Accumulators and decumulators — the daily-accrual structured
products (“I-kill-you-later”): the holder is committed to trade a
fixed quantity at a fixed price on every observation date while the
structure is alive, with a knock-out barrier on the favorable side
and geared (typically doubled) quantity on the adverse side.
Forward-start options: the strike is fixed at a future date t_f as a
fraction k of the then-prevailing spot; the payoff at expiry T is
(S_T - k * S_{t_f})^+ (call) or the mirrored put.
2-D ADI finite-difference engine for the Heston PDE — the grid
counterpart of the Monte Carlo QE engine, and the independent
cross-check for early exercise under stochastic volatility.
Perpetual (infinite-maturity) American options — Merton (1973)
closed forms. Unlike the finite-maturity approximations
(baw,
bjerksund_stensland) these are
exact: with no expiry the American value solves the stationary ODE
1/2 sigma^2 S^2 V'' + b S V' - r V = 0 with value matching and
smooth pasting at a constant exercise boundary.
Stochastic Local Volatility (SLV): Heston-style stochastic variance
multiplied by a leverage function calibrated so the model
reprices the market’s vanilla surface exactly (in the limit):