Arbitrage Research and Trading

0	Foreword and Highlights for the TG2 Series
1	Foreword and Highlights for TG2 Options Vol 1 and Caveat

PART I – Options Basic and Trading Foundation

2	First and Foremost: Trading is a Business
3	The Pay-out Formula, Contracts, and the Deliverable
4	Basic Options Structures, Pay-Out Profiles, and Usage

PART II – Pricing, Valuation, & Risk Machinery

5	Valuation Overview: Market Models vs. Options Models
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
10	Options Risk – Part 2: Measurement vs. Hedging vs. P&L
11	Valuation Under Uncertainty – Part 3:  (Some) More Reality
12	A Little 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” & Forwards
16	Generalised Black-Scholes-Merton Usage Summary & Tables
17	Option Types and Asset Classes 3:  (Basic) Exotics & Hybrids/Correlation Products
18	Introduction to Quantitative Methods for Options
19	Connection to other books (TG2 Options Vol 2 - Trading, XO's, Hybrids, Credit Derivatives, etc)

PART III – Introduction to Position Keeping and Strategies

20	Introduction to Trading & Position Keeping Strategies
21	Advanced Topics and Strategy Analyses

Appendices
References
Subject Index

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 Pay-out Formula, Contracts, and the Deliverable
3.1	Spot vs. Forward vs. Basket Contracts – What is a Derivative?
3.2	Contingent vs. Non-Contingent Instruments Basics
3.3	The Pay-Out Formula, Deliverable, and Settlement
3.4	Options vs. Contingent Derivatives: Hedging vs. Provisioning
3.5	The Risk-Neutral/Arbitrage-Free Framework Demands Liquidity

4	Basic Options Structures, Pay-Out Profiles, and Usage
4.1	Non-Contingent Derivatives:  Futures, Forwards, and (most) Underlyings
4.2	Puts, Calls, and Put-Call Parity
4.3	Pay-Out 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 Multi-Dimensional 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	Up-Side 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	End-Users 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	Multi-Asset 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	Cash-and-Carry vs. Risk-Neutrality (the “pure” market maker)
6.2	Is Cash-and-Carry Really Risk-Neutral? (often not)
6.3	(Classical) Arbitrage
6.4	Arbitrage-Free Forward Prices (“fair value”?)
6.5	Fair Value Reality for Options Trading (“42”?)
6.6	Arbitrage-Free 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	Re-coupling and De-coupling 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 Re-visited
7.7	Developing a Time-Extended (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/Root-2 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	Arbitrage-Free 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 Black-Scholes-Merton Framework (risk-neutral/arbitrage-free delivery) – The Trader’s Version
8.3.1	The Delta Risk-Neutral Hedging Strategy – Synthetic Replication
8.3.2	The Delta Risk-Neutral Hedging Strategy – Synthetic Replication with Continuous Trading
8.3.3	Dynamic Rebalancing/Synthetic Replication vs. Risk/Return
8.3.4	Risk-Free Synthetic Replication vs. Risk/Return vs. The Market Model
8.4	The Black-Scholes-Merton Framework (risk-neutral/arbitrage-free delivery) – The Quant’s Version
8.4.1	The Delta Risk-Neutral 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 Black-Scholes-Merton 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	Put-Call 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 Put-Call Parity
8.6.2	Units
8.6.3	Time vs. Intervals/Year Fractions and “Basis”
8.6.4	Forward Values (Arbitrage-Free?)
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 pro-active?)
9.4.10	(Static) Multi-Dimensional 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 Term-Structure
9.6.9	Basic VaR Summary
9.6.10	Reality Impact and Future Considerations
9.7	Profit-at-Risk (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. Black-Scholes-Merton & the Greeks
10.3.4	Summary: General Greeks Reporting/Hedging
10.4	Scenario Analysis/Reporting
10.4.1	Un-Weighted/Uniformly-Weighted Scenario Analyses
10.4.2	P&L Scenarios vs. Sensitivity Scenarios
10.4.3	Multi-Dimensional Scenarios
10.4.4	Probability-Weighted Scenario Analyses
10.4.5	Instrument/Structure Analyses vs. Portfolio Analyses
10.5	Types of Hedging
10.6	(1-Dimensional) Sensitivity Hedging with (Some) Variations
10.6.1	1-Dimensional Hedges (Greeks and 01’s)
10.6.2	Delta
10.6.3	Gamma
10.6.4	Delta + Gamma (Higher-Order 1-Dimensional)
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 “Look-Ahead” Optimisation
10.7.8	Quasi-Optimisation (a solution for the common man)
10.7.9	Single-Period Dynamic Hedge Optimisation
10.8	Multi-Index/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	Risk-Neutral/Arbitrage-Free (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 Mean-Reverting
11.1.5	Constant Elasticity of Variance (CEV)
11.1.6	Jump-Diffusion
11.1.7	Ornstein-Ühlenbeck: 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 Fat-tailed Distributions
11.2.4	General Distributions
11.3	Non-Stochastic Market Models
11.3.1	Fractal Dimension Adjusted Options Pricing
11.4	Instrument Effects – such as Pull-to-Par
11.5	Multi-Index/Multi-Factor Problems
11.5.1	Multi-Index Contracts: 2-Factor Valuation
11.5.2	Spread Options
11.5.3	Stochastic Volatility
11.5.4	n-Factor Valuation vs. n-Factor Forecasting
11.6	Term-Structure Models
11.6.1	Basic Terminology
11.6.2	A simple One-Factor Model (non-traditional)
11.6.3	A simple Two-Factor Model (non-traditional)
11.6.4	Traditional Term-Structure Representation
11.6.5	Comparison of Selected Term-structure Models
11.6.6	Traditional Term-Structure: How Many Factors are “Best”?
11.6.7	Traditional Term-Structure: Calibration
11.7	Term-Structure 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 – Binomial-Tree Illustration/Valuation
13.3	American Exercise – Barone-Adesi/ 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	Sub-Optimal Early Exercise Scenarios
13.4.2	American Option Put-Call-Parity
13.4.3	First thoughts on “path dependence” for early exercise
13.4.4	Is the BAW-like (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) Early-Exercise 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 IRP-PPP
14.2.3	The US Dollar, Economy, and Financial Markets
14.2.4	Risk-Neutral/Arbitrage-Free (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- & Rate-based)
14.6.5	Log-Normal Prices vs. Log-Normal Yields
14.6.6	Pull-to-Par Revisited:  Pull-to-Par of What (price-based vs. yield-based)?
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	Pull-to-Par for Swaptions
14.6.12	Serial Options (Caps, Floors, and Collars)
14.6.13	Put-Call-Parity for Caps/Floors
14.6.14	IR Option Position Keeping:  Curves, Buckets, and More
14.6.15	Term-Structure of Rates vs. Term-Structure of Volatility
14.6.16	Term-Structure Models (Mean-reversion, 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	Mark-to-Market/Valuation Issues
14.6.23	Interest Rates and Currencies
14.6.24	As Components of Structured/Hybrid Products
14.6.25	A Real Trade – Call-Spreads Revisited
14.7	FX Options
14.7.1	FX Forwards: ERA’s vs. FXA’s
14.7.2	Market Convention Valuation
14.7.3	Fat-Tailed
14.7.4	Jump-Diffusion
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	End user vs. other (gold: inflation/safe-haven/currency)
14.8.4	Softs

