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

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

Description

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_path(
  t,
  n = 5000,
  continuous.model,
  jump.model = NULL,
  parameters = NULL,
  IC = NULL
)

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
IC	list of initial conditions, model dependent, see details

Details

The parameters list may be empty if continuous.model is specified as any of "bm", "pbm", "sbm" without jump-dynamics. If jump dynamics are present then one must specifiy lambda as 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 continuous.model == "vasicek" (or equally "cir") parameters should additionally contain

• theta the speed of mean-reversion to the long-term mean level

• mu the long-term mean level of the short-rate

• volat the annual volatility of the short-rate

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 = "dkou", 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

• ku the displacement of upward jumps from the origin

• kd the displacement of downward jumps from the origin

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.