Lab |

[ 1.1 ] Equities

[ 1.2 ] Currencies

[ 1.2.1 ] Exchange rates

[ 1.2.2 ] Contracts

[ 1.3 ] Fixed-income

[ 1.3.1 ] Zero-coupon bond

[ 1.3.2 ] Rolling value

[ 1.3.3 ] Yield to maturity

[ 1.3.4 ] Alternative representations

[ 1.3.5 ] Parsimonious representations

[ 1.3.6 ] Spreads

[ 1.4 ] Derivatives

[ 1.4.1 ] Call option

[ 1.4.2 ] Rolling value

[ 1.4.3 ] Implied volatility

[ 1.4.4 ] Alternative representations

[ 1.4.5 ] Parsimonious representations

[ 1.4.6 ] Pure volatility products

[ 1.5 ] Credit

[ 1.5.1 ] Definitions

[ 1.5.2 ] Conditioning risk drivers

[ 1.5.3 ] Aggregate risk drivers

[ 1.6 ] Insurance

[ 1.7 ] Operations

[ 1.8 ] High frequency

[ 1.8.1 ] Market microstructure

[ 1.8.2 ] Activity time

[ 1.8.3 ] Time-changed variables

[ 1.9 ] Strategies

[ 1.10 ] Points of interest, pitfalls, practical tips

[ 1.10.1 ] Spurious heteroscedasticity

[ 1.10.2 ] Spot, par, yield, forward, zero, risk-free,...which rate and curve?

[ 2.1 ] Efficiency: random walk

[ 2.1.1 ] Continuous-state random walk

[ 2.1.2 ] Discrete-state random walk

[ 2.1.3 ] Flexible combinations

[ 2.2 ] Mean-reversion (continuous state): ARMA

[ 2.2.1 ] AR(1) process

[ 2.2.2 ] AR(1) generalizations

[ 2.3 ] Mean-reversion (discrete state)

[ 2.3.1 ] Markov chains

[ 2.3.2 ] Markov chains for credit

[ 2.3.3 ] Structural models for credit

[ 2.3.4 ] Connection Markov chains/structural models

[ 2.4 ] Long memory: fractional integration

[ 2.5 ] Volatility clustering

[ 2.5.1 ] GARCH

[ 2.5.2 ] Extensions of GARCH

[ 2.5.3 ] Stochastic volatility

[ 2.6 ] Multivariate quest

[ 2.6.1 ] Copula-marginal models

[ 2.6.2 ] Efficiency: multivariate random walk

[ 2.6.3 ] Mean reversion (continuous state): VAR(I)MA

[ 2.6.4 ] Mean reversion (discrete state)

[ 2.6.5 ] Volatility clustering

[ 2.6.6 ] Toward machine learning

[ 2.7 ] Cointegration

[ 2.7.1 ] Modeling

[ 2.7.2 ] Detection

[ 2.8 ] Points of interest, pitfalls, practical tips

[ 2.8.1 ] Returns are not invariants

[ 2.8.2 ] Sampling step size

[ 3.1 ] (Dynamic) copula-marginal

[ 3.1.1 ] Static copula

[ 3.1.2 ] Application: credit risk

[ 3.1.3 ] Dynamic copula

[ 3.2 ] Points of interest, pitfalls, practical tips

[ 3.2.1 ] Standardization

[ 3.2.2 ] Non-synchronous data

[ 3.2.3 ] High-frequency volatility/correlation

[ 4.1 ] One-step historical projection

[ 4.2 ] Univariate analytical projection

[ 4.2.1 ] Efficiency: Lévy processes

[ 4.2.2 ] Mean-reversion (continuous state)

[ 4.2.3 ] Mean-reversion (discrete state)

