The binomial model works with the continuous process, while the Cox-Ross-Rubinstein model works with the discrete process. Option price depends upon stock price, strike price, interest rates, volatility, and time to expiry. We will use the package fOption
for the Black-Scholes model. The following commands install and load this into the workspace:
> install.packages("fOptions") > library(fOptions)
Let us consider an example of call
and put
options using hypothetical data in June 2015 with a maturity of September 2015, that is, 3 months to time to maturity. Assume that the current price of the underlying stock is USD 900, the strike price is USD 950, the volatility is 22%, and the risk-free rate is 2%. We also have to set the cost of carry (b
); in the original Black-Scholes model (with underlying paying no dividends), it equals the risk-free rate.
The following command GBSOption()
calculates the call
option price using all other parameters. The first...