CosValueOption {RMOPI}

Approximate the Option Price with the COS Method

Description

Approximate the standard European call option price with the COS method, an option pricing method based on the Fourier-cosine series.

Usage

CosValueOption(ValueOption, GBMChf, r, tau, N, a, b, method = "integrate")

Arguments

ValueOption

the value function of the option

GBMChf

the characteristic function for GBM

r

the r parameter of GBM

tau

the tau parameter of GBM

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 approximated euro call option price

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
GBMChf <- function(u){NormChf(u,mu,sigma)}
ValueOption <- function(x){EuroCallOption(x,K)}
CosValueOption(ValueOption, GBMChf,r,tau, N, a, b)