[ 4.2.4 ] Long memory: fractional Brownian motion

[ 4.2.5 ] Volatility clustering

[ 4.3 ] Multivariate analytical projection

[ 4.4 ] Monte Carlo

[ 4.4.1 ] Markov models

[ 4.4.2 ] State-space models

[ 4.4.3 ] Generalizations

[ 4.5 ] Historical

[ 4.5.1 ] Historical bootstrapping

[ 4.5.2 ] Hybrid Monte Carlo-historical

[ 4.6 ] Application to credit risk

[ 4.6.1 ] Copula-marginal approach

[ 4.7 ] Square-root rule and generalizations

[ 4.7.1 ] Thin-tailed random walk

[ 4.7.2 ] Thick-tailed random walk

[ 4.7.3 ] Multivariate random walk

[ 4.7.4 ] General processes

[ 4.8 ] Points of interest, pitfalls, practical tips

[ 4.8.1 ] Consecutive (non-)overlapping sequences

[ 4.8.2 ] Semi-analytical random walk projection via fast Fourier transform

[ 4.8.3 ] GARCH generalized next-step

[ 4.8.4 ] Projection step at a later stage of the Checklist

[ 4.8.5 ] Pitfalls for square-root rule

[ 4.8.6 ] Thick tails from thin tails

[ 4.8.7 ] Martingales

[ 4.8.8 ] Linear versus compounded returns

[ 4.8.9 ] FFT for moving averages

[ 4.8.10 ] Scenario projection enhancements by probability twisting

[ 4.8.11 ] Jumps versus diffusion

[ 5.1 ] Exact repricing

[ 5.1.1 ] Equities

[ 5.1.2 ] Currencies

[ 5.1.3 ] Fixed-income

[ 5.1.4 ] Derivatives

[ 5.1.5 ] Credit

[ 5.1.6 ] High frequency

[ 5.2.3 ] Fixed-income

[ 5.2.4 ] Derivatives

[ 5.2.5 ] Other asset classes

[ 5.3 ] Taylor approximations

[ 5.3.1 ] Equities

[ 5.3.2 ] Fixed-income

[ 5.3.3 ] Derivatives

[ 5.3.4 ] Other asset classes

[ 5.4 ] Hybrid Taylor/repricing approximation

[ 5.4.1 ] Global quadratic approximation

[ 5.4.2 ] Interpolated residual

[ 5.5 ] Joint P&L distribution

[ 5.5.1 ] Analytical approach

[ 5.5.2 ] Scenario-based approach

[ 5.6 ] Testing the pricing function

[ 5.7 ] Pitfalls and practical tips

[ 5.7.1 ] Pricing at the horizon and arbitrage

[ 5.7.2 ] Path dependence

[ 5.7.3 ] “Pricing at the horizon”versus “asset pricing/valuation theory”

[ 5.7.4 ] Black-Merton-Scholes is exactly correct!

