| Library: | times |
| See also: | simGBM simgOU |
| Quantlet: | simHeston | |
| Description: | Simulation of the spot price and volatility processes in the Heston stochastic volatility model: dS(t) = mu S(t) dt + v^0.5 S(t) dW1(t) dv(t) = kappa (theta - v(t)) dt + sigma (v(t)^0.5) dW2(t) Cov[dW1(t), dW2(t)] = rho dt |
| Usage: | x = simHeston(n,s0,v0,mu,kappa,theta,sigma,rho,delta) | |
| Input: | ||
| n | scalar, time. The number of observations is represented by (ceil(n/delta)+1). | |
| s0 | scalar, starting value of the spot price process | |
| v0 | scalar, starting value of the volatility process | |
| mu | scalar, drift of the spot price process | |
| kappa | scalar, speed of mean reversion of the volatility process | |
| theta | scalar, long-term mean of the volatility process | |
| sigma | scalar, volatility of the volatility process | |
| rho | scalar, correlation between the spot price and volatility processes | |
| delta | scalar, time step size. The process is simulated at time points 0, delta, 2*delta, ..., n*delta | |
| Output: | ||
| x | (n+1) x 2 matrix, simulated trajectories of the spot price S(t) and volatility v(t) | |
library("multi")
library("times")
library("plot")
randomize(123)
days = 250
time =(0:days)/days
L = 0.1 ; long-term mean
x = 100*simHeston(1,0.1,3,L,0.29,3,0.9,0.5,1/days) ; interest rate in %
s1 = setmask(time~x[,1],"line","black","thin","solid")
s2 = setmask(time~x[,2],"line","black","thin","solid")
d1 = createdisplay(2,1)
show(d1,1,1,s1)
show(d1,2,1,s2)
setgopt(d1,1,1, "xlabel", "Time [years]", "ylabel", "Interest rate [%]")
setgopt(d1,2,1, "xlabel", "Time [years]", "ylabel", "Volatility")
A display containing sample trajectories of the spot price and volatility processes in the Heston model.