Assumptions and limitations

AbaQuant models are deterministic or numerical research tools. They do not remove market, model, estimation, liquidity, counterparty, legal, accounting, operational, tax, or provider-data risk.

Global assumptions

  • Inputs use decimal annual rates and volatilities unless a function states otherwise.

  • Maturities are usually measured in years.

  • Historical estimates assume the input sample is relevant to the period being analyzed.

  • Optimizers assume the objective and constraints adequately represent the user’s decision problem.

  • Provider data are treated as inputs, not as verified truth.

Black–Scholes–Merton and Black-76

Black–Scholes–Merton assumes:

  • lognormal underlying dynamics;

  • constant volatility;

  • constant risk-free rate;

  • continuous trading;

  • frictionless markets;

  • no jumps;

  • idealized borrowing and lending;

  • known continuous dividend yield when supplied.

Black-76 applies a similar lognormal assumption to forwards or futures.

Failure modes:

  • volatility smile/skew;

  • discrete dividends;

  • early exercise;

  • jumps and halts;

  • stochastic rates;

  • transaction costs and bid-ask spreads;

  • illiquid options.

Bachelier model

Bachelier assumes normal price dynamics. It can be useful when rates or underlyings can be negative, but normal volatility is not interchangeable with lognormal volatility.

Heston

Heston introduces stochastic variance. It can represent volatility clustering and skew, but calibration is often non-convex and parameter estimates can be unstable.

Important risks:

  • local minima;

  • parameter non-identifiability;

  • numerical integration error;

  • poor extrapolation outside observed strikes and maturities;

  • violation of parameter constraints such as positivity or Feller-type conditions.

SABR

SABR is often used to interpolate volatility smiles. Hagan-style approximations are convenient but can become unreliable for extreme strikes, very short maturities, or parameter regimes outside approximation assumptions.

Jump and Levy models

Merton jump diffusion, NIG, and Variance-Gamma add skew, kurtosis, and discontinuities. They require more parameters than BSM and are correspondingly more exposed to calibration error.

Exotic options

Closed-form and approximate exotic formulas are convention-sensitive. Barrier monitoring, averaging method, rebate timing, exercise style, and settlement assumptions can materially change prices.

Portfolio optimization

Portfolio optimizers are sensitive to:

  • expected returns;

  • covariance estimates;

  • constraints and bounds;

  • missing data;

  • non-stationary correlations;

  • transaction costs;

  • turnover;

  • sampling frequency;

  • estimation window;

  • survivorship bias;

  • look-ahead bias.

Mean-variance optimization is especially sensitive to small changes in expected returns.

Backtesting

Backtests are historical simulations. They do not prove that a strategy will work out of sample.

Backtest failure modes include:

  • missing delisted assets;

  • stale prices;

  • unrealistic fills;

  • ignored taxes;

  • ignored borrow costs;

  • ignored capacity and market impact;

  • using revised data unavailable at the historical decision time;

  • optimizing after seeing the test period.

Credit proxy scoring

Fundamentals-based credit proxy scoring is an accounting heuristic, not a credit rating. It does not replace full credit analysis.

Missing dimensions include:

  • debt maturity ladder;

  • secured versus unsecured priority;

  • covenant package;

  • liquidity facilities;

  • off-balance-sheet obligations;

  • sector-specific adjustments;

  • macro regime;

  • issuer access to capital markets;

  • management quality and event risk.

Gaussian copula credit models

Copula outputs depend heavily on default probabilities, recoveries, exposures, and correlations. One-factor Gaussian copulas can understate clustered tail dependence in stress regimes.

CDS and CDO analytics

Credit derivative calculations depend on hazard-rate assumptions, premium frequency, accrual conventions, discount curves, recovery assumptions, counterparty risk, and legal definitions of credit events.

Rate curves

Manual and FRED-backed rate curves are convenient proxies. They are not production-grade curve construction.

Limitations include:

  • no bootstrapped zero-coupon curve by default;

  • no collateral curve distinction;

  • no cross-currency basis;

  • no issuer-specific funding curve;

  • no liquidity adjustment;

  • no intraday curve dynamics.

Market data

Live provider data can be stale, delayed, missing, restated, adjusted, subject to licensing restrictions, or inconsistent across providers.

Visualization and reports

Charts and reports summarize model outputs. They do not validate the economic assumptions behind those outputs.