akumidv/alphavar/pricing-and-iv

Price options & solve implied vol (Black-76) in alphavar

USAGE skill (concept → function → how to apply). Verified against src/ — re-confirm the API before relying on it.

Concept

alphavar prices futures-settled options with Black-76 (the forward variant of Black-Scholes): price is a function of forward, strike, time, vol, and rate. Implied volatility is the σ that makes the model reproduce an observed market price, solved numerically.

Source: Hull (Black-76, implied volatility). iv/price are the normalized model

output; the venue's quoted values are exch_iv / exch_mark_iv / exch_mark_price (R4).

Implementing functions

Pure functions — alphavar.options.lib.pricer.black_scholes:

• bs_forward_price(forward, strike, t_years, sigma, is_call, rate=0.0) — Black-76 price.
• bs_vega(forward, strike, t_years, sigma, rate=0.0) — vega (∂price/∂σ).
• implied_vol(price, forward, strike, t_years, is_call, rate=0.0, lo=1e-6, hi=5.0, iters=100)

— implied vol by bisection; returns NaN where the price is outside the no-arbitrage bracket (no σ reproduces it). Vectorized.

DataFrame enrichment — alphavar.options.lib.pricer: add_fair_price(...), add_model_iv(...), years_to_expiry(...).

Facade — alphavar.options.pricer_class.OptionsPricer (from OptionsData):

• add_iv(market_col=EXCH_MARK_PRICE, rate=0.0) → Self — add a model-IV column.
• add_price(vol_col=IV, rate=0.0) → Self — add a fair-price column.
• get_iv(...) → DataFrame; fit_smile(...) → smile fit (see

fit-volatility-smile).

How to apply

import numpy as np
from alphavar.options.lib.pricer.black_scholes import bs_forward_price, bs_vega, implied_vol
price = bs_forward_price(forward=100.0, strike=105.0, t_years=0.25, sigma=0.6, is_call=True)
vega  = bs_vega(forward=100.0, strike=105.0, t_years=0.25, sigma=0.6)
iv    = implied_vol(price=4.2, forward=100.0, strike=105.0, t_years=0.25, is_call=True)

from alphavar.options.pricer_class import OptionsPricer
OptionsPricer(options_data).add_iv().add_price()   # adds model iv + fair price columns

Conventions & failure modes

• Black-76 uses the forward, not spot — pass forward, not the underlying spot.
• Vol in decimals (0.6, not 60); time in years; rate is continuously compounded.
• implied_vol returns NaN for prices outside [intrinsic, forward-bound] — check for

NaN rather than trusting a silent value.

• Only `bs_vega` exists among the Greeks. Delta/gamma/theta/rho are not implemented

— do not claim them; they are a tracked gap (see `skills/README.md`).