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Introduction
The “Checklist”
Equities
1.1
Equity short time-scale risk drivers: share value
1.2
Equity large time-scale risk drivers: dividend adjusted log-value
Currencies
1.3
Currency risk drivers: exchange rate vs log-exchange rate
Fixed-income
1.5
Fixed-income risk drivers: rolling value construction
1.7
Fixed-income risk drivers: yield to maturity construction
1.8
Fixed-income risk drivers: yield curve
1.9
Yields, log-transformed and inverse-call transformed yields
1.12
Fixed-income risk drivers: Nelson-Siegel yield curve
1.13
Parametric swap curve generated by Vasicek risk drivers
1.14
Fixed-income risk drivers: spread curve
Derivatives
1.15
Derivatives risk drivers: from option values to rolling values
1.17
Derivatives risk drivers: equity implied volatility surface
1.18
Derivatives risk drivers: currency implied volatility surface
1.19
Derivatives risk drivers: log vs inverse-call implied volatility
1.21
Derivatives risk drivers: SVI implied volatility surface
1.22
Derivatives risk drivers: Heston arbitrage-free implied volatility surface
Credit
1.24
Credit risk drivers: cumulative rating transitions
1.25
Interaction between rating and scoring
1.26
Credit risk drivers: Merton structural model
High frequency
1.27
High frequency risk drivers: microprice, volume, etc
1.29
High frequency risk drivers: tick-time vs clock-time evolution
1.30
High frequency risk drivers: volume-time vs clock-time evolution
Strategies
1.34
Strategy risk driver over a short horizon: cumulative P&L
The final output
1.36
The Checklist - Step 1. Risk drivers identification.
Efficiency: random walk
2.1
Equity log-return: ellipsoid invariance test
2.2
Equity log-return: Kolmogorov-Smirnov invariance test
2.3
Microprice changes: ellipsoid invariance test
2.4
Microprice changes: Kolmogorov-Smirnov invariance test
2.5
Daily yield changes: ellipsoid invariance test
2.6
Daily yield changes: Kolmogorov-Smirnov invariance test
2.7
SVI parameters changes: ellipsoid invariance test
2.8
SVI parameter changes: Kolmogorov-Smirnov invariance test
2.11
High frequency trade intervals: ellipsoid invariance test
2.12
High frequency trade intervals: Kolmogorov-Smirnov invariance test
2.13
Tick-time increments: ellipsoid invariance test
2.14
Heavy tails: normal mixture vs Student t fit
Mean-reversion (continuous state): ARMA
2.16
Autocorrelation: AR(1) yield process vs residuals
Mean-reversion (discrete state): Markov chains
2.20
Conditional cdf of Markov chain transitions
Long memory: fractional integration
2.24
Long memory: autocorrelation ellipsoid of high frequency order sign
2.25
Long memory: autocorrelation ellipsoid of fractional integration fit
Volatility clustering
2.26
Volatility clustering: autocorrelation ellipsoid of absolute returns
2.27
Volatility clustering: autocorrelation ellipsoid of absolute GARCH residual
2.28
Volatility clustering: absolute P&L vs absolute GARCH residual
2.29
Volatility clustering: autocorrelation ellipsoid of ACD residual
2.30
Stochastic volatility fit and real-measure leverage effect
Multivariate quest
2.32
VAR(1) fit of the yield curve
The final output
2.36
The Checklist - Step 2. Quest for invariants: modeling.
2.37
The Checklist - Step 2. Quest for invariants: fitting.
2.38
The Checklist - Step 2. Quest for invariants: testing.
2.39
The Checklist - Step 2. Quest for invariants: output.
Setting the flexible probabilities
3.1
Flexible probabilities: exponential decay
3.2
Flexible probabilities: crisp
3.3
Flexible probabilities: Gaussian kernel state conditioning
3.4
Flexible probabilities: time and state conditioning via minimum relative entropy
Historical
3.6
Historical mean and covariance with flexible probabilities
Maximum likelihood
3.7
Location-dispersion: MLFP ellipsoid
Bayesian
3.11
Bayesian estimation: stocks
Shrinkage
3.12
Sample mean shrinkage: James-Stein estimator
3.13
Stocks Markov network structure via graphical lasso of correlation
Generalized method of moments
3.15
Method of moments with flexible probabilities
3.17
Generalized method of moments with flexible probabilities
Robustness
3.19
Non-robustness of sample mean and covariance
3.20
Local robustness measure: jackknife ellipsoid sensitivity
3.22
Global robustness measure: breakdown point of mean vs median
3.23
High breakdown location-dispersion ellipsoid
3.24
Farthest outlier detection with flexible probabilities
3.25
Recursive outlier rejection with flexible probabilities
Missing data
3.26
Expectation-maximization location and dispersion with missing data
3.27
Maximum likelihood location and dispersion with series of different length
3.28
Proxy estimation in the absence of data
(Dynamic) copula-marginal
3.29
Copula estimation
3.30
Copula-marginal estimation of heterogeneous invariants
3.31
Conditional correlation fit via DCC
The final output
3.32
The Checklist - Step 3. Estimation: historical.
