of Securities Prices
7.1.2 Some Simplifying Assumptions for Economics and Finance
7.2 Prices vs. Returns (distance vs. speed)
7.2.1 Relative vs. Absolute Processes
7.3 Continuous Time vs. Discrete Time
7.4 Markets vs. Models vs. Solutions
7.4.1 Models vs. Solutions (speed vs. distance, again)
7.4.2 Market Models vs. Options (Hedging) Models & Instrument Models
7.5 Market Models and Forecasting Prices/Returns – The Basic Idea
7.5.1 The “Goal” (what is possible vs. what you can have)
7.5.2 A First Qualitative Model of Price Dynamics: Trends and Wobbles
7.6 Developing a First Valuation Model Under Uncertainty
7.6.1 Down to Earth Explanation of the (Statistical) Terminology
7.6.2 Expectations
7.6.3 Recoupling and Decoupling Drift
7.6.4 Expectations and Distributions Summary
7.6.5 Making a Bet or Pricing an Option? – 1st (Crude) Valuations under Uncertainty
7.6.6 A First Quasi Forecasting Model of Uncertainty
7.6.7 Forecasting Prices vs. Forecasting Returns Revisited
7.7 Developing a TimeExtended (First) Model of Uncertainty
7.7.1 A First “Good” Shape of Uncertainty
7.7.2 A First Calibration of the Uncertainty
7.7.3 A First Model for the Time Evolution of Uncertainty
7.7.4 Formalising the First (proper) Model of Uncertainty
7.7.5 Calibration of Uncertainty and Annualisation
7.8 Putting it all together: A First “Complete” Model Under Uncertainty
7.8.1 First Valuation of Digital Options
7.8.2 The Valuation Profile with Gaussian/Root2 Uncertainty: Curvature
7.8.3 Holding Period Income
7.9 Other Valuation Models Under Uncertainty
7.10 Summary: A First “Complete” Market Model Under Uncertainty
8 Valuation Under Uncertainty – Part 2: Options Models
8.1 Market Uncertainty vs. Risk Preferences
8.1.1 The Market Price of Risk, Risk Preference, and Market Models
8.1.2 One Interpretation of Valuation/Risk due to Risk Preferences
8.1.3 Practical Illustration of Market Return vs. Risk Preference Return
8.1.4 ArbitrageFree Market Return vs. Risk Preference Return
8.2 Shortcomings of Options Pricing with Market Models
8.2.1 Risk Preference Dependence
8.2.2 Market Model Delivery Process via Provisioning
8.2.3 Why Not A Market Model for Options Prices (c.f. Forward Prices)?
8.3 The BlackScholesMerton Framework (riskneutral/arbitragefree delivery) – The Trader’s Version
8.3.1 The Delta RiskNeutral Hedging Strategy – Synthetic Replication
8.3.2 The Delta RiskNeutral Hedging Strategy – Synthetic Replication with Continuous Trading
8.3.3 Dynamic Rebalancing/Synthetic Replication vs. Risk/Return
8.3.4 RiskFree Synthetic Replication vs. Risk/Return vs. The Market Model
8.4 The BlackScholesMerton Framework (riskneutral/arbitragefree delivery) – The Quant’s Version
8.4.1 The Delta RiskNeutral Hedging Strategy and Ito’s Lemma
8.4.2 Financial Derivatives vs. Mathematical Derivatives and Ito’s Lemma
8.4.3 Ito’s Lemma – The Trader’s Version
8.4.4 Ito’s Lemma – The Math Guy’s Version
8.4.5 Derivation of the “Core” BSM Formula
8.5 The BlackScholesMerton Options “Pricing” Formula
8.5.1 The Basic Option Pricing Formula
8.5.2 Some “Interpretation” of the BSM Option Formula
8.5.3 Discussion of the Assumptions in the BSM Option Formula
8.5.4 PutCall Parity (Implying one option from another)
8.6 Basic BSM Properties, 1st Example Usage, and Units