[ 5.7.5 ] Greeks for intra-day updates

[ 5.7.6 ] Greeks at the horizon

[ 5.7.7 ] Bond carry versus accrued interest

[ 5.7.8 ] Option carry versus theta

[ 6.1 ] Stock variables

[ 6.2 ] Credit value adjustment

[ 6.3 ] Liquidity value adjustment

[ 6.4 ] Static market/credit risk

[ 6.4.1 ] Standardized holdings and weights

[ 6.4.2 ] Scenario-probability distribution

[ 6.4.3 ] Elliptical distribution

[ 6.4.4 ] Quadratic-normal distribution

[ 6.5 ] Dynamic market/credit risk

[ 6.6 ] Stress-testing

[ 6.6.1 ] Theory

[ 6.6.2 ] Why have stress-tests

[ 6.6.3 ] Panic copula

[ 6.6.4 ] Extreme copula

[ 6.7 ] Enterprise risk management

[ 6.7.1 ] Portfolio: balance sheet

[ 6.7.2 ] Performance: income statement

[ 6.7.3 ] Operational risk

[ 6.7.4 ] Banking simplified regulatory framework

[ 6.7.5 ] Insurance simplified framework

[ 6.8 ] Points of interest and pitfalls

[ 6.8.1 ] Solvency and collateral

[ 6.8.2 ] CreditRisk+ approximation

[ 7.1 ] Stochastic dominance

[ 7.2 ] Satisfaction/risk measures

[ 7.3 ] Mean-variance trade-off

[ 7.3.1 ] Mean

[ 7.3.2 ] Variance

[ 7.3.3 ] Standard deviation

[ 7.3.4 ] Mean-variance trade-off

[ 7.3.5 ] A strange success story

[ 7.4 ] The fundamental risk quadrangle

[ 7.4.1 ] Relevant cases

[ 7.4.2 ] Generalizations

[ 7.5 ] Expected utility and certainty-equivalent

[ 7.5.1 ] Common examples

[ 7.5.2 ] Computation

[ 7.6 ] Value at Risk and quantile

[ 7.6.1 ] Definition

[ 7.6.2 ] Computation

[ 7.7 ] Expected shortfall and sub-quantile

[ 7.7.1 ] Definition

[ 7.7.2 ] Computation

[ 7.8 ] Spectral/distortion satisfaction measures

[ 7.8.1 ] Definition

[ 7.8.2 ] Common examples

[ 7.8.3 ] Computation

[ 7.9 ] Coherent satisfaction measures

[ 7.9.1 ] Definition

[ 7.9.2 ] Common examples

[ 7.9.3 ] Computation

[ 7.10 ] Induced expectations

[ 7.10.1 ] Definition

[ 7.10.2 ] Common examples

[ 7.10.3 ] Computation

[ 7.11 ] Non-dimensional ratios

[ 7.11.1 ] Signal-to-noise ratio

[ 7.11.2 ] Downside ratios

[ 7.11.3 ] Correlation

[ 7.12 ] Enterprise risk management

[ 7.13 ] Pitfalls, points of interest and practical tips

[ 7.13.1 ] The Arrow-Pratt approximation of the certainty-equivalent

[ 7.13.2 ] Utility versus quantile

[ 7.13.3 ] Utility versus spectrum functions

[ 7.13.4 ] The Buhlmann and Esscher expectations are not distortion expectations

[ 7.13.5 ] Satisfaction measures under normality

[ 8a.1 ] Bottom-up exposures

[ 8a.1.1 ] Pricing factors

[ 8a.1.2 ] Style factors/smart beta

[ 8a.2 ] Top-down exposures: factors on demand

[ 8a.2.1 ] Analytical computation

[ 8a.2.2 ] Cardinality constraints

[ 8a.3 ] Relationship between bottom-up and top-down exposures

[ 8a.3.1 ] Subportfolios

[ 8a.3.2 ] Style factors/smart beta

[ 8a.4 ] Joint distribution

[ 8a.4.1 ] Elliptical distribution

[ 8a.4.2 ] Scenario-probability distribution

[ 8a.5 ] Application: hedging

[ 8a.6 ] Pitfalls and practical tips

[ 8a.6.1 ] Estimation versus attribution

[ 8a.6.2 ] The ex-ante attribution is not a regression on past data

[ 8b.1 ] General criteria

[ 8b.1.1 ] Isolated/“first in”proportional attribution

[ 8b.1.2 ] “Last in”proportional attribution

[ 8b.1.3 ] Sequential attribution

[ 8b.1.4 ] Shapley attribution

[ 8b.2 ] Euler decomposition

[ 8b.2.1 ] Standard deviation and variance