3.33
The Checklist - Step 3. Estimation: copula-marginal.
Points of interest, pitfalls, practical tips
3.34
Conditional vs unconditional estimation
3.36
Invariants and standardized counterparts
3.38
Non-synchronous estimation via overlapping series
3.39
Non-synchronous historical estimation: tweaking scenarios vs probabilities
3.41
Univariate vs multivariate outlier detection
3.42
Exponentially weighted moving features of return series
3.45
Backward/forward exponentially weighted moving features of return series
One-step historical projection
4.1
One-step historical projection
Analytical
4.7
Projection of the multivariate Ornstein-Uhlenbeck process
Historical
4.13
Projection of stock log-value via bootstrapping
4.16
Projection of yields via historical bootstrapping
Application: multivariate Markov chains
4.19
Joint rating migrations over different time horizons
The final output
4.24
The Checklist - Step 4. Projection: one-step historical.
4.25
The Checklist - Step 4. Projection: Monte Carlo.
Points of interest, pitfalls, practical tips
4.26
Projection of historical distribution to shifting time horizon
4.27
Random walk with shifted lognormal shocks
4.28
Random walk with historical (with flexible probabilities) shocks
Exact repricing
5.2
Pricing at the horizon: equity P&L
5.3
Pricing at the horizon: foreign exchange
5.4
Pricing at the horizon: zero coupon bond value
5.5
Pricing at the horizon: coupon bond value
5.6
Pricing at the horizon: cash-flow stream
5.7
Pricing at the horizon: coupon bond P&L
5.8
Pricing at the horizon: call option value
5.9
Pricing at the horizon: defaultable bond
Carry
5.13
Foreign exchange carry of a short forward contract
5.15
Bond carry
5.16
Vega carry of variance swap
Taylor approximations
5.17
Greek approximation pricing: equity P&L
5.20
Greek approximation pricing: coupon bond P&L
5.21
Taylor approximation of a call option P&L
The final output
5.26
Pricing of a call option: historical
5.27
The Checklist - Step 5. Pricing: exact repricing via scenarios.
Static market/credit risk
6.1
Historical repriced portfolio P&L distribution with flexible probabilities
6.3
Normal approximation of portfolio distribution
6.4
Quadratic-normal pricing of portfolio P&L
Stress-testing
6.5
Stress-testing via panic copula
The final output
6.8
The Checklist - Step 6. Aggregation: scenarios.
The final output
7.1
The Checklist - Step 7. Ex-ante evaluation: scenarios.
Top-down exposures: factors on demand
8a.2
Performance of heuristic selection routines
Application: hedging
8a.3
Hedging: Black-Scholes-Merton vs. factors on demand approach
The final output
8a.4
The Checklist - Step 8a. Ex-ante attribution: performance.
Minimum-torsion bets attribution of variance
8b.1
Minimum-torsion diversification distribution
8b.2
Relative marginal diversification distribution
The final output
8b.3
The Checklist - Step 8b. Ex-ante attribution: risk.
The final output
9a.1
The Checklist - Step 9. Construction: portfolio optimization.
Simplistic portfolio construction
9b.1
Market portfolio
9b.2
High minus low portfolio
9b.3
small minus big
9b.4
Size-neutral high minus low portfolio
Advanced portfolio construction
9b.9
Characteristic portfolio of reversal strategy
9b.10
Flexible characteristic portfolio of reversal strategy
Expected utility maximization
9c.3
Time series strategies: buy and hold
9c.4
Time series strategies: maximum utility/constant weights
Option based portfolio insurance
9c.11
Time series strategies: delta hedging
Rolling horizon heuristics
9c.14
Time series strategies: constant proportion portfolio insurance
9c.15
Time series strategies: constant proportion drawdown control
Signal induced strategy
9c.16
P&L of signal-induced strategy
Convexity analysis
9c.18
Statistics of signal-induced strategy
The final output
10.3
The Checklist - Step 10.Execution.