8.6.1 A Simple Pricing Example – Calls, Puts, and PutCall Parity
8.6.2 Units
8.6.3 Time vs. Intervals/Year Fractions and “Basis”
8.6.4 Forward Values (ArbitrageFree?)
8.6.5 Funding Rates and Income Yield (real vs. imagined)
8.6.6 Volatility: the Standard Deviation of Returns (it’s not market vol)
8.6.7 Intrinsic Value vs. Time Value
8.6.8 Valuation Scenarios: Profiles, Surfaces, and Portfolios
8.6.9 At the money forward and Moneyness
8.6.10 Delta and Curvature
8.6.11 A Couple of (First) “Sanity Checks”
8.7 Basic Determinants of Options Prices
8.7.1 Price and Strike
8.7.2 Volatility
8.7.3 Time (to Expiration)
8.7.4 Funding Rate, Income Yield, and Drift
8.7.5 Curvature: The Value in Options
8.8 Does It Actually Work? (yes and no, and for surprising reasons)
8.8.1 Reality Impact: Replication, Credit, Liquidity, and on and on …
8.8.2 P&L and Risk/Return vs. Pricing
8.8.3 The Market and BSM Options Pricing (a first comment)
8.9 The Story So Far: (a first) Option Model
9 Options Risk – Part 1: Types of Risk and Risk Measurement
9.1 Types of Risk
9.1.1 Types of Risk
9.1.2 Types of Risk Measures
9.2 Position Keeping vs. Risk Management
9.3 Overview of Risk Measurement and Hedging Basics
9.3.1 Risk Assessment & Control Objectives
9.3.2 Valuation Under Certainty vs. Valuation Under Uncertainty
9.4 Basic Options Sensitivity Risk – “The Greeks” and “V01’s”
9.4.1 Position Sensitivity Measures
9.4.2 Delta
9.4.3 Gamma
9.4.4 Vega
9.4.5 Theta
9.4.6 Rho
9.4.7 Other Greeks
9.4.8 Which Greek is “More Important?”
9.4.9 Sensitivities of Sensitivities vs. Scenario Analyses (can we be proactive?)
9.4.10 (Static) MultiDimensional Risk/Sensitivities and Correlations
9.4.11 Instrument Risk vs. Position/Portfolio Risk
9.5 Introduction to Profile Matching
9.5.1 Position keeping with “Singularities” and Model “Mismatch”
9.5.2 Hedge Strategy for (singular) Exotic Options
9.6 Basic Options VaR Risk Measures
9.6.1 Illustration of the Basic VaR Idea
9.6.2 Introduction to Types of VaR Measurement
9.6.3 Historical Methods: HVaR
9.6.4 Covariance VaR Methods: CVaR
9.6.5 Monte Carlo methods: MCVaR
9.6.6 Backtesting and Verification of VaR
9.6.7 Other VaR Based Methods (Credit, Economic Capital, etc.)
9.6.8 VaR and TermStructure
9.6.9 Basic VaR Summary
9.6.10 Reality Impact and Future Considerations
9.7 ProfitatRisk (PaR) and Holding Period Optimal Methods
9.8 Basic Risk Measurement Summary
10 Options Risk – Part 2: Measurement vs. Hedging vs. P&L
10.1 Risk Measurement vs. Hedging vs. Position Keeping (P&L is everything)
10.2 Hedging vs. Trading vs. Arbitrage
10.3 A General View of Slopes vs. Predictions vs. (Dynamic/Static) Replication
10.3.1 Taylor vs. Sensitivities vs. Predictions
10.3.2 The Total (Mathematical) Derivative vs. Position Value
10.3.3 Taylor vs. BlackScholesMerton & the Greeks
10.3.4 Summary: General Greeks Reporting/Hedging
10.4 Scenario Analysis/Reporting
10.4.1 UnWeighted/UniformlyWeighted Scenario Analyses
10.4.2 P&L Scenarios vs. Sensitivity Scenarios
10.4.3 MultiDimensional Scenarios
10.4.4 ProbabilityWeighted Scenario Analyses
10.4.5 Instrument/Structure Analyses vs. Portfolio Analyses
10.5 Types of Hedging
10.6 (1Dimensional) Sensitivity Hedging with (Some) Variations
10.6.1 1Dimensional Hedges (Greeks and 01’s)
