fastmm::options Namespace Reference

Classes
struct	Greeks
struct	IvResult

Enumerations
enum class	CallPut : std::uint8_t { Call = 0 , Put = 1 }
enum class	IvStatus : std::uint8_t {   Ok = 0 , AtIntrinsic = 1 , OutOfBounds = 2 , BadInput = 3 ,   NoConvergence = 4 }

Functions
double	norm_pdf (double x) noexcept
	Standard normal density and distribution. erfc keeps the far tail accurate (no 1 - N(x)).
double	norm_cdf (double x) noexcept
constexpr double	year_fraction (std::int64_t expiry_ns, std::int64_t now_ns) noexcept
	Year fraction between two epoch-ns timestamps (ACT/365); negative once expired.
Greeks	black76 (CallPut cp, double forward, double strike, double t_years, double sigma, double rate=0.0) noexcept
	Price and greeks.
double	black76_price (CallPut cp, double forward, double strike, double t_years, double sigma, double rate=0.0) noexcept
IvResult	implied_vol (CallPut cp, double price, double forward, double strike, double t_years, double rate=0.0, double price_tol=1e-12, int max_iterations=100) noexcept
	Implied volatility of a Black-76 price.
double	to_coin_price (double quote_value, double forward) noexcept
	Quote-currency value -> price in the base coin (Deribit BTC options: USD / underlying price).
constexpr double	coin_delta (double delta, double coin_price) noexcept
	Delta of a coin-quoted option in coin units.

Variables
constexpr double	kSecondsPerYear = 365.0 * 86400.0
	ACT/365, as Deribit's theta.
constexpr double	kMinVol = 1e-4
	0.01 % annualised
constexpr double	kMaxVol = 10.0
	1000 % annualised

Enumeration Type Documentation

CallPut

enum class fastmm::options::CallPut : std::uint8_t

strong

Enumerator
Call
Put

IvStatus

enum class fastmm::options::IvStatus : std::uint8_t

strong

Enumerator
Ok
AtIntrinsic	price at (or within tolerance of) the no-arbitrage lower bound: vol 0
OutOfBounds	below intrinsic, or above what kMaxVol can produce
BadInput	non-positive forward/strike/time or non-finite price
NoConvergence	iteration bound hit; vol is the best bracket midpoint

Function Documentation

norm_pdf()

double fastmm::options::norm_pdf ( double  x )

inlinenoexcept

Standard normal density and distribution. erfc keeps the far tail accurate (no 1 - N(x)).

< 1 / sqrt(2 pi)

norm_cdf()

double fastmm::options::norm_cdf ( double  x )

inlinenoexcept

< 1 / sqrt(2)

year_fraction()

constexpr double fastmm::options::year_fraction ( std::int64_t  expiry_ns, std::int64_t  now_ns  )

constexprnoexcept

Year fraction between two epoch-ns timestamps (ACT/365); negative once expired.

black76()

Greeks fastmm::options::black76 ( CallPut  cp, double  forward, double  strike, double  t_years, double  sigma, double  rate = 0.0  )

inlinenoexcept

Price and greeks.

Degenerate inputs (T <= 0 or sigma <= 0) return the discounted intrinsic value with a step delta and zero gamma/vega/theta; F <= 0 or K <= 0 return all zeros.

black76_price()

double fastmm::options::black76_price ( CallPut  cp, double  forward, double  strike, double  t_years, double  sigma, double  rate = 0.0  )

inlinenoexcept

implied_vol()

IvResult fastmm::options::implied_vol ( CallPut  cp, double  price, double  forward, double  strike, double  t_years, double  rate = 0.0, double  price_tol = 1e-12, int  max_iterations = 100  )

inlinenoexcept

Implied volatility of a Black-76 price.

price_tol is the absolute price tolerance (same unit as price); iterations never exceed max_iterations.

Work undiscounted: the bounds are then [max(F-K, 0), F] for calls, [max(K-F, 0), K] for puts.

Brenner-Subrahmanyam start (exact at the money), kept inside the bracket.

Newton left the bracket (or produced NaN): bisect.

to_coin_price()

double fastmm::options::to_coin_price ( double  quote_value, double  forward  )

inlinenoexcept

Quote-currency value -> price in the base coin (Deribit BTC options: USD / underlying price).

coin_delta()

constexpr double fastmm::options::coin_delta ( double  delta, double  coin_price  )

constexprnoexcept

Delta of a coin-quoted option in coin units.

With V_coin = V / F, the coin value of the position changes by F * dV_coin/dF = dV/dF - V / F = delta - V_coin per unit move of F.

Variable Documentation

kSecondsPerYear

constexpr double fastmm::options::kSecondsPerYear = 365.0 * 86400.0

inlineconstexpr

ACT/365, as Deribit's theta.

kMinVol

constexpr double fastmm::options::kMinVol = 1e-4

inlineconstexpr

0.01 % annualised

kMaxVol

constexpr double fastmm::options::kMaxVol = 10.0

inlineconstexpr

1000 % annualised