Unit 14 of 14
Execution calibration and mathematical production
- 8 lessons
- Videos 105 to 112
Models are used through trades, calibration and code. This unit covers order books, price impact, execution and market making, then automatic differentiation, calibration and model validation.
A queue model gives fill probabilities in an order book, and adverse selection explains a spread even without price impact. Implementation shortfall measures execution against the decision price, and the Almgren-Chriss model balances impact cost against price risk. Market making sets quotes around a reservation price that depends on inventory. Automatic differentiation computes sensitivities through pricing code but needs care with discontinuous payoffs. Calibration is an inverse problem that can fail to identify parameters, and validation checks invariants, numerical convergence and drift.
Every lesson will be one video. The videos are coming soon, and each lesson page already has the definitions and an example for every key term.
Order books, execution and market making
Limit order books and queueing models
How a FIFO queue model of the limit order book gives the probability that a resting order fills by a deadline, using arrival intensities, Poisson counts, Erlang waiting times and birth-death extensions.
Video 105
Order flow adverse selection and price impact
How signed order flow and price response are measured, how adverse selection gives an informational bid and ask by Bayes' rule, and how stipulated permanent and temporary impact differ from that spread.
Video 106
Transaction cost analysis and execution benchmarks
How transaction cost analysis measures implementation shortfall against a paper portfolio, splits it at the arrival price into delay, execution and opportunity cost, and compares it with a VWAP benchmark.
Video 107
Optimal execution and the Almgren Chriss model
How the continuous Almgren-Chriss model weighs temporary impact cost against a variance risk penalty, and how the Euler-Lagrange equation gives the unique optimal inventory trajectory and its execution urgency.
Video 108
Market making and inventory control
How a market maker with exponential utility prices inventory risk through a certainty equivalent, derives reservation bid and ask prices, and sets approximate quotes from an exponential fill intensity.
Video 109
Differentiation, calibration and validation
Differentiable pricing and automatic differentiation
How automatic differentiation applies the chain rule to a pricing computational graph in forward and reverse mode, when pathwise derivatives may be exchanged with expectation, and why a digital payoff breaks that exchange.
Video 110
Calibration inverse problems and identifiability
How calibration inverts a forward pricing map with a weighted loss, how the price Jacobian shows which parameters quotes identify, what ridge selection adds and what an out-of-sample hedge tests.
Video 111
Model validation reproducibility and monitoring
How model validation checks a model through financial invariants and numerical convergence tests, how drift monitoring raises alerts after deployment, and what reproducibility and documented model limitations require.
Video 112