10.6.2 Delta
10.6.3 Gamma
10.6.4 Delta + Gamma (HigherOrder 1Dimensional)
10.6.5 Theta
10.6.6 Vega – Simple
10.6.7 Vega – “Pure Vol and Some Reality”
10.6.8 Vega and Volatility Skew
10.6.9 Vega and Implied Volatility
10.6.10 Rho
10.6.11 Credit Risk
10.7 Simple Position Hedging and “Hedge/Rebalance Optimisation”
10.7.1 A Puzzle Inside an Enigma Wrapped in a Riddle
10.7.2 Paralysis by Analysis vs. Trading Objectives
10.7.3 Static vs. Dynamic Revisited
10.7.4 What Does Optimisation Actually Mean?
10.7.5 Optimisation Objective(s)
10.7.6 Static Hedge/Rebalance Optimisation
10.7.7 (Near) Static “LookAhead” Optimisation
10.7.8 QuasiOptimisation (a solution for the common man)
10.7.9 SinglePeriod Dynamic Hedge Optimisation
10.8 MultiIndex/Portfolio Risk/Hedging
10.9 Operational Issues vs. Risk/Position Keeping
10.9.1 Transactions Costs: Hedging vs. Prop Trading/Investing
10.9.2 Premia/Cash Management
10.10 Hapless Snapshots Do Not a Movie Make
10.11 Which Strategy is Best for Me?
10.11.1 The Right Tool for the Right Job
10.11.2 Market Maker
10.11.3 Arb/Directional
10.12 The Story so Far: Single Period Hedging
11 Valuation Under Uncertainty – Part 3: (Some) More Reality
11.1 Selected Additional (Standard) Market/Options Models
11.1.1 RiskNeutral/ArbitrageFree (or not, and how can you tell?)
11.1.2 Geometric Brownian Motion (our old friend)
11.1.3 Arithmetic Brownian Motion
11.1.4 All Markets are MeanReverting
11.1.5 Constant Elasticity of Variance (CEV)
11.1.6 JumpDiffusion
11.1.7 OrnsteinÜhlenbeck: Mean Reverting & CEV
11.2 Generalised Distributions
11.2.1 Yield Curve Slope Options
11.2.2 MBS Spread Options
11.2.3 Truncated and Fattailed Distributions
11.2.4 General Distributions
11.3 NonStochastic Market Models
11.3.1 Fractal Dimension Adjusted Options Pricing
11.4 Instrument Effects – such as PulltoPar
11.5 MultiIndex/MultiFactor Problems
11.5.1 MultiIndex Contracts: 2Factor Valuation
11.5.2 Spread Options
11.5.3 Stochastic Volatility
11.5.4 nFactor Valuation vs. nFactor Forecasting
11.6 TermStructure Models
11.6.1 Basic Terminology
11.6.2 A simple OneFactor Model (nontraditional)
11.6.3 A simple TwoFactor Model (nontraditional)
11.6.4 Traditional TermStructure Representation
11.6.5 Comparison of Selected Termstructure Models
11.6.6 Traditional TermStructure: How Many Factors are “Best”?
11.6.7 Traditional TermStructure: Calibration
11.7 TermStructure of Volatility (is everything)
11.8 Fancy Models vs. Fancy Inputs
11.8.1 Fancy Pricing Model vs. Fancy Volatility Model
11.8.2 Fancy Replication/Strategy vs. Fancy Models
11.9 Path Dependence
11.10 Completely General Models (and valuation philosophy)
11.11 The Story So Far: To Be (Advanced) or Not To Be (Advanced)
12 A Little Present Value Theory for Options
12.1 Cash Flow Schedules and Discount Factors
12.2 Interest Rates and Yields (are Not Necessarily Returns)
12.3 Compounding Frequency (c.f. cash flow frequency)
12.4 Spot Rates vs. Forward Rates
12.5 Coupon Bearing vs. Money Markets, and Yield to Maturity
12.5.1 “Par” Products
12.6 Fixed Income Products vs. Floating Rate Products
12.7 Accrued Interest
12.8 Price to Yield vs. Yield to Price
12.9 Yield Curves
12.10 Curve Building
12.11 Interest Basis
