Malliavin_Asian_Greeks {greeks} | R Documentation |
Computes the Greeks of an Asian option with the Malliavin Monte Carlo Method in the Black Scholes model, or for Asian options, also in a Jump Diffusion model
Description
Asian options are path-dependent.
If S_t
is the price of the underlying asset at time t
, the
execution of an Asian option depends on the average price of option,
\frac{1}{T} \int_0^T S_t dt
, where T
is the time-to-maturity of
the option.
For more details on the definition of Greeks in general see Greeks.
For a description of Malliavin Monte Carlo Methods for Greeks see for example (Hudde & Rüschendorf, 2023).
Usage
Malliavin_Asian_Greeks(
initial_price = 100,
exercise_price = 100,
r = 0,
time_to_maturity = 1,
volatility = 0.3,
dividend_yield = 0,
payoff = "call",
greek = c("fair_value", "delta", "rho", "vega", "theta", "gamma"),
model = "black_scholes",
lambda = 0.2,
alpha = 0.3,
jump_distribution = function(n) stats::rt(n, df = 3),
steps = round(time_to_maturity * 252),
paths = 10000,
seed = 1,
antithetic = FALSE
)
Arguments
initial_price |
|
exercise_price |
|
r |
|
time_to_maturity |
|
volatility |
|
dividend_yield |
|
payoff |
|
greek |
|
model |
|
lambda |
|
alpha |
|
jump_distribution |
|
steps |
|
paths |
|
seed |
|
antithetic |
|
Value
Named vector containing the values of the Greeks specified in the
parameter greek
.
References
Hudde, A., & Rüschendorf, L. (2023). European and Asian Greeks for Exponential Lévy Processes. Methodol Comput Appl Probab, 25 (39). doi:10.1007/s11009-023-10014-5
See Also
BS_Malliavin_Asian_Greeks for a faster computation, but only in the Black Scholes model and with a smaller set of Greeks
Examples
Malliavin_Asian_Greeks(initial_price = 110, exercise_price = 100,
r = 0.02, time_to_maturity = 4.5, dividend_yield = 0.015, volatility = 0.22,
greek = c("fair_value", "delta", "rho"), payoff = "put")