| Title: | Monte Carlo Option Pricing Algorithms for Jump Diffusion Models with Correlational Companies |
|---|---|
| Description: | Option is a one of the financial derivatives and its pricing is an important problem in practice. The process of stock prices are represented as Geometric Brownian motion [Black (1973) <doi:10.1086/260062>] or jump diffusion processes [Kou (2002) <doi:10.1287/mnsc.48.8.1086.166>]. In this package, algorithms and visualizations are implemented by Monte Carlo method in order to calculate European option price for three equations by Geometric Brownian motion and jump diffusion processes and furthermore a model that presents jumps among companies affect each other. |
| Authors: | Masashi Okada [aut, cre] |
| Maintainer: | Masashi Okada <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.4 |
| Built: | 2025-02-12 04:56:31 UTC |
| Source: | https://github.com/jirotubuyaki/jdmbs |
A dataset containing a matrix of correlation coefficients between all pair companies. 6 row and 6 col.
datadata
An object of class function of length 1.
A Monte Carlo Option Pricing Algorithm for Jump Diffusion Model
jdm_bs( day = 180, monte_carlo = 1000, start_price = start_price, mu = mu, sigma = sigma, lambda = lambda, K = K, plot = TRUE )jdm_bs( day = 180, monte_carlo = 1000, start_price = start_price, mu = mu, sigma = sigma, lambda = lambda, K = K, plot = TRUE )
day |
: an integer of a time duration of simulation. |
monte_carlo |
: an integer of an iteration number for monte carlo. |
start_price |
: a vector of company's initial stock prices. |
mu |
: a vector of drift parameters of geometric Brownian motion. |
sigma |
: a vector of volatility parameters of geometric Brownian motion. |
lambda |
: an integer of how many times jump in unit time. |
K |
: a vector of option strike prices. |
plot |
: a logical type of whether plot a result or not. |
option prices : a list of (call_price, put_price)
jdm_bs(100,10,c(5500,6500,8000),c(0.1,0.2,0.05),c(0.11,0.115,0.1),2,c(6000,7000,12000),plot=TRUE)jdm_bs(100,10,c(5500,6500,8000),c(0.1,0.2,0.05),c(0.11,0.115,0.1),2,c(6000,7000,12000),plot=TRUE)
A Monte Carlo Option Pricing Algorithm for Jump Diffusion Model with Correlational Companies
jdm_new_bs( correlation_matrix, day = 180, monte_carlo = 1000, start_price = start_price, mu = mu, sigma = sigma, lambda = lambda, K = K, plot = TRUE )jdm_new_bs( correlation_matrix, day = 180, monte_carlo = 1000, start_price = start_price, mu = mu, sigma = sigma, lambda = lambda, K = K, plot = TRUE )
correlation_matrix |
: a matrix of a correlation coefficient of companies |
day |
: an integer of a time duration of simulation. |
monte_carlo |
: an integer of an iteration number for monte carlo. |
start_price |
: a vector of company's initial stock prices. |
mu |
: a vector of drift parameters of geometric Brownian motion. |
sigma |
: a vector of volatility parameters of geometric Brownian motion. |
lambda |
: an integer of how many times jump in unit time. |
K |
: a vector of option strike prices. |
plot |
: a logical type of whether plot a result or not. |
option prices : a list of (call_price, put_price)
price <- jdm_new_bs(matrix(c(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9),nrow=3, ncol=3), day=100,monte_carlo=20, c(1000,500,500), c(0.002, 0.012, 0.005),c(0.05,0.05,0.06), 3, c(1500,1000,700),plot=TRUE )price <- jdm_new_bs(matrix(c(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9),nrow=3, ncol=3), day=100,monte_carlo=20, c(1000,500,500), c(0.002, 0.012, 0.005),c(0.05,0.05,0.06), 3, c(1500,1000,700),plot=TRUE )
A Normal Monte Carlo Option Pricing Algorithm
normal_bs( day = 100, monte_carlo = 1000, start_price = start_price, mu = mu, sigma = sigma, K = K, plot = TRUE )normal_bs( day = 100, monte_carlo = 1000, start_price = start_price, mu = mu, sigma = sigma, K = K, plot = TRUE )
day |
: an integer of a time duration of simulation. |
monte_carlo |
: an integer of an iteration number for monte carlo. |
start_price |
: a vector of company's initial stock prices. |
mu |
: a vector of drift parameters of geometric Brownian motion. |
sigma |
: a vector of volatility parameters of geometric Brownian motion. |
K |
: a vector of option strike prices. |
plot |
: a logical type of whether plot a result or not. |
option prices : a list of (call_price, put_price)
price <- normal_bs(100,10,c(300,500,850),c(0.1,0.2,0.05),c(0.05,0.1,0.09),c(600,700,1200),plot=TRUE)price <- normal_bs(100,10,c(300,500,850),c(0.1,0.2,0.05),c(0.05,0.1,0.09),c(600,700,1200),plot=TRUE)