12.12 Calendar or Business Day Basis
12.13 Holidays
12.14 A Few Comments on PV Issues for Options
12.15 Credit Spreads
12.16 A Few Useful Formulas (Rate conversion, Annutisation, etc)
12.16.1 A Couple PV Formulas
12.16.2 Frequency and Related IR Conversions
12.16.3 Annutisation – In Perpetuity
12.16.4 Annutisation – Finite Term
13 Exercise Style: European, Bermudian, and American
13.1 How to Decided on Early Exercise – Part 1
13.2 American Exercise – BinomialTree Illustration/Valuation
13.3 American Exercise – BaroneAdesi/ Whaley
13.3.1 BAW American Call
13.3.2 BAW American Greeks
13.3.3 BAW American Put
13.3.4 BAW Basic Valuation Properties
13.4 BAW American Options: (Some) More Properties
13.4.1 SubOptimal Early Exercise Scenarios
13.4.2 American Option PutCallParity
13.4.3 First thoughts on “path dependence” for early exercise
13.4.4 Is the BAWlike (market convention) early exercise “trigger strategy” sensible?
13.4.5 Drift and Continuous vs. Discrete Income Yield
13.4.6 Some (first) discussion of hedging and rebalancing strategies
13.5 BAW American Call & Put – VBA Code & Greeks
13.6 Other Formulations and Early Exercise Models
13.6.1 Early Exercise Date Formulas
13.6.2 Bjerksund & Stensland
13.6.3 N[d1], N[d2], and other “friends”
13.7 Bermudian Options and A “Cheap & Cheerful” Approach
13.8 (Some) EarlyExercise Reality Impact
13.8.1 Why would “You” exercise early? & What is the value of early exercise to you?
13.8.2 Will the value of early exercise change after exercising (or assignment)?
13.8.3 Transactions costs, liquidity etc,
13.8.4 Operating issues
13.8.5 The Real World Price of Early Exercise
14 Option Types and Asset Classes 1: Market Convention “Spot”
14.1 Market Models vs. Instrument Models Revisited
14.2 Asset Class Implications for Vanilla Options
14.2.1 Interest Rate Parity (IRP)
14.2.2 Purchasing Power Parity (PPP) and IRPPPP
14.2.3 The US Dollar, Economy, and Financial Markets
14.2.4 RiskNeutral/ArbitrageFree (or not, and how can you tell?)
14.2.5 Spot vs. Forward
14.3 Preliminary Comments on Volatility
14.4 Some Comments on Heuristics and Realty
14.5 Equity Options
14.5.1 A Good Story vs. Macro/Fundamentals
14.5.2 Market Convention Equity Option Valuation
14.5.3 Liquidity and Repo’s
14.5.4 Market Dynamics and Instrument/Forward Proxies – Some Heuristics
14.5.5 Dilution
14.5.6 Splits
14.5.7 A Real Trade – Directional Call to “Catch the Rebound”
14.5.8 Some Volatility Trading Issues
14.5.9 As Components of Correlation/Hybrid Products
14.6 IR Options
14.6.1 Term Products
14.6.2 Forward Rates and Loans vs. Settled for Difference
14.6.3 Options on Forward Rates, Forward Delivery, and Black76
14.6.4 Bond Options (Price & Ratebased)
14.6.5 LogNormal Prices vs. LogNormal Yields
14.6.6 PulltoPar Revisited: PulltoPar of What (pricebased vs. yieldbased)?
14.6.7 Bond Option Position Keeping: Lots of Tricky Bits
14.6.8 Bond Options: Interim Market Conventions Review
14.6.9 Swaptions
14.6.10 Payer/Receiver: which is really a Call or a Put?
14.6.11 PulltoPar for Swaptions
14.6.12 Serial Options (Caps, Floors, and Collars)
14.6.13 PutCallParity for Caps/Floors
14.6.14 IR Option Position Keeping: Curves, Buckets, and More
14.6.15 TermStructure of Rates vs. TermStructure of Volatility
