EBS – How to Price Options – Binomial & Black-Scholes Models Option Pricing Models There are two option pricing models; the binomial, a discrete time period model, and the Black-Scholes, which is a continuous time model. If you were given the same pricing information for each model, the answers generated would be very close together. Black Scholes uses continuous compounding, whereas the binomial uses annualised compounding. Both models will have the share price, exercise price, time to expiry and interest rate as pricing variables. They also both have volatility, but different wasy of representing it. With the binomial, volatility is captured through an upward price or a downward price that the underlying could move to. With the Black Scholes model volatility is represented by the standard deviation of returns on the underlying asset. The more it moves about, the higher the volatility. Binomial Pricing Model The formula for the binomial is as follows; Y= Cu – Cd S0(u – d) Z= uCd – dCu (u – d)(1+rf)t C= YS0 + Z Where Cu is the payoff from the option if the asset price goes up (ie, = uS0 –X, the up share price minus the exercise price). Cd is the payoff to the option if the price goes down. This is dS0 – X, which is usually a negative number and since you cannot have a negative payoff to an option, this would be fully written out as; (maximum: dS0 – X, 0). This will be 0. u and d are the upward and downward multipliers. u = up asset price/starting asset price, and d = down asset price/starting share price. For example if a question says, the current share price is 200p and can rise to 340p or fall to 140p, with an exercise price of 180p, time to expiry of one year and an interest rate of 5%, then the values for u, d, Cu and Cd will be; u = 340/200 = 1.7 d = 140/200 = 0.7 Cu = 340 – 180 = 160 Cd = 0 (max of: 140 – 180 or 0) Any binomial question you will be asked, you will have to work out the above before you can start on solving the Y and Z equations. 1 EB