Greeks

This class provides methods to calculate Greeks for various types of options using Malliavin calculus. The methods use Monte Carlo simulation and are particularly useful for complex options where closed-form solutions are not available.

Malliavin Greeks for european_option_greeks

from torchquantlib.core.risk.greeks.greeks import Greeks

greeks = Greeks()
results = greeks.european_option_greeks(S0=100, K=100, T=1, r=0.05, sigma=0.2)
print(results)

Malliavin Greeks for Digital Options

results = greeks.digital_option_greeks(S0=100, K=100, T=1, r=0.05, sigma=0.2, Q=10)
print(results)

Malliavin Greeks for Barrier Options

results = greeks.barrier_option_greeks(S0=100, K=100, H=120, T=1, r=0.05, sigma=0.2, option_type='up-and-out')
print(results)

Malliavin Greeks for Lookback Options

delta = greeks.lookback_option_delta(S0=100, T=1, r=0.05, sigma=0.2)
print(delta)

Malliavin Greeks for Basket Options

S0 = [100, 110]
sigma = [0.2, 0.25]
rho = [[1, 0.5], [0.5, 1]]
weights = [0.6, 0.4]
results = greeks.basket_option_greeks(S0=S0, K=105, T=1, r=0.05, sigma=sigma, rho=rho, weights=weights)
print(results)

Malliavin Greeks for Asian Options:

results = greeks.asian_option_greeks(S0=100, K=100, T=1, r=0.05, sigma=0.2)
print(results)

Note:

All methods use PyTorch tensors for calculations and can leverage GPU acceleration if available.
The number of Monte Carlo paths and other simulation parameters can be adjusted for a trade-off between accuracy and computation time.
For some complex options, only specific Greeks are calculated due to the complexity of the calculations.