| Library: | finance |
| See also: | asset bitree bs1 optstart stocksim stockest stockestsim |
| Quantlet: | tgarsim | |
| Description: | plots the difference between call option prices calculated by the Black & Scholes model and between risk neutral GARCH or Treshold GARCH models. |
| Usage: | tgarsim() or tgarsim(S,r,sigma,tau,n,lambda,alpha,beta,a1,a2,b) | |
| Input: | ||
| S | scalar, value of the stock at time t = 0 | |
| r | scalar, interest rate [0%, 100%] | |
| sigma | scalar, constant parameter of (T-)GARCH model representing the Black & Scholes volatility | |
| tau | scalar, days to maturity | |
| n | scalar, number of tossings | |
| lambda | scalar, factor for the influence of the volatility in the price process | |
| alpha | scalar, alpha parameter of the GARCH model | |
| beta | scalar, beta parameter of the GARCH model | |
| a1 | scalar, alpha1 parameter of the TGARCH (case: eps>0) | |
| a2 | scalar, alpha2 parameter of the TGARCH (case: eps<0) | |
| b | scalar, beta parameter of the TGARCH | |
2) The lower left display represents the difference of option prices calculated by the (T-)GARCH model and the Black & Scholes model.
3) The lower right display represents the ratio of ((T-)GARCH - Black & Scholes) / Black & Scholes.
library("finance")
tgarsim()
Opens interactive menus where you are asked to specify the characteristics of your stocks and the models used to calculate the option prices. A display of four different graphics is depicted showing in the upper left corner the stock price simulated by the (T-)GARCH and the Black & Scholes model and in the upper right corner the corresponding option prices. The display in the lower left corner shows the absolute difference and the one in the lower right corner the relative difference of option prices calculated by the (T-)GARCH and the Black & Scholes model.
library("finance")
S = 685.7 ; value of stock at time t=0
r = 8 ; interest rate
sigma = 0.0001641 ; constant parameter of(T-)GARCH model
tau = 15 ; days to maturity
n = 100 ; number of tossings
lambda = 0.001 ; factor for the influence of the volatility in the price process
alpha = 0.00614 ; alpha parameter of GARCH model
beta = 0.09244 ; beta parameter of GARCH model
a1 = 0.9*alpha ; Parameter for TGARCH(case: eps>0)
a2 = 0.2*alpha ; Parameter for TGARCH(case: eps<0)
b = 0.09244 ; beta parameter of TGARCH model
tgarsim(S,r,sigma,tau,n,lambda,alpha,beta,a1,a2,b)
A display plotting the stock price simulation, the option prices as well as the absolute and relative difference of option prices calculated by the (T-)GARCH and the Black & Scholes model.