For simulation exercises, you may use any software or programming language of your choice, but Matlab or R should be easier to use.
economics
Description
For simulation exercises, you may use any software or programming language of your choice, but Matlab or R should be easier to use.
with zt ∼ NID(0, 1), and σ
2
t = ω + α(σt−1zt − θσt−1)
2 + βσ2
t−1
.
Using GARCH parameters ω = 0.00001524, α = 0.1883, β = 0.7162, θ = 0, and λ = 0.007452,
simulate the GARCH call option price with a strike price of 100 and 20 days to maturity. Assume
r = 0.02/365 and assume that today’s stock price is 100. Assume today’s variance is 0.00016. Compare the GARCH price with the BS price using a daily variance of 0.00016 as well. (Indication: Make
sure to derive and show the risk-neutral dynamics to simulate from.)
