Property specifications

Each property below is an exported function that returns bool: call it with your own inputs to check that a finance relationship holds there before you rely on it. For example, put_call_parity_holds(cast(100.0, f32), cast(100.0, f32), cast(0.05, f32), cast(0.2, f32), cast(1.0, f32)) is true when the call minus the put is within 0.001 of s - k * exp(-r * t). A true covers the point you passed, not every input.

Pricing properties

Module: Shoals.Properties.Pricing.

• put_call_parity_holds(s, k, r, sigma, t): the call minus the put equals s - k * exp(-r * t).
• call_price_nonneg and put_price_nonneg: check non-negative prices.
• call_bounded_by_spot(s, k, r, sigma, t): checks that the call price does not exceed spot at the supplied point.
• matches_textbook_reference and matches_textbook_reference_put: bs_call_scalar and bs_put_scalar are within 5e-5 of the textbook formulas in Textbook references at the supplied point.
• mc_matches_textbook_mc_reference(template, s0, k, r, sigma, t): under a shared seed the optimized Monte Carlo agrees with the scalar Monte Carlo reference to within five percent.

No-arbitrage properties

Module: Shoals.Properties.NoArbitrage.

• bull_spread_nonneg(s, k_low, k_high, r, sigma, t): checks that a lower-strike call costs at least as much as a higher-strike call.
• butterfly_nonneg(s, k, h, r, sigma, t): checks that c(k - h) - 2 c(k) + c(k + h) >= -0.001, an absolute price tolerance. Use 0 < h < k; a false means the call prices are not convex in strike at that point by more than 0.001.

Greek properties

Module: Shoals.Properties.Greeks.

• fd_delta_in_unit_range_for_call: the finite-difference call delta lies in [0, 1].
• fd_delta_matches_analytic: the finite-difference call delta agrees with the analytic N(d1).
• vega_nonneg: the finite-difference vega is non-negative.

Monte Carlo properties

Module: Shoals.Properties.MonteCarlo.

• same_literal_seed_same_price(template, s, k, r, sigma, t): two Monte Carlo runs under the same literal seed return the identical price.
• mc_within_5pct_of_analytic(template, s, k, r, sigma, t): the Monte Carlo price is within five percent of the closed form.

Curve properties

Module: Shoals.Properties.Curves.

• parallel_shift_uniformly_lifts and parallel_shift_zero_is_identity: a parallel shift lifts the interpolated rate by exactly the shift, and a zero shift changes nothing.
• twist_at_midpoint_is_average: a twist applies the average of the short and long shifts at the midpoint.
• key_rate_shift_localized_at_unmoved_pillar: a key-rate shift does not move the rate at an untouched pillar.
• scale_rates_linear: scaling multiplies the interpolated rate by the factor.

Volatility-surface properties

Module: Shoals.Properties.VolSurface.

• vs_total_variance_nonneg_for_atm: the at-the-money total variance is non-negative.
• vs_implied_vol_matches_sqrt_variance: the implied vol equals sqrt(max(w, 0) / t).
• implied_vol_round_trip(spot, strike, r, t, sigma_true): pricing a call at a known volatility and inverting recovers that volatility.

Distribution properties

Module: Shoals.Properties.Distributions.

• lognormal_pdf_matches_textbook, lognormal_cdf_matches_textbook, student_t_pdf_matches_textbook, bvn_pdf_matches_textbook: each density or cumulative agrees with its Shoals.References.Distributions reference.
• lognormal_pdf_nonneg: the lognormal density is non-negative.
• student_t_pdf_symmetric_at_zero: the Student-t density is symmetric.

Date properties

Module: Shoals.Properties.Date.

Year fractions are exact rationals, so every date property is an equality, not a tolerance.

• actual_matches_reference(start, end): ACT/360 and ACT/365 Fixed equal the reference day count over 360 and over 365.
• isda_matches_reference(start, end): ACT/ACT ISDA equals the per-year reference sum.
• icma_matches_reference(start, end, period_start, period_end, frequency): ACT/ACT ICMA equals the reference ratio.
• whole_isda_year_is_exactly_one(year): a whole calendar year is exactly one ACT/ACT ISDA year, leap or not.
• additive_under_isda(a, b, c): the ACT/ACT ISDA fraction over a..c is the exact sum of those over a..b and b..c.

These properties describe calendar and tenor relationships. They do not imply that make_bar validates market-data ordering; its input checks are described in Scope and limitations.

Tenor properties

Module: Shoals.Properties.Tenor.

• schedule_is_increasing_and_bounded(start, end, months): a short-final schedule of whole-month tenors starts at start, ends at end, and is strictly increasing, whatever the day of month.

