Exotic Derivatives¶

qufin supports pricing and analysis of exotic derivatives beyond vanilla European options.

Bermudan Options (Longstaff-Schwartz)¶

Bermudan options can be exercised at specific dates before expiration. Priced via Least-Squares Monte Carlo (LSM).

from qufin.derivatives.bermudan_lsm import price_bermudan_put

price = price_bermudan_put(
    s0=100,
    strike=105,
    r=0.05,
    sigma=0.2,
    T=1.0,
    n_steps=12,          # monthly exercise dates
    n_paths=100_000,
    basis_functions=3,   # polynomial degree for continuation value
)
print(f"Bermudan put price: {price:.4f}")

Basket Options¶

Options on a weighted basket of multiple underlying assets.

from qufin.derivatives.basket import price_basket_option

price = price_basket_option(
    spots=[100, 110, 95],
    weights=[0.4, 0.35, 0.25],
    strike=100,
    r=0.05,
    sigma=[0.2, 0.25, 0.18],
    corr_matrix=corr,    # 3x3 correlation matrix
    T=1.0,
    n_paths=100_000,
    option_type="call",
)

Autocallable Notes¶

Structured products that automatically redeem if the underlying exceeds a barrier on observation dates.

from qufin.derivatives.autocallable import price_autocallable

price = price_autocallable(
    s0=100,
    autocall_barrier=1.05,    # 105% of initial
    coupon_rate=0.08,         # 8% annual coupon
    ki_barrier=0.70,          # 70% knock-in barrier
    observation_dates=[0.25, 0.5, 0.75, 1.0],  # quarterly
    r=0.05,
    sigma=0.25,
    T=1.0,
    n_paths=100_000,
)

Path-Dependent Options¶

Lookback Options¶

The payoff depends on the maximum or minimum price during the option's life.

from qufin.derivatives.path_dependent import price_lookback

price = price_lookback(
    s0=100,
    r=0.05,
    sigma=0.2,
    T=1.0,
    n_steps=252,
    n_paths=100_000,
    lookback_type="floating_strike",  # or "fixed_strike"
    option_type="call",
)

Cliquet Options¶

Options with periodic resets that lock in gains at each observation date.

from qufin.derivatives.path_dependent import price_cliquet

price = price_cliquet(
    s0=100,
    r=0.05,
    sigma=0.2,
    T=1.0,
    reset_dates=[0.25, 0.5, 0.75, 1.0],
    local_cap=0.05,      # 5% cap per period
    local_floor=0.0,     # 0% floor per period
    global_floor=0.0,
    n_paths=100_000,
)

Pricing Methods Comparison¶

Derivative	Method	Convergence	Notes
Bermudan	LSM (Monte Carlo)	O(1/sqrt(N))	Basis function choice matters
Basket	Monte Carlo	O(1/sqrt(N))	Correlation structure critical
Autocallable	Monte Carlo	O(1/sqrt(N))	Path-dependent, many barriers
Lookback	Monte Carlo	O(1/sqrt(N))	Needs fine time discretization
Cliquet	Monte Carlo	O(1/sqrt(N))	Cap/floor interactions complex

Quantum pricing

Multi-asset and path-dependent QAE pricing is planned for v0.2.0. Currently, quantum amplitude estimation is available for single-asset European options via qufin.options.amplitude_estimation.