Lab |

[ 39a.2 ] Fundamental theorem of asset pricing

[ 39a.2.1 ] Linear pricing equation

[ 39a.2.2 ] Numeraire

[ 39a.2.3 ] Identification issues

[ 39a.3 ] Risk-neutral pricing

[ 39a.3.1 ] Discrete-time rebalancing

[ 39a.3.2 ] No rebalancing: forward measure

[ 39a.3.3 ] Continuous rebalancing limit

[ 39a.4 ] Capital asset pricing framework

[ 39a.4.1 ] Maximum Sharpe ratio portfolio

[ 39a.4.2 ] Security market line

[ 39a.4.3 ] Connections to CAPM and linear factor models

[ 39a.5 ] Covariance principle

[ 39b.1 ] Completeness

[ 39b.1.1 ] General statement

[ 39b.1.2 ] Arrow-Debreu securities

[ 39b.1.3 ] European options

[ 39b.2 ] Equilibrium: capital asset pricing model

[ 39b.3 ] Arbitrage pricing theory

[ 39b.3.1 ] Standard derivation: linear factor model for instruments

[ 39b.4 ] Intertemporal consistency

[ 39b.4.1 ] The framework

[ 39b.4.2 ] Intertemporal linear pricing equation

[ 39b.4.3 ] Intertemporal fundamental theorem of asset pricing

[ 39c.1 ] Fundamental axioms

[ 39c.1.1 ] Law of one price

[ 39c.1.2 ] Non-linearity

[ 39c.1.3 ] Arbitrage

[ 39c.2 ] Valuation as evaluation

[ 39c.2.1 ] Variance and other shift principles

[ 39c.2.2 ] Certainty-equivalent principle

[ 39c.2.3 ] Distortion principles

[ 39c.2.4 ] Esscher principle

[ 39c.3 ] Intertemporal consistency

[ 39c.3.1 ] Continuous time variables

[ 39c.3.2 ] Non-linear “martingales”?

[ 39c.4 ] Point of interest and pitfalls

[ 39c.4.1 ] Linear (mis)uses of non-linear pricing

[ 39d.1 ] Equities

[ 39d.1.1 ] Discounted cash-flows

[ 39d.1.2 ] Multiples

[ 39d.2 ] Options

[ 39d.2.1 ] Bachelier

[ 39d.2.2 ] Black-Scholes

[ 39d.2.3 ] Heston

[ 39d.2.4 ] Valuation recipe

[ 39d.3 ] Fixed-income

[ 39d.3.1 ] Vasicek

[ 39d.3.2 ] Other models

[ 39d.3.3 ] Valuation recipe

[ 39d.4 ] Insurance

[ 39d.4.1 ] Life insurance

[ 39d.4.2 ] Non-life insurance

[ 39d.5 ] Real assets

[ 40.1 ] Equities

[ 40.2 ] Currencies

[ 40.2.1 ] Exchange rates

[ 40.2.2 ] Contracts

[ 40.3 ] Fixed-income

[ 40.3.1 ] Zero-coupon bond

[ 40.3.2 ] Rolling value

[ 40.3.3 ] Yield to maturity

[ 40.3.4 ] Alternative representations

[ 40.3.5 ] Parsimonious representations

[ 40.3.6 ] Spreads

[ 40.4 ] Derivatives

[ 40.4.1 ] Call option

[ 40.4.2 ] Rolling value

[ 40.4.3 ] Implied volatility

[ 40.4.4 ] Alternative representations

[ 40.4.5 ] Parsimonious representations

[ 40.4.6 ] Pure volatility products

[ 40.5 ] Credit

[ 40.5.1 ] Definitions

[ 40.5.2 ] Conditioning risk drivers

[ 40.5.3 ] Aggregate risk drivers

[ 40.6 ] Insurance

[ 40.7 ] Operations

[ 40.8 ] High frequency

[ 40.8.1 ] Market microstructure

[ 40.8.2 ] Activity time

[ 40.8.3 ] Time-changed variables

[ 40.9 ] Strategies

[ 40.10 ] Points of interest, pitfalls, practical tips

[ 40.10.1 ] Spurious heteroscedasticity

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

[ 41.1 ] Multivariate quest

[ 41.1.1 ] Copula-marginal models

[ 41.1.2 ] Efficiency: multivariate random walk

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

[ 41.1.4 ] Mean reversion (discrete state)