15	Option Types and Asset Classes 2:  Market Convention “Listed/Futures” & Forwards
15.1	Spot-based vs. Forward-based Underlying
15.2	Listed vs. OTC Options Contracts
15.2.1	OTC
15.2.2	Listed
15.2.3	EFP
15.2.4	Delivery Cycles
15.2.5	Margining
15.2.6	Clearing vs. Execution
15.2.7	Rolls, Strikes, Staggered Expirations, and other realities
15.2.8	Rotation effects (cap/swaptions vs. futures/strips)
15.2.9	Price Based vs. Rate Based/FRA-Convexity
15.2.10	A Real Trade – Ratio Call Spread

16	Generalised Black-Scholes-Merton Usage Summary & Tables
17	Option Types and Asset Classes 3:  (Basic) Exotics & Hybrids/Correlation Products
17.1	Exotic Options (in ten words or less)
17.1.1	Forward Start Options
17.1.2	Contingent Premium Options
17.1.3	Asian Options
17.1.4	Digital Options
17.1.5	Barrier Options
17.1.6	Lookback Options
17.1.7	Chooser Options
17.2	Introduction to Hybrids and Multi-Factor/Correlation Products
17.2.1	Callable/Putable and Extendible/Retractable
17.2.2	Convertible Bonds CB’s
17.2.3	Up-Side Participation Structures
17.2.4	Fair-Way Bonds/Accrual Notes
17.2.5	Quanto’s
17.2.6	Credit Protected Bonds

18	Introduction to Quantitative Methods for Options
18.1	Models vs. Solutions
18.2	Analytic Methods vs. Numerical Methods
18.3	Introduction to Monte Carlo Methods
18.3.1	Market Model vs. Options Model
18.3.2	Vanilla Options
18.3.3	Asian Options
18.3.4	Mean-Reverting Option Valuation
18.3.5	Issues with MC Methods
18.4	Introduction to Tree Methods
18.4.1	Market Model vs. Options Model
18.4.2	Vanilla Options
18.4.3	American Options
18.4.4	Issues with Tree Methods
18.5	Introduction to Finite Difference Methods
18.5.1	Market Model vs. Options Model
18.5.2	Vanilla Options
18.5.3	Issues with Tree Methods
18.6	Introduction to Multi-Factor Methods

19	Connection to other books (TG2 Options Vol 2 - Trading, XO's, Hybrids, Credit Derivatives, etc)

PART III – Introduction to Position Keeping and Strategies

20	Introduction to Trading & Position Keeping Strategies
20.1	Does the BSM Risk-Neutral Methodology Work?
20.2	Trading with Risk-Neutral Valuation Under Uncertainty
20.2.1	Synthetic Replication Delta Hedging Example 1
20.2.2	Synthetic Replication Delta Hedging Example 2
20.2.3	Synthetic Replication Gamma Hedging Example
20.3	Risk Neutral Valuation Summary
20.4	-Trade Idea Generation
20.5	-Directional - Underlying
20.6	-Directional - Vol
20.7	-Directional – Rotation

21	Advanced Topics and Strategy Analyses
21.1	Volatility
21.1.1	Historical Volatility
21.1.2	Implied and Model Volatility
21.1.3	“Traded/Rebalance” Volatility
21.1.4	Model Arbitrage
21.2	Volatility Cheap/Dear Analyses
21.3	Directional Volatility Trading vs. Volatility Arbitrage
21.4	Scenario Analyses
21.5	PaR – For the Sophisticated

Appendices

Appendix A: Notation/Abbreviations
Abbreviations
Currencies
Greek Letters
Alphanumeric Letters
Mathematical Operators

Appendix B: ARTicles

References

Subject Index