sample_path2: Simulate Ito-Levy process by model name and parameters

In shill1729/FeynmanKacSolver: Feynman-Kac PDE solver for Ito diffusions and processes

Description

TO BE DEPRECATED——–Simulate stock prices under either the real or the risk-neutral measure for a combination of jump-diffusion models, including geometric Brownian motion, local volatility Gaussian mixtures, for the continuous-diffusion part, and the double exponential Kou model, the Merton normal jump-diffusion model, and uniformly distributed jumps for the discontinuous jump part. See details for specifics on parameters.

Usage

sample_path2(t, n, continuous.model, jump.model, parameters, measure = "Q")

Arguments

t	terminal time
n	number of nodes-1
continuous.model	"gbm" or "lvm"
jump.model	"kou", "norm", or "unif"
parameters	parameter list depending on models, see details
measure	either "P" or "Q"

Details

Regardless of the models parameters should contain

• spot the current stock price or interest rate level

• rate the risk-neutral rate

• lambda the mean rate of jumps function (see below)

where lambda is a function of (x,t) describing the mean rate of arrivals of jumps,

for continuous.model == "gbm" parameters should additionally contain

• mu the annual mean return of the stock in the geometric Brownian motion model for stock prices

• volat the annual volatility of the stock in the geometric Brownian motion model for stock prices

for continuous.model = "lvm", parameters should additionally contain

• probs the vector of probabilities for each mixture component

• mus the vector of annual mean-returns for each mixture component

• sigmas the vector of annual volatilitys for each mixture component

for jump.model = "kou", parameters should additionally contain

• p the probability of positive jump

• alpha the inverse of the mean size of positive jumps

• beta the inverse of the mean size of negative jumps

for jump.model = "runif" parameters should additionally contain

• min the smallest possible jump size

• max the largest possible jump size

and finally for jump.model = "norm" parameters should additionally contain

• mean the mean jump-size

• sd the volatility of the jump-size

Value

data.frame

shill1729/FeynmanKacSolver documentation built on May 19, 2020, 8:23 p.m.