volkit.utils

volkit.utils.discount_to_rate(discount_rate, *, t=None, days=None, days_per_year=365)[source]

Convert a discount factor into a continuously compounded annualized rate.

Exactly one of t or days must be provided to specify the time horizon.

Parameters:

  • discount_rate (float) – Discount factor. Must be finite and strictly positive (> 0).

  • t (float, optional) – Time horizon in years. Mutually exclusive with days.

  • days (int or float, optional) – Time horizon in days. Mutually exclusive with t.

  • days_per_year (int or float, default=365) – Number of days per year used to convert days into years.

Returns:

Continuously compounded annualized rate corresponding to the discount factor.

Return type:

float

Raises:

ValueError – If neither or both of t and days are provided. If discount_rate is not finite or not strictly positive. If the resulting time horizon (years) is not strictly positive.

Examples

>>> discount_to_rate(0.95, t=0.5)  # roughly half a year
0.102586...
>>> discount_to_rate(0.95, days=90)  # 90 trading days with 365/yr
0.20802...
>>> discount_to_rate(1.0, t=1.0)
0.0
volkit.utils.rate_to_discount(rate, *, t=None, days=None, days_per_year=365)[source]

Convert a continuously compounded annualized rate into a discount factor.

Exactly one of t or days must be provided to specify the time horizon.

Parameters:

  • rate (float) – Continuously compounded annualized rate. May be negative or positive, but must be finite (no NaN/Inf).

  • t (float, optional) – Time horizon in years. Mutually exclusive with days.

  • days (int or float, optional) – Time horizon in days. Mutually exclusive with t.

  • days_per_year (int or float, default=365) – Number of days per year used to convert days into years.

Returns:

Discount factor in (0, +inf) given by exp(-rate * t_years).

Return type:

float

Raises:

ValueError – If neither or both of t and days are provided. If rate is not finite. If the resulting time horizon (years) is not strictly positive.

Examples

>>> rate_to_discount(0.1, t=0.5)
0.9512...
>>> rate_to_discount(0.1, days=90)
0.9756...
>>> rate_to_discount(0.0, t=1.0)
1.0