Financial Mathematics, Derivatives and Structured Products (Springer Finance)

Preface
Acknowledgments
Contents
Acronyms
Notation
Part I Financial Markets
	1 Introduction to Financial Markets
		1.1 Investable Assets and Financial Instruments
		1.2 Investment Returns and Risks
		1.3 Investment Performance Measures
		1.4 Financial Markets
		1.5 Central Counterparty (CCP)
		1.6 Securities Lending and Repo
		1.7 Derivatives Activities
		Exercises
	2 Financial Transactions and Counterparty Risk Management*
		2.1 Concepts in the Life Cycle of a Financial Transaction
		2.2 Margining Methods for Mitigating Counterparty Risk
		2.3 Exchange-Traded Derivatives*
		2.4 OTC Derivatives*
			2.4.1 OTC Derivatives Documentation*
			2.4.2 Centralized Clearing*
			2.4.3 Non-Centrally Cleared Derivatives*
		2.5 Risk Management for Investment Financing*
		Exercises
	3 Interest Rate Instruments: I
		3.1 Interest Rate Conventions
			3.1.1 Day Count Convention
			3.1.2 Business Day Convention
		3.2 Interest Rate Types and Zero Coupon Bond
			3.2.1 Simple Rate
			3.2.2 Compound Rate
			3.2.3 Continuous Rate
			3.2.4 Conversion of Interest Rates
			3.2.5 Zero Coupon Bond
		3.3 Money Market Instruments
		3.4 Reference (Floating) Rates in Financial Market
			3.4.1 Front-Fixed Reference Rates
				IBOR (Interbank Offered Rate)
				Repo Rate
			3.4.2 Rear-Fixed Reference Rates
				Overnight Reference Rates
				Rear-Fixed Term Reference Rates
		3.5 Bonds
			3.5.1 Bond Features and Types
			3.5.2 Bond Quotation and Yield to Maturity
			3.5.3 Duration, Modified Duration, BPV, DV01 and Convexity
		3.6 Credit Rating
		3.7 Main Risks for a Debt Security
		Exercises
	4 Interest Rate Instruments: II
		4.1 Forward Rate Agreement and Single-Period Swap
		4.2 Interest Rate Futures
			4.2.1 Short-Term Interest Rate (STIR) Futures
			4.2.2 Treasury Bond Futures*
		4.3 Interest Rate Swap (IRS)
			4.3.1 Asset Swap as an IRS Application
			4.3.2 IRS Valuation
			4.3.3 Overnight Indexed Swap (OIS)
			4.3.4 Other Interest Rate Swaps*
			4.3.5 Swap Clearing*
			4.3.6 Swap Futures*
		4.4 Yield Curve Construction
			4.4.1 Yield Curve
			4.4.2 Interpolation Method for Yield Curve
			4.4.3 Bootstrapping Method
			4.4.4 Illustration Example for Yield Curve Construction
		4.5 Multiple Zero-Coupon Curves*
		Exercises
	5 Equities and Equity Indices
		5.1 Equity
		5.2 Corporate Actions
			5.2.1 Stock Dividend
			5.2.2 Stock Split, Reverse Stock Split, Rights Issue*
			5.2.3 Impact of Corporate Actions*
			5.2.4 No-Arbitrage Condition for Derivatives Price and Contract Terms Adjustment*
			5.2.5 Total Return Asset*
			5.2.6 Historical Price Adjustment due to CorporateActions*
		5.3 Equity Index
		5.4 Equity Forward and Cash and Carry Strategy
		5.5 Equity Index Futures
		5.6 Equity Swap*
		Exercises
	6 Foreign Exchange Instruments
		6.1 Quotation Conventions
		6.2 FX Spot, Forward, Swap, Non-deliverable Forward (NDF)
		6.3 Interest Rate Parity for FX Forward
		6.4 Cross Currency Swap and Non-deliverable Swap (NDS)
		Exercises
	7 Commodities
		7.1 Commodities Overview
		7.2 Commodity Forward and Futures
		7.3 A Special Commodity: Gold
		Exercises