14.6.16 TermStructure Models (Meanreversion, etc)
14.6.17 American vs. Bermudian vs. European
14.6.18 Negative Interest Rates
14.6.19 Different Types of “Convexity Adjustments”
14.6.20 Spreads, Butterflies, and Correlation
14.6.21 “Credit Spread” and Related Issues
14.6.22 MarktoMarket/Valuation Issues
14.6.23 Interest Rates and Currencies
14.6.24 As Components of Structured/Hybrid Products
14.6.25 A Real Trade – CallSpreads Revisited
14.7 FX Options
14.7.1 FX Forwards: ERA’s vs. FXA’s
14.7.2 Market Convention Valuation
14.7.3 FatTailed
14.7.4 JumpDiffusion
14.7.5 Its All About “Pips” (or is it?)
14.7.6 A Real Trade – A Single American vs. a Strip of European Options
14.8 Commodity Options
14.8.1 Energy
14.8.2 Metals
14.8.3 Softs
14.8.4 CheapesttoDeliver Commodities
14.8.5 Supply/Demand vs. Liquidity/Arbitrage for Commodity Options
14.8.6 Commodity Curves: Backwardation and Contango
14.8.7 Convenience Yields (what is this really?)
14.8.8 Market Convention Commodity Options and Example
15 Option Types and Asset Classes 2: Market Convention “Listed/Futures”
15.1 Spotbased vs. Forwardbased Underlying
15.2 Listed vs. OTC Options Contracts
15.2.1 OTC
15.2.2 Listed
15.2.3 Futures Contracts
15.2.4 EFP vs. Cash/Difference Settled
15.2.5 End of Day Settlement and “Rotation”
15.2.6 Delivery Rules/Cycles, and Futures Trading
15.2.7 Margining
15.2.8 Clearing vs. Execution
15.2.9 Calendars, Strikes, Rolls, and Other Realities
15.2.10 “Serial Contracts” vs. Serial Options
15.2.11 “Cabinet Bid/Offer”?
15.2.12 Rotation Effects (Skews, Correlations, Strips, etc)
15.2.13 American vs. European
15.2.14 Price Based vs. Rate Based: Well which is it?
15.2.15 Price Based vs. Rate Based: FRAConvexity
15.2.16 Price Based vs. Rate Based: Varying TickValue
15.2.17 Futures Tick Value vs. Options Tick Value
15.2.18 Regulatory Minutia
15.3 Market Convention Options on Futures
15.3.1 A Quick Review of Futures Pricing, Listed Options Deliverables, and
Black76
15.3.2 A Real Trade – A Ratio Call Spread 16 Option Types and Asset Classes 3: (Basic) Exotics & Hybrids/Correlation Products
16 Option Types and Asset Classes 3: Exotics & Hybrids/Correlation Products
16.1 Exotic Options (in ten words or less)
16.1.1 Forward Start Options and Serial Vanilla Options
16.1.2 Asian Options (Average Rate Options)
16.1.3 Lookback Options (The Best PayOut Possible)
16.1.4 Digital Options (All or Nothing)
16.1.5 Contingent Premium Options
16.1.6 Barrier Options (KnockOut/KnockIn)
16.1.7 Portfolio Options: Spreads, ExchangeofAssets, Baskets, etc.
16.1.8 Compound options (Options on Options)
16.1.9 Chooser Options (Do I want a call or put?)
16.1.10 Quanto’s
16.2 Introduction to Hybrids and MultiFactor/Correlation Products
16.2.1 Structured Risk/Return
16.2.2 Callable/Putable and Extendible/Retractable
16.2.3 Convertible Bonds (CB’s)
16.2.4 UpSide Participation/Capital Protected Structures
16.2.5 FairWay Bonds/Accrual Notes
16.2.6 Mortgages: PrePayment, Index Amortisation, and Much More
16.2.7 Securitisation
16.2.8 Supply Push vs. Demand Pull
16.3 The Story so Far: All Roads Lead to BSM (sort of); But Should They? 17 Quotations, Contracts & Confirms, Clearing, and Much Minutia
