Module heston 

Heston (1993) stochastic volatility model.

Dynamics under the risk-neutral measure:

dS = (r - q) S dt + sqrt(v) S dW_s
dv = kappa (theta - v) dt + vol_of_vol * sqrt(v) dW_v,   d<W_s, W_v> = rho dt

Semi-analytic pricing uses the characteristic function in the “little Heston trap” formulation (Albrecher et al. 2007), which is branch-cut stable under the principal complex logarithm, integrated with composite Simpson. Vanilla calls/puts and both binary types come from the same two probabilities: call = S e^{-qT} P1 - K e^{-rT} P2, cash-or-nothing = e^{-rT} P2, asset-or-nothing = S e^{-qT} P1.

Monte Carlo simulation lives in the Monte Carlo engine (full-truncation Euler; the Andersen QE scheme is the planned upgrade).

Structs

HestonParams

Heston parameters. theta is the long-run variance, v0 the initial variance, vol_of_vol the volatility of variance (often written xi or sigma), rho the spot-variance correlation.

Functions

analytic_delta

analytic_gamma

analytic_npv

analytic_rho

analytic_theta

analytic_vega

Sensitivity to a parallel shift of the instantaneous and long-run vol.

heston_binary_asset_price

Semi-analytic Heston price of an asset-or-nothing binary (S e^{-qT} P1 for a call).

heston_binary_cash_price

Semi-analytic Heston price of a cash-or-nothing binary (cash * e^{-rT} * P(S_T beyond K)).

heston_price

Semi-analytic Heston price of a European vanilla option.