	8 Credit Derivatives
		8.1 Credit Default Swap (CDS)
		8.2 CLN (Credit Linked Note)
		8.3 Credit Index*
		8.4 Collateralized Debt Obligation (CDO)*
			8.4.1 Synthetic CDO*
			8.4.2 Single Tranches on Credit Index*
		Exercises
	9 Investment Funds
		9.1 Funds
			9.1.1 Fund NAV and Fees
			9.1.2 Fund Organization*
			9.1.3 Share Classes*
		9.2 Mutual Fund
		9.3 Hedge Fund*
		9.4 Fund Structures*
		9.5 Fund Derivatives*
		Exercises
	10 Options
		10.1 Option General Features
			10.1.1 Option Style
			10.1.2 Moneyness of an Option
			10.1.3 Notional Amount Definition
		10.2 Option Price, Intrinsic Value and Time Value
		10.3 Vanilla Options
			10.3.1 Equity Options
			10.3.2 Foreign Exchange Options
			10.3.3 Commodity Options
			10.3.4 Interest Rate Options*
				Cap/Floor
				Swaption
			10.3.5 Option Pricing, Hedging, and Execution*
				Option Hedging/Pricing
				Option Order Execution
				Vanilla Option Pricing
				Option Quotation
			10.3.6 Implied Volatility*
			10.3.7 Put-Call Parity
			10.3.8 Popular Strategies with European Options
			10.3.9 American Options
		10.4 Exotic Options
			10.4.1 Barrier Option
			10.4.2 Binary (or Digital) Option
			10.4.3 In-Out Parity*
			10.4.4 Asian Option or Average Option
			10.4.5 Lookback Option
			10.4.6 Quanto Option and Composite Option
			10.4.7 Basket Option, Worst-of, and Rainbow Options
		10.5 Derivatives Modelling Framework*
			10.5.1 Purpose of Derivatives Modelling
			10.5.2 Model Input Parameters and Calibration*
			10.5.3 Historical Volatility and Correlation*
		Exercises
	11 Introduction to Structured Products
		11.1 Background and Purpose of Structured Products
		11.2 Principal Protected Product Example
		11.3 Non-principal Protected Product Example
		11.4 Quanto Feature in Structured Products
		11.5 Risks of Structured Products to Investors
		Exercises
Part II Stochastic Calculus and Financial Modelling
	12 Review of Basic Probability Concepts
		12.1 Probability Space, Measure, and Properties
		12.2 Independence and Conditional Probability
		12.3 Random Variable and Distribution
			12.3.1 Distribution
			12.3.2 Expectation
			12.3.3 Variance and Covariance
			12.3.4 Independent Random Variables
			12.3.5 Conditional Probability Distribution
			12.3.6 Conditional Expectation Given Event
			12.3.7 Characteristic and Moment Generating Functions
			12.3.8 Normal Distribution
			12.3.9 Exponential Distribution
			12.3.10 Poisson Distribution
		12.4 Limit Theorems
			12.4.1 Law of Large Numbers
			12.4.2 Central Limit Theorem
			12.4.3 Confidence Interval
		Exercises
	13 Stochastic Calculus: I
		13.1 Stochastic Process
		13.2 Conditional Expectation Given σ-Algebra*
		13.3 Martingale, Stopping Time
		13.4 Markov Property*
		13.5 Quadratic Variation
		13.6 Brownian Motion
		13.7 Itô Integral and Itô Calculus
		13.8 Poisson Process*
		Exercises
	14 Black–Scholes–Merton Model for Option Pricing
		14.1 The Black–Scholes–Merton Model
		14.2 Derivation of the Black–Scholes Equation
		14.3 Black–Scholes Formulas for Vanilla Options
		14.4 Derivatives Price Sensitivities (Greeks)
		14.5 Practical Issues in Hedging*
