Conventions and notation¶

AbaQuant uses explicit but compact financial conventions. This page defines the common symbols and units used across the package.

Glossary¶

Term	Meaning
Annual decimal rate	A rate such as `0.05` meaning 5% per year.
Annual decimal volatility	A volatility such as `0.20` meaning 20% annualized volatility.
Maturity	Time to expiration or cash-flow date, usually measured in years.
Simple return	\(R_t = P_t/P_{t-1}-1\).
Log return	\(r_t = \log(P_t/P_{t-1})\).
Discount factor	Present-value multiplier applied to a future cash flow.
Risk-neutral valuation	Pricing by discounted expected payoff under a risk-neutral measure.
Provenance	Metadata describing source, provider, cache status, request, and transformations.

Most model inputs use decimal annual rates:

risk_free_rate = 0.05  # 5% per year, not 5.0
volatility = 0.20      # 20% annual volatility, not 20.0

Continuous discounting is commonly represented as:

\[D(T)=e^{-rT}\]

where:

Symbol	Meaning
\(D(T)\)	discount factor to maturity \(T\)
\(r\)	annual continuously compounded rate
\(T\)	maturity in years

The RateCurve.discount_factor() method supports continuous, annual, and simple compounding modes.

Symbol	Meaning
\(S_0\)	spot price
\(K\)	strike price
\(T\)	maturity in years
\(r\)	risk-free rate
\(q\)	dividend yield or carry yield
\(\sigma\)	annualized volatility
\(N(\cdot)\)	standard normal cumulative distribution function

Black–Scholes–Merton call value:

\[C=S_0e^{-qT}N(d_1)-Ke^{-rT}N(d_2)\]

with:

\[d_1=\frac{\ln(S_0/K)+(r-q+\frac12\sigma^2)T}{\sigma\sqrt{T}}, \qquad d_2=d_1-\sigma\sqrt{T}.\]

Long-only fully invested portfolios commonly satisfy:

\[\mathbf{1}^\top w=1, \qquad w_i\ge 0.\]

Expected return and variance:

\[\mu_p=w^\top\mu, \qquad \sigma_p^2=w^\top\Sigma w.\]

Sharpe ratio:

\[\operatorname{Sharpe}(w)=\frac{w^\top\mu-r_f}{\sqrt{w^\top\Sigma w}}.\]

Symbol	Meaning
\(P_{ij}\)	transition probability from rating \(i\) to destination state \(j\)
\(PD\)	default probability
\(LGD\)	loss given default
\(R\)	recovery rate
\(\rho\)	asset-correlation parameter in a one-factor copula

The Gaussian one-factor form can be written as:

\[X_i=\sqrt{\rho}\,Z+\sqrt{1-\rho}\,\epsilon_i,\]

where \(Z\) is the systematic factor and \(\epsilon_i\) is an idiosyncratic factor.

Option strategy long positions are positive quantities.
Option strategy short positions are negative quantities.
Premiums are generally entered as positive paid/received amounts; strategy logic applies the position sign.
Portfolio weights are decimal fractions; 0.25 means 25% of capital.
Transaction costs in backtests are basis points when parameters end in _bps.

Provider facades may return empty frames or raise provider-specific errors when data are unavailable.
Financial-statement normalization may be incomplete if source facts do not map to canonical line items.
Credit proxy metrics can be unavailable when required denominator or historical fields are missing.