[ 41.1.5 ] Volatility clustering

[ 41.1.6 ] Toward machine learning

[ 41.2 ] Cointegration

[ 41.2.1 ] Modeling

[ 41.2.2 ] Detection

[ 41.3 ] Points of interest, pitfalls, practical tips

[ 41.3.1 ] Returns are not invariants

[ 41.3.2 ] Sampling step size

[ 42.1 ] (Dynamic) copula-marginal

[ 42.1.1 ] Static copula

[ 42.1.2 ] Application: credit risk

[ 42.1.3 ] Dynamic copula

[ 42.2 ] Points of interest, pitfalls, practical tips

[ 42.2.1 ] Standardization

[ 42.2.2 ] Non-synchronous data

[ 42.2.3 ] High-frequency volatility/correlation

[ 43.1 ] One-step historical projection

[ 43.2 ] Univariate analytical projection

[ 43.2.1 ] Efficiency: Lévy processes

[ 43.2.2 ] Mean-reversion (continuous state)

[ 43.2.3 ] Mean-reversion (discrete state)

[ 43.2.4 ] Long memory: fractional Brownian motion

[ 43.2.5 ] Volatility clustering

[ 43.3 ] Multivariate analytical projection

[ 43.4 ] Monte Carlo

[ 43.4.1 ] Markov models

[ 43.4.2 ] State-space models

[ 43.4.3 ] Generalizations

[ 43.5 ] Historical

[ 43.5.1 ] Historical bootstrapping

[ 43.5.2 ] Hybrid Monte Carlo-historical

[ 43.6 ] Application to credit risk

[ 43.6.1 ] Copula-marginal approach

[ 43.7 ] Square-root rule and generalizations

[ 43.7.1 ] Thin-tailed random walk

[ 43.7.2 ] Thick-tailed random walk

[ 43.7.3 ] Multivariate random walk

[ 43.7.4 ] General processes

[ 43.8 ] Points of interest, pitfalls, practical tips

[ 43.8.1 ] Consecutive (non-)overlapping sequences

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

[ 43.8.3 ] GARCH generalized next-step

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

[ 43.8.5 ] Pitfalls for square-root rule

[ 43.8.6 ] Thick tails from thin tails

[ 43.8.7 ] Martingales

[ 43.8.8 ] Linear versus compounded returns

[ 43.8.9 ] FFT for moving averages

[ 43.8.10 ] Scenario projection enhancements by probability twisting

[ 43.8.11 ] Jumps versus diffusion

[ 44.1 ] Exact repricing

[ 44.1.1 ] Equities

[ 44.1.2 ] Currencies

[ 44.1.3 ] Fixed-income

[ 44.1.4 ] Derivatives

[ 44.1.5 ] Credit

[ 44.1.6 ] High frequency

[ 44.1.7 ] Strategies

[ 44.2 ] Carry

[ 44.2.1 ] Equities

[ 44.2.2 ] Currencies

[ 44.2.3 ] Fixed-income

[ 44.2.4 ] Derivatives

[ 44.2.5 ] Other asset classes

[ 44.3 ] Taylor approximations

[ 44.3.1 ] Equities

[ 44.3.2 ] Fixed-income

[ 44.3.3 ] Derivatives

[ 44.3.4 ] Other asset classes

[ 44.4 ] Hybrid Taylor/repricing approximation

[ 44.4.1 ] Global quadratic approximation

[ 44.4.2 ] Interpolated residual

[ 44.5 ] Joint P&L distribution

[ 44.5.1 ] Analytical approach

[ 44.5.2 ] Scenario-based approach

[ 44.6 ] Testing the pricing function

[ 44.7 ] Pitfalls and practical tips

[ 44.7.1 ] Repricing and arbitrage

[ 44.7.2 ] Path dependence

[ 44.7.3 ] “Repricing”versus “asset pricing/valuation theory”

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

[ 44.7.5 ] Greeks for intra-day updates

[ 44.7.6 ] Greeks at the horizon

[ 44.7.7 ] Bond carry versus accrued interest

[ 44.7.8 ] Option carry versus theta

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