Module asian 

Analytic pricing of Asian (average) options.

• Geometric average price: exact closed form — the geometric average of lognormals is lognormal. Supports discrete equally spaced averaging (n points, matching Monte Carlo monitoring) and the continuous limit.
• Arithmetic average price: Turnbull-Wakeman (1991) lognormal moment-matching approximation, continuous averaging.

Both assume the averaging period spans the whole life of the option and has not yet started. Floating-strike (average strike) Asians have no implemented closed form and price on the Monte Carlo engine.

Enums

AsianStrikeType

Fixed strike (average price) vs floating strike (average strike).

AveragingType

How the average is computed along the path.

Functions

geometric_asian_price

Exact price of a geometric average-price Asian.

geometric_average_strike_price

Exact price of a geometric average-strike (floating-strike) Asian: the call pays (S_T - G)+ and the put (G - S_T)+, with G the geometric average of n equally spaced fixings (continuous averaging when None).

turnbull_wakeman_average_strike_price

Arithmetic average-strike (floating-strike) Asian via the Henderson-Wojakowski (2002) symmetry: at inception under GBM, a floating-strike call paying (S_T - A)+ is exactly a fixed-strike put struck at spot with the roles of r and q interchanged (and vice versa for the put). The fixed-strike side is then priced with the Turnbull-Wakeman moment match, so the symmetry step is exact and TW is the only approximation layer. Continuous averaging; exact put-call parity C - P = e^{-rT} (E[S_T] - E[A]) is preserved.

turnbull_wakeman_price

Turnbull-Wakeman approximation for an arithmetic average-price Asian (continuous averaging): the first two moments of the average are matched to a lognormal and priced with Black’s formula.