17.1 Restrictions and Authorisations
17.2 Quotation Conventions
17.2.1 Listed Quotation
17.2.2 OTC Quotation
17.3 End of Day, Settlement, and MarkToMarket
17.3.1 End of Day: Tickets, Blotters, CheckOuts, Confirms, etc.
17.3.2 Deal Breakers
17.4 Official Reports
17.5 Example Contract/Specifications
17.5.1 Listed Contracts
17.5.2 (Some) Listed Contracts Quotation Nomenclature
17.5.3 OTC Contracts
17.6 Regulatory Approval 18 (Partial) BSM Formulas Summary
19 Introduction to Quantitative Methods for Options
19.1 Cumulative Normal Approximations
19.1.1 Univariate (1Dimensional) Cumulative Normal Approximation
19.1.2 Bivariate (2Dimensional) Cumulative Normal Approximation
19.2 Root Finding
19.2.1 Newton’s Method
19.2.2 Bisection
19.3 A First Description of Three Important Numerical “Solvers”
19.3.1 Models vs. Solutions
19.3.2 Forecasting (Market) Models vs. Valuation Models
19.4 Introduction to Monte Carlo Methods
19.4.1 Monte Carlo Basics
19.4.2 Pricing a Vanilla Option with Monte Carlo Simulation
19.4.3 Pricing a Barrier Option with Monte Carlo Simulation
19.4.4 MC Methods: The Story so Far
19.4.5 (Some Advanced) Considerations for MC Methods
19.4.6 PaR, Arbitrage, & Position Keeping with Monte Carlo Simulation
19.4.7 Monte Carlo Simulation: Pros/Cons
19.5 Introduction to Trees Methods
19.5.1 (Binomial) Trees  The Basic Idea
19.5.2 Binomial Tree Vanilla (European) Option
19.5.3 Binomial Tree Vanilla (American) Option
19.5.4 (Some) Consideration for Trees and Lattices: Pros/Cons
19.6 Introduction to Finite Difference Methods
19.6.1 The Basic Idea
19.6.2 The Explicit Finite Difference Scheme
19.6.3 Explicit Finite Difference Black–Scholes Formulation
19.6.4 (Some) Numerical Considerations
19.6.5 FD for Complex Problems in a Homogenous Valuation Framework
19.6.6 Finite Difference Methods: Pros/Cons
19.7 MultiFactor Methods 20 Volatility
20.1 Preliminary Comments on Some (Volatility) Concepts
20.1.1 Absolute vs. Relative Vol Revisited
20.1.2 Basis Point Vol (AKA Absolute Vol) and IR Vol
20.1.3 Caveat
20.1.4 Volatility Interpolation
20.1.5 Volatility as a “Fudge Factor” and “Circular Valuation”
20.2 Implied/Traded (Model) Volatility
20.2.1 Implied Volatility(s)
20.2.2 Implied Volatility: Direct Usage
20.2.3 Exotic & Structured (Model) Implied Volatilities/Moments
20.2.4 TermStructure Model Volatility and Calibration
20.2.5 The Relationship between Price Vol and Yield Vol for IR Products
20.2.6 Deposit Futures Options Volatilities
20.3 Traded/Quoted and “ImpliedImplied” Volatility
20.3.1 Term structure of Volatility as Curves & Surfaces
20.3.2 Volatility Skew
20.3.3 Mean Reverting Volatility and Other Effects
20.3.4 HJM: Volatility isn’t Everything, it’s the Only Thing
20.4 Historical (or Statistical or Empirical) Volatility
20.4.1 Characterising (empirical) Volatility
20.4.2 Validity, Convergence, Stationarity, and Confidence Intervals
20.4.3 Sampling length, Frequency, and Calendar Effects
20.4.4 Correlation/Covariance
20.4.5 Price vs. Returns (and Absolute vs. Relative)
20.4.6 Histories of “Historicals”
20.4.7 Relationship to Distributions and Calibration
20.4.8 Daily, IntraDay, Open/High/Low/Close vs. Where Can “you” Rebalance?
20.4.9 Application of “Historical” Methods to Real World Options Pricing
20.4.10 Absolute vs. Relative Historical Vols Example
20.4.11 Application of “Histories of Historicals” Methods to Real World Options Pricing
20.4.12 Application of “Historical” Methods to Real World Options Pricing with Correlation
20.4.13 ConstantMaturity Historical Volatilities
20.5 Implied vs. Historical (Model) Volatility
20.5.1 Forward Looking vs. Backward Looking Volatilities
20.5.2 Return Maps: Implieds vs. Historicals
20.6 Volatility Indices
20.7 “Trading” Volatility
20.7.1 Option Pricing Trading Volatility vs. Portfolio Trading Volatility
20.7.2 Trader Performance and OHLC Efficiency
20.7.3 The “Actual Value” of a Trade  Revisited
20.8 “P&L” Volatility
20.9 Advanced Volatility Concepts
20.9.1 Cheap/Dear Analysis – Traditional
20.9.2 Cheap/Dear Analysis – Volatility Cones
20.9.3 Data Modelling: TSA, Spectral, Chaos, etc.