Market-data properties

Module: Shoals.Properties.MarketData.

• quote_round_trip(side, value, d): a constructed quote reads back its value.
• md_bar_high_gte_low, md_bar_close_in_high_low_range, md_bar_open_in_high_low_range: check a supplied bar's OHLC ordering. make_bar does not enforce that ordering.
• snapshot_empty_has_no_quote(d, key): an empty snapshot returns no quote.

Signatures

Every property returns bool:

def put_call_parity_holds(s: f32, k: f32, r: f32, sigma: f32, t: f32) -> bool
def call_price_nonneg(s: f32, k: f32, r: f32, sigma: f32, t: f32) -> bool
def put_price_nonneg(s: f32, k: f32, r: f32, sigma: f32, t: f32) -> bool
def call_bounded_by_spot(s: f32, k: f32, r: f32, sigma: f32, t: f32) -> bool
def matches_textbook_reference(s: f32, k: f32, r: f32, sigma: f32, t: f32) -> bool
def matches_textbook_reference_put(s: f32, k: f32, r: f32, sigma: f32, t: f32) -> bool
def bull_spread_nonneg(s: f32, k_low: f32, k_high: f32, r: f32, sigma: f32, t: f32) -> bool
def butterfly_nonneg(s: f32, k: f32, h: f32, r: f32, sigma: f32, t: f32) -> bool
def mc_matches_textbook_mc_reference[n](template: tensor[n, f32], s0: f32, k: f32, r: f32, sigma: f32, t: f32) -> bool
def same_literal_seed_same_price[n](template: tensor[n, f32], s: f32, k: f32, r: f32, sigma: f32, t: f32) -> bool
def mc_within_5pct_of_analytic[n](template: tensor[n, f32], s: f32, k: f32, r: f32, sigma: f32, t: f32) -> bool
def fd_delta_in_unit_range_for_call(s: f32, k: f32, r: f32, sigma: f32, t: f32) -> bool
def fd_delta_matches_analytic(s: f32, k: f32, r: f32, sigma: f32, t: f32) -> bool
def vega_nonneg(s: f32, k: f32, r: f32, sigma: f32, t: f32) -> bool
def parallel_shift_uniformly_lifts(c: YieldCurve[3], delta: f32, probe_t: f32) -> bool
def parallel_shift_zero_is_identity(c: YieldCurve[3], probe_t: f32) -> bool
def twist_at_midpoint_is_average(c: YieldCurve[3], short_d: f32, long_d: f32, t_mid: f32) -> bool
def key_rate_shift_localized_at_unmoved_pillar(c: YieldCurve[3], pillar_idx: i64, delta: f32, far_t: f32) -> bool
def scale_rates_linear(c: YieldCurve[3], factor: f32, probe_t: f32) -> bool
def vs_total_variance_nonneg_for_atm(p: SVI) -> bool
def vs_implied_vol_matches_sqrt_variance(p: SVI, k: f32, t: f32) -> bool
def implied_vol_round_trip(spot: f32, strike: f32, r: f32, t: f32, sigma_true: f32) -> bool
def lognormal_pdf_matches_textbook(x: f32, mu: f32, sigma: f32) -> bool
def lognormal_cdf_matches_textbook(x: f32, mu: f32, sigma: f32) -> bool
def student_t_pdf_matches_textbook(x: f32, nu: f32) -> bool
def bvn_pdf_matches_textbook(x: f32, y: f32, mu_x: f32, mu_y: f32, sigma_x: f32, sigma_y: f32, rho: f32) -> bool
def lognormal_pdf_nonneg(x: f32, mu: f32, sigma: f32) -> bool
def student_t_pdf_symmetric_at_zero(nu: f32, dx: f32) -> bool
def actual_matches_reference(start: Date, end: Date) -> bool
def isda_matches_reference(start: Date, end: Date) -> bool
def icma_matches_reference(start: Date, end: Date, period_start: Date, period_end: Date, frequency: i64) -> bool
def whole_isda_year_is_exactly_one(year: i64) -> bool
def additive_under_isda(a: Date, b: Date, c: Date) -> bool
def schedule_is_increasing_and_bounded(start: Date, end: Date, months: i64) -> bool
def quote_round_trip(side: Side, value: f32, d: Date) -> bool
def md_bar_high_gte_low(b: Bar) -> bool
def md_bar_close_in_high_low_range(b: Bar) -> bool
def md_bar_open_in_high_low_range(b: Bar) -> bool
def snapshot_empty_has_no_quote(d: Date, key: string) -> bool

See Scope and limitations for a description of what these properties do and do not establish.