Stock Option Pricing Using Binomial Trees with Implied Volatility

Abstract

The Black-Scholes model provides an analytical solution in option pricing and has been widely used in finance. This model assumes constant volatility. Pricing option incorporating implied volatility is conducted using implied binomial tree. This study aims to simulate the prices of put options and call options using implied binomial trees, binomial trees and the Black-Scholes model and determine the factors that influence option prices. The simulation was conducted using Matlab. The option price resulted from implied binomial tree and binomial tree are compared with the option prices of the Black-Scholes model to determine the difference of option prices with constant volatility and option prices incorporating implied volatility. The implied binomial tree method provides better option prices than the binomial tree based on small relative error value to the Black-Scholes model. This is caused by the transition probability value of stock price movements in the implied binomial tree at each point is different, whereas in the binomial tree the value of transition probability is same. Furthermore, increasing the time step causes the option prices obtained from the implied binomial tree converge to the Black-Scholes. It is concluded that these three methods can be used in option pricing. Factors that influence the option price are stock price, strike price, interest rate and maturity date, are also obtained