Financial Instruments and Markets: A Casebook

18

Note on Option Valuation

As we know from earlier, options are contracts that give the right, but not the obligation, to either buy or sell a specific underlying security for a specified price on or before a specific date. The option holder has the freedom of action to decide whether to exercise the option or not, depending on market movements. The option writer, by contrast, engages in a liability. For each option, a fair price has to be established; a price that reflects both the risk that the writer takes and the freedom that