			14.5.1 Hedging Instruments and Hedging Ratios
			14.5.2 Discrete Hedging
			14.5.3 Delta-Hedging P/L
			14.5.4 Motivation for Volatility Modelling
			14.5.5 Transaction Cost*
		Exercises
	15 Stochastic Calculus: II
		15.1 Change of Probability
		15.2 Predictable Martingale Representation
		15.3 Stochastic Differential Equations
		15.4 Kolmogorov Equations*
		15.5 Breeden–Litzenberger Formulas*
		15.6 Further Properties of Brownian Motion (BM)*
			15.6.1 Covariance of Brownian Motions
			15.6.2 First Passage Time
			15.6.3 Extremum to Date
			15.6.4 Reflection Principle
			15.6.5 Distribution of First Passage Time
			15.6.6 Joint Distribution for BM Extremum
			15.6.7 Conditional Distribution for Drifted BM Extremum
		Exercises
	16 Risk-Neutral Pricing Framework
		16.1 Money Market Account and Discounting
		16.2 Self-Financing Portfolio
			16.2.1 Properties of a Self-Financing Portfolio
			16.2.2 Excess Return, Self-Financing and Portfolio Return
		16.3 Risk-Neutral Probability Measure
		16.4 Pricing and Hedging of Derivatives
		16.5 Discussion on Hedging, Pricing and Risk-Neutral Framework
		16.6 The Black–Scholes–Merton Model Revisited
			16.6.1 Closed-Form Formulas for European VanillaOptions
			16.6.2 Vega-Gamma Relationship*
		16.7 Dividend Modelling
			16.7.1 Dividend Types
			16.7.2 Continuous Dividend Modelling
			16.7.3 Discrete Dividend Modelling*
			16.7.4 Adjustment to Derivatives for Corporate Actions*
		16.8 Collateralized Derivative Pricing and FVA*
		16.9 Futures and Forward Modelling*
			16.9.1 Futures
			16.9.2 Forward
			16.9.3 Futures/Forward Convexity Adjustment
		16.10 Overview on Numerical Methods for Option Pricing
		Exercises
	17 Numéraires and Vanilla Interest Rate Options Pricing*
		17.1 Introduction of Numéraire
		17.2 Change of Numéraire
		17.3 Generalized Risk-Neutral Framework
		17.4 Usual Numéraires and Vanilla Interest Rate Options Pricing
			17.4.1 Money Market Account Numéraire
			17.4.2 Zero-Coupon Bond Numéraire and Cap/FloorPricing
				Pricing of Cap or Floor
			17.4.3 Annuity Factor Numéraire and Swaption Pricing
				Pricing of Swaption
			17.4.4 SABR Model for Vanilla Interest Rate Options
		Exercises
	18 Foreign Exchange Modelling
		18.1 Stochastic Model for Foreign Exchange Rate
			18.1.1 Cross Rate Volatility
		18.2 Pricing Formulas for Vanilla Options and FX Option Duality
			18.2.1 FX Option Duality
		18.3 SDE for Foreign Asset Under Domestic Risk-NeutralProbability
		18.4 Quanto Option
		18.5 Composite Option
		18.6 Discussions on Hedging*
		Exercises
	19 American and Exotic Options*
		19.1 American Options
			19.1.1 General Analysis on American Options
			19.1.2 American Option Price Process*
			19.1.3 Partial Differential Inequality*
		19.2 Pricing of Some Exotic Options under the BSM Model*
			19.2.1 European Binary Options
			19.2.2 American Binary and Barrier Options
			19.2.3 Asian Options with Continuous Sampling*
				A Useful Result
	20 Hedging/Pricing Options and Structured Products in Practice*
		20.1 Barrier Risk and the Mitigation Methods
			20.1.1 Smoothing for European Barrier
			20.1.2 Smoothing for American Barrier
		20.2 Correlation Risk
			20.2.1 Sources of Correlation Risk
			20.2.2 Correlation Risk Management
		20.3 Large Delta Issue
		Exercises
	21 Numerical Method (1): Monte Carlo Simulation
		21.1 Monte Carlo Method for Pricing European Options
			21.1.1 Simulation Under the Black–Scholes–MertonModel
		21.2 Generating One-Dimensional Normal Variate
			21.2.1 Inverse Sampling
			21.2.2 Box–Muller Method*
		21.3 Generating Multi-Dimensional Normal Variates*
			21.3.1 Cholesky Factorization
			21.3.2 Eigenvector Factorization*
		21.4 Simulation Accuracy Measure*
		21.5 Variance Reduction Techniques*
			21.5.1 Antithetic Sampling
			21.5.2 Control Variables
			21.5.3 Importance Sampling
			21.5.4 Stratified Sampling*
			21.5.5 Moment Matching
		21.6 Quasi-Monte Carlo*
			21.6.1 Low-Discrepancy Sequences
				One Dimensional Low-Discrepancy Sequence
				Multi-Dimensional Low-Discrepancy Sequence
			21.6.2 Principal Component Method*
			21.6.3 Brownian Bridge Method*
		21.7 Monte Carlo Approach for American Options*
			21.7.1 Introduction
			21.7.2 Least-Squares Method for Lower Bound
			21.7.3 Martingale Method for Upper Bound*
		Exercises
	22 Numerical Method (2): Binomial and Trinomial Trees
		22.1 Binomial Tree Method
			22.1.1 Tree Construction
			22.1.2 Determination of the Parameters
			22.1.3 European Option Pricing
			22.1.4 American Option Pricing
			22.1.5 Greeks*
			22.1.6 Accuracy and Stability Analysis*
				Accuracy Analysis
				Stability Analysis
		22.2 Trinomial Tree Method*
		22.3 Discrete Dividends*
		22.4 Barrier and Path-Dependent Options Pricing Issues*
			22.4.1 Barrier Options
			22.4.2 Other Path-Dependent Options
		Exercises
	23 Numerical Method (3): PDE Approach*
		23.1 Introduction to Finite Difference Method
			23.1.1 Derivatives Approximation
			23.1.2 Discretization Grid
			23.1.3 Resolution Equations
			23.1.4 Boundary Conditions
				Specific Boundary Conditions
				General Boundary Conditions with Zero Gamma
			23.1.5 Terminal Condition
		23.2 Finite Difference Schemes
			23.2.1 Explicit Scheme
			23.2.2 Implicit Scheme
			23.2.3 Crank–Nicolson Scheme and θ-Scheme*
		23.3 Numerical Resolution for Finite Difference Methods*
			23.3.1 Direct Method
			23.3.2 Iterative Method
		23.4 Numerical Resolution for American Options*
		23.5 Multi-Dimensional PDE Derivation*
			23.5.1 Dynamic Hedging Portfolio Approach
			23.5.2 Risk-Neutral Framework Approach
		23.6 Alternating Direction Implicit (ADI) Method*
		23.7 ADI Method with Mixed Derivative Terms*
		23.8 Discrete Dividend*
		23.9 Discrete Observation/Sampling*
			23.9.1 No-Arbitrage Condition for Discrete Sampling*
			23.9.2 Discrete Sampling for Backward Pricing Approach
		23.10 Accuracy and Consistency Analysis*
		23.11 Stability and Convergence Analysis*
		Exercises
Part III Extensions to Financial Modelling
	24 Static Hedging, Variance Swap and Volatility Index*
		24.1 Static Hedging for European Style Options
		24.2 Variance Swap
			24.2.1 Valuation of Variance Swap
		24.3 Volatility Index*
		Exercises
	25 Local and Stochastic Volatility Models
		25.1 Local Volatility Model
			25.1.1 Local Volatility Calculation by Call Option Prices
			25.1.2 Local Volatility Calculation by ImpliedVolatilities*
			25.1.3 Local Volatility Calculation with DiscreteDividends*
			25.1.4 Practical Implementation
		25.2 Stochastic Volatility Models*
			25.2.1 Heston Model
				1st PDE Derivation Method
				2nd PDE Derivation Method
				Closed-Form Solution for European Options Under Heston Model
				Numerical Approaches for Closed-Form Solution
			25.2.2 Forward Variance Model
				Bergomi\'s Multi-Factor Forward Variance Model
				Bergomi\'s Discrete Forward Variance Model
			25.2.3 Local-Stochastic Volatility (LSV) Model
		Exercises
	26 Jump-Diffusion Models*
		26.1 Compound Poisson Process
		26.2 Simulating a Poisson Process and Compound PoissonProcess
		26.3 Stochastic Calculus for Jump-Diffusion Processes
		26.4 Jump-Diffusion Model for Option Pricing
		26.5 European Call or Put Option Pricing
		26.6 PIDE for European Style Options*
			26.6.1 Derivation of PIDE
			26.6.2 Finite Difference Method for PIDE
		26.7 Discussion on Hedging Under Jump-Diffusion Model*
		Exercises
	27 Interest Rate Term Structure Modelling*
		27.1 Continuous-Time Modelling of Interest Rate
			27.1.1 Zero Coupon Bond
			27.1.2 Short Rate
			27.1.3 Forward Rate
		27.2 Heath–Jarrow–Morton Framework
			27.2.1 No-Arbitrage Short Rate Model
			27.2.2 Markovian Characterization for Short Rate Models
		27.3 Short Rate Models
			27.3.1 Hull–White One-Factor Model
			27.3.2 Two-Factor LGM (Linear Gaussian Markov)
				Extension for Volatility Skew
			27.3.3 CIR (Cox-Ingersoll-Ross) One-Factor Model
			27.3.4 Affine-Yield Models*
				Interest Rate Derivatives Pricing with Short Rate Models
		27.4 BGM Model
			27.4.1 Factor Reduction
			27.4.2 Stochastic Volatility
		Exercises
	28 Credit Modelling*
		28.1 Credit Modelling
			28.1.1 Structural Model
			28.1.2 Intensity Model
		28.2 CDS (Credit Default Swap)
		28.3 Credit Triangle
		28.4 Pricing and Hedging of Multi-Name Credit Derivatives*
			28.4.1 Copula
			28.4.2 One-Factor Gaussian Copula Model
			28.4.3 Multi-Name Credit Derivatives Pricing
				First-To-Default Swap
				Single Tranche CDO Swap
			28.4.4 Hedging Multi-Name Credit Derivatives*
		28.5 Counterparty Risk Measures
			28.5.1 PFE (Potential Future Exposure)
			28.5.2 VaR (Value-at-Risk)
			28.5.3 Close-Out Risk
			28.5.4 EPE (Expected Positive Exposure)
			28.5.5 CVA (Credit Value Adjustment)
			28.5.6 Wrong-Way Risk
			28.5.7 Basel Risk Weight Function*
		Exercises
	29 Commodity Modelling*
		29.1 Spot Model
		29.2 Futures Model
		29.3 Multi-Factor Models*
		Exercises
Part IV Structured Products and Solutions
	30 Structured Products: Structuring Topics
		30.1 Building Blocks
		30.2 Underliers
		30.3 Wrapper or Instrument
		30.4 Payoff Structuring Techniques
		30.5 Investment Leveraging
		30.6 Pricing and Hedging
		30.7 Funding Management
		30.8 Back-Testing
	31 Popular Option Based Structured Products
		31.1 Equity Structured Products
			31.1.1 Equity Linked Note (ELN)
			31.1.2 Fixed Coupon Callable Note (FCN)
			31.1.3 Daily Range Accrual Callable Note (DAC)
			31.1.4 Phoenix Callable Note
			31.1.5 Snowball Structure
			31.1.6 Issuer Callable Structure
			31.1.7 Shark-Fin
			31.1.8 Accumulator
			31.1.9 Decumulator
			31.1.10 Bonus Enhanced Note (BEN)
			31.1.11 Twin-Win
			31.1.12 Tracker+ Note
			31.1.13 Booster Note
			31.1.14 Wedding Cake
			31.1.15 Stellar Note
			31.1.16 CBBC: Callable Bull/Bear Contract
			31.1.17 Cliquet Option
			31.1.18 Himalaya
		31.2 Fixed-Income Structured Products
			31.2.1 Range Accrual
			31.2.2 Inverse Floater
			31.2.3 Zero Coupon Callable Note
			31.2.4 Reverse Convertible Note on Rate
			31.2.5 Yield Spread Structure
		31.3 Foreign-Exchange Structured Products
			31.3.1 Dual Currency Investment (DCI)
			31.3.2 FX Accumulator
			31.3.3 Target Redemption Forward (TARF)
				Variations of TRF: Pivot Structures
		31.4 Commodities Structured Products
		31.5 Hybrid Structured Products
			31.5.1 Best-of Profile
			31.5.2 Callable Range Accrual
			31.5.3 Gap Note*
		31.6 Fund Linked Structured Products
			31.6.1 Bullish Note
			31.6.2 Bullish Coupon Note
		31.7 Credit Linked Structured Products
			31.7.1 Credit Linked Note (CLN)
			31.7.2 CLN on Credit Index
		31.8 Equity Derivatives for Corporates
			31.8.1 Financing
				Convertible Bonds (CB)
				Margin Loan
				Collar Financing
			31.8.2 Shares Buy-Back and Disposal
				Structures for Fixed Price but Uncertain Quantity
				Structures for Fixed Quantity but Uncertain Price
			31.8.3 Greenshoe (Over-Allotment) Option*
		Exercises
	32 Structured Products with Dynamic Asset Allocationand Systematic Strategies
		32.1 Principal Protection with Dynamic Asset Allocation
			32.1.1 Volatility Target
			32.1.2 Actively Managed Portfolio with Protection
			32.1.3 Gap Risk Based Asset Allocation: CPPI and TIPP
				CPPI (Constant Proportion Portfolio Insurance)
				TIPP (Time Invariant Portfolio Protection)
		32.2 Structured Products with Systematic Strategies
			32.2.1 Introduction to Factor Models
				Single-Factor Model: Capital Asset Pricing Model (CAPM)
				Multi-Factor Asset Pricing Models
				Some Well-Known Factors
			32.2.2 Portfolio Approach
				Notations and Basic Properties for Portfolios
				Mean-Variance Optimization (MVO)
				Structured Products with Rebalancing Portfolios
		Exercises
A Some Elements in Probability Theory, Linear Algebraand Analysis
	A.1 Multivariate Random Variable
	A.2 Multivariate Normal Distribution
	A.3 Unbiased Estimators
	A.4 Multiple Least-Squares Regression
	A.5 Plackett\'s Identity
	A.6 Dirac Delta Function
	A.7 Box–Muller Method for Uniform Variables
	A.8 Approximation of Distribution Function for NormalVariables
	A.9 Inversion of Characteristic Functions
B Closed-Form Solutions to Some Options
	B.1 Vanilla Options on Stocks
	B.2 Vanilla Options on Foreign Exchange Rate
	B.3 Vanilla Options on Futures
	B.4 Barrier Options
C Sobol Method for Low-Discrepancy Sequence
	C.1 Sobol Sequence Generation
	C.2 Simplification of Sobol Sequence Generation with Gray Code
	C.3 Direction Numbers
	C.4 Comments on Uniformity
	C.5 Comments on the Rationale of the Method
D Some Results of Portfolio Theory
E Representation of CIR Process as a Squared Bessel Process
	E.1 Squared Bessel Process
	E.2 Representation of CIR Process
References
Index