V_k {RMOPI}

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)