| Type: | Package |
| Version: | 1.4 |
| 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. |
| Date: | 2020-07-23 |
| Author: | Masashi Okada [aut, cre] |
| Maintainer: | Masashi Okada <okadaalgorithm@gmail.com> |
| Depends: | R (≥ 3.6.0) |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Imports: | igraph, graphics, stats, utils, png, ggplot2 |
| Suggests: | R.rsp |
| VignetteBuilder: | R.rsp |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.1.0 |
| NeedsCompilation: | no |
| Packaged: | 2020-07-24 13:03:32 UTC; jirotubuyaki |
| Repository: | CRAN |
| Date/Publication: | 2020-07-24 13:22:10 UTC |
correlation coefficients between all pair companies
Description
A dataset containing a matrix of correlation coefficients between all pair companies. 6 row and 6 col.
Usage
data
Format
An object of class function of length 1.
A Monte Carlo Option Pricing Algorithm for Jump Diffusion Model
Description
A Monte Carlo Option Pricing Algorithm for Jump Diffusion Model
Usage
jdm_bs(
day = 180,
monte_carlo = 1000,
start_price = start_price,
mu = mu,
sigma = sigma,
lambda = lambda,
K = K,
plot = TRUE
)
Arguments
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. |
Value
option prices : a list of (call_price, put_price)
Examples
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
Description
A Monte Carlo Option Pricing Algorithm for Jump Diffusion Model with Correlational Companies
Usage
jdm_new_bs(
correlation_matrix,
day = 180,
monte_carlo = 1000,
start_price = start_price,
mu = mu,
sigma = sigma,
lambda = lambda,
K = K,
plot = TRUE
)
Arguments
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. |
Value
option prices : a list of (call_price, put_price)
Examples
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
Description
A Normal Monte Carlo Option Pricing Algorithm
Usage
normal_bs(
day = 100,
monte_carlo = 1000,
start_price = start_price,
mu = mu,
sigma = sigma,
K = K,
plot = TRUE
)
Arguments
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. |
Value
option prices : a list of (call_price, put_price)
Examples
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)