V_k: V_k Series

In RMOPI: Risk Management and Optimization for Portfolio Investment

V_k Series

Description

Calculate the V_k Series for Option Pricing with the COS Method, an option pricing method based on the Fourier-cosine series.

Usage

V_k(ValueOption, N, a, b, method = "integrate")

Arguments

ValueOption	the value function of the option
N	the number of cos term for summation
a	the lower limit of the truncation interval
b	the upper limit of the truncation interval
method	how to calculate the integral, one of "integrate" and "jiahe"

Value

The V_k series

References

Fang F. and Oosterlee C.W. 2008. "A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions", Siam Journal on Scientific Computing. 31(2): 826-848. doi: 10.1137/080718061.

Examples

r <- 0.1
sigmaS0 <- 0.2
tau <- 10
S0 <- 1
K <- 1
mu <- log(S0) + (r - 0.5 * sigmaS0^2) * tau
sigma <- sigmaS0 * sqrt(tau)
a <- -10
b <- 10
N <- 64
ValueOption <- function(x){EuroCallOption(x,K)}
V_k(ValueOption, N, a, b)

RMOPI documentation built on Aug. 22, 2022, 5:07 p.m.