Points of interest, pitfalls, practical tips
10.4
Trading trajectories maximizing the mean-variance trade off in the multid. Almgren-Chriss model
Factor models and learning
Regression LFM’s
13.3
Cross-correlations among residuals in regression LFM
Principal component LFM’s
13.5
Correlations among residuals in principal-component LFM
Systematic-idiosyncratic LFM’s
13.6
Systematic-idiosyncratic LFM on the stock market
Cross-sectional LFM’s
13.8
Correlations among residuals in cross-sectional LFM
Ensemble learning
16.6
Flexible probabilities: crisp selection via bootstrapping
16.7
Flexible probabilities: Dirichlet distribution
16.9
Hellinger distance among stocks
16.10
Flexible probabilities: ensemble posterior classical equivalent
16.11
Flexible probabilities: ensemble posterior curse of dimensionality
Dynamic principal component
18.1
Dynamic principal component on bivariate VAR(1)
Linear state space models
18.3
State space model fit of the swap curve
Hidden Markov models
18.4
Hidden Markov model fit for panic/calm transition in the stock market
Finite set of times to maturity
19.1
Swap curve: eigenvectors, r-square and eigenvalues
19.2
Principal component analysis of the swap curve
The continuum limit
19.3
Correlations among changes in interest rates
19.4
Swap curve: the continuum limit
Maximum likelihood
20.2
Maximum likelihood regression under normal assumption
20.3
Maximum likelihood regression under Student
Bayesian
20.7
Bayesian estimation: stocks
Regularization
20.9
Factor selection: ridge vs lasso
20.11
Factor selection: ridge vs lasso for stocks
Logistic regression
21.3
Default prediction: logistic regression
Interactions
21.4
Default prediction: logistic regression with interactions
Encoding
21.5
Default prediction: logistic regression with interactions and categorical features
Regularization
21.6
Default prediction: logistic regression with lasso
Trees
21.7
Default prediction: CART classifier ROC curve
Gradient boosting
21.8
Default prediction: CART with gradient boosting classifier ROC curve
k-means clustering
22.1
Sector clustering versus statistical (correlation) clustering
Valuation
Fundamental axioms
25a.2
put-call parity
Stochastic discount factor
25a.4
Future payoff and current value
25a.5
Gaussian-smoothed densities of stochastic discount factors
25a.6
Correct vs incorrect stochastic discount factor
Fundamental theorem of asset pricing
25a.7
Stochastic discount factor, Radon-Nikodym derivative and inflator
Risk-neutral pricing
25a.10
Risk-neutral density
Capital asset pricing model framework
25a.11
CAPM-like identity: empirical verification
25a.12
Future random payoffs and current fair values in large no-arbitrage market
Completeness
25b.2
Heat map of European call
Intertemporal consistency
25b.6
Heat map of cash-flow adjusted values at different horizons
25b.7
Numeraire-discounted values for different instruments are martingales
Options
27.2
Option prices fitted by the quadratic volatility curve
Fixed-income
27.3
Yield curve fitted by the Vasicek model
Performance analysis
Pitfalls and practical tips
29.1
Linear and compounded return difference increases with investment horizon
Quant toolbox
Efficiency: Lévy processes
46.2
Arithmetic Brownian motion with drift
46.3
Poisson process
46.4
Compound Poisson process
46.5
Stable Lévy process with Cauchy increments
Mean-reversion (discrete state)
46.8
Rating migrations over different time horizons
Long memory: fractional Brownian motion
46.9
Projection of fractional Brownian motion
Volatility clustering
46.10
Projection of Heston process
46.11
Projection of Heston process as stochastic time-changed Brownian motion
Ornstein-Uhlenbeck
47.1
Projection of the Ornstein-Uhlenbeck process
Technical signals
49.3
Cointegration signal
Microstructure signals
49.4
Trade autocorrelation signal
49.5
Order imbalance signal
49.6
Price prediction signal
49.7
Volume clustering signal
Signal processing
49.8
Effect of smoothing and scoring on the time series of a momentum signal
49.9
Scored momentum versus ranked momentum
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