20.9.4 Time Series Analysis: Traditional Statistical
20.9.5 Spectral Analysis
20.9.6 NonLinear Dynamics
20.9.7 Implied Distributions
20.9.8 Principle Component Analysis
20.9.9 Model Arbitrage
20.10 Volatility Summary 21 ProfitatRisk (PaR): Optimal RiskAdjusted P&L
21.1 Introduction to the PaR Methodology
21.1.1 Trading, Hedging, Selling, Managing, and Real World P&L
21.1.2 Trading, Hedging, Selling, Managing, and Simulated P&L
21.2 Comments on Software and Programming Issues
21.3 Forward Testing vs. Back Testing
21.3.1 Generating Forward Market Scenarios
21.3.2 Back Testing with Historical Market Data
21.4 Embedding a Dealing System in a Scenario Generator
21.5 Embedding Strategies: Prop Trading & Position Keeping Rules
21.6 Accounting & Reporting: Cash Flow vs. P&L, Interperiod Risk(s), and Much More
21.7 Riskadjusted Performance Calculations
21.8 “Optimal” Holding Period RiskAdjusted Returns PaR via Efficient Frontiers
21.9 PaR Verification and Usage
21.10 What a PaR Calculator Might “Look Like”
21.10.1 A Spreadsheet Example (Suitable for simple positions)
21.10.2 A “full blown” Example (Suitable for almost anything)
21.11 Mathematically Optimal vs. Holding Period P&L Optimal Trading & Hedging
21.12 A Simple Forward/Backward PaR Example: Bonds/Bond Futures
21.12.1 Forward Testing (with a 1factor Model)
21.12.2 Back Testing the Hedging Strategy and the (1factor) model
21.13 PaR Summary: Theory vs. Reality PART III – Introduction to Position Keeping and Strategies 22 Introduction to Trading & Position Keeping Strategies
22.1 Rebalance Triggers
22.1.1 Time/Calendar Trigger
22.1.2 Delta and Greeks Trigger
22.1.3 Other Triggers
22.2 Does BSM Work? Delta/Calendar Rebalancing
22.2.1 Premia Certainty vs. P&L Certainty and Trading Volatility
22.2.2 Synthetic Replication: Delta Hedging when Long Gamma
22.2.3 Synthetic Replication: Delta Hedging when Short Gamma
22.2.4 PaR Synthetic Replication: Calendar Trigger – Idealised
22.2.5 PaR “Optimal RiskAdjusted Trading Strategy”
22.2.6 PaR Synthetic Replication: Calendar Trigger – Real’ish
22.3 Market Convention Delta/Delta Trigger Rebalancing
22.3.1 PaR Synthetic Delta Replication: Delta Triggers
22.4 Market Convention Delta/Gamma/Pyramid Rebalancing
22.4.1 Synthetic Replication Gamma Hedging
22.4.2 PaR Synthetic Replication: Delta/Gamma, Pyramid Triggers
22.5 BSM/Risk Neutral Valuation a la PaR: The Story So Far
22.6 More Reality: Transactions Costs, P&L Skew’s, and “Policy”
22.6.1 Skewed P&L’s
22.6.2 Complex Options Hedging and “Operating Policy”
22.6.3 Provisioning vs. Greeks
22.7 Market Making/Position Keeping
22.8 Trade Idea Generation
22.9 Directional – Underlying
22.9.1 PaR: Risk Neutral vs. Risk Preference Usage
22.10 Directional – Vol
22.11 Directional – Rotation
22.12 Directional Volatility Trading vs. Volatility/Options Arbitrage
22.13 Generalisations of Rebalance Strategies and Analysis
22.13.1 Liquidity and Other Realities
22.13.2 Profile Matching, Rebalance Optimisers, etc.
22.13.3 Structured Products and Correlation
22.13.4 MultiDimensional Efficient Frontiers and Cardinality
22.14 Hedging vs. Directional Spread vs. “Cash” vs. “Proof”
22.14.1 Cash is King
22.14.2 Proof: PaR Forward Testing
22.14.3 Real Proof: PaR Backward Testing
22.14.4 Really Real Proof: Test Trades and Audits
22.15 Introduction to Position Keeping: Summary
22.15.1 Do You Still Want To Be An Options Trader?
22.16 Does the BSM RiskNeutral Methodology Work?
22.17 Trading with RiskNeutral Valuation Under Uncertainty
22.17.1 Synthetic Replication Delta Hedging Example 1
22.17.2 Synthetic Replication Delta Hedging Example 2
22.17.3 Synthetic Replication Gamma Hedging Example
22.18 Risk Neutral Valuation Summary
22.19 –Market Making/Position Keeping
22.20 Trade Idea Generation
22.21 Directional  Underlying
22.22 Directional  Vol
22.23 Directional – Rotation
22.24 Directional Volatility Trading vs. Volatility Arbitrage
Appendices
Appendix A: Notation/Abbreviations
Abbreviations
Currencies
Greek Letters
Alphanumeric Letters
Mathematical Operators Appendix B: ARTicles References Subject Index
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