[ 8b.2.2 ] Certainty-equivalent

[ 8b.2.3 ] Quantile

[ 8b.2.4 ] Sub-quantile

[ 8b.2.5 ] Spectral satisfaction measures

[ 8b.2.6 ] Coherent measures

[ 8b.2.7 ] Economic capital

[ 8b.3 ] Linear attribution for induced expectations

[ 8b.3.1 ] Actuarial pricing

[ 8b.4 ] Minimum-torsion bets attribution of variance

[ 8b.4.1 ] Minimum-torsion bets

[ 8b.4.2 ] Effective number of bets

[ 9a.1 ] Mean-variance framework

[ 9a.1.1 ] Special portfolios

[ 9a.1.2 ] Quadratic target formulation

[ 9a.1.3 ] Setting the inputs

[ 9a.2 ] Analytical mean-variance

[ 9a.2.1 ] Total return

[ 9a.2.2 ] Excess return over risk-free

[ 9a.2.3 ] Excess return over benchmark

[ 9a.2.4 ] Total versus excess return

[ 9a.3 ] Numerical mean-variance

[ 9a.3.1 ] Constraints on positions/trade size

[ 9a.3.2 ] Constraints on number of positions

[ 9a.3.3 ] Transaction costs

[ 9a.4 ] Fundamental law of active management

[ 9a.4.1 ] Monetary impact of one signal

[ 9a.4.2 ] Information coefficient

[ 9a.4.3 ] Monetary impact of multiple signals

[ 9a.4.4 ] Aggregation

[ 9a.4.5 ] Transfer coefficient

[ 9a.5 ] Pitfalls, points of interest and practical tips

[ 9a.5.1 ] Black-Litterman equilibrium inputs via minimum relative entropy

[ 9b.1 ] Estimation risk measurement

[ 9b.2 ] Sample-based allocation

[ 9b.3 ] Prior allocation

[ 9b.4 ] Estimation (=input) uncertainty: Bayesian allocation

[ 9b.5 ] Allocation (=output) uncertainty: Robust allocation

[ 9b.6 ] Diversification management

[ 9c.1 ] Simplistic portfolio construction

[ 9c.1.1 ] Backtesting

[ 9c.2 ] Advanced portfolio construction

[ 9c.2.1 ] Signal-induced factor

[ 9c.2.2 ] Flexible factor

[ 9c.2.3 ] Backtesting

[ 9c.3 ] Relationship with FLAM and APT

[ 9c.3.1 ] Signal-induced moments of the P&L

[ 9c.3.2 ] Fundamental law of active management

[ 9c.3.3 ] APT assumption

[ 9c.4 ] Multiple portfolios

[ 9c.4.1 ] Characteristic portfolios

[ 9c.4.2 ] Signal-induced factors

[ 9c.4.3 ] Flexible factors

[ 9c.4.4 ] Relationship with FLAM and APT

[ 9c.5 ] Points of interest, pitfalls, practical tips

[ 9c.5.1 ] Machine learning

[ 9d.1 ] The market

[ 9d.1.1 ] Risky investment

[ 9d.1.2 ] Low-risk investment

[ 9d.1.3 ] Strategies

[ 9d.2 ] Expected utility maximization

[ 9d.2.1 ] The objective

[ 9d.2.2 ] Optimization

[ 9d.3 ] Option based portfolio insurance

[ 9d.3.1 ] Payoff design

[ 9d.3.2 ] Partial differential equation

[ 9d.3.3 ] Budget

[ 9d.3.4 ] Policy

[ 9d.3.5 ] A unified approach

[ 9d.4 ] Rolling horizon heuristics

[ 9d.4.1 ] Constant proportion portfolio insurance

[ 9d.4.2 ] Drawdown control

[ 9d.5 ] Signal induced strategy

[ 9d.6 ] Convexity analysis

[ 10.1 ] Market impact modeling

[ 10.1.1 ] Liquidity curve

[ 10.1.2 ] Exogenous impact

[ 10.1.3 ] Endogenous impact

[ 10.2 ] Order scheduling

[ 10.2.1 ] Trading P&L decomposition

[ 10.2.2 ] Model P&L

[ 10.2.3 ] Moments of model P&L

[ 10.2.4 ] Model P&L optimization

[ 10.2.5 ] Quasi-optimal P&L distribution

[ 10.3 ] Order placement

[ 10.3.1 ] Step 1: order scheduling

[ 10.3.2 ] Step 2: order placement

[ 10.4 ] Points of interest, pitfalls, practical tips

[ 10.4.1 ] Mean-variance optimization in complex models

[ 10.4.2 ] Price manipulation

[ 10.4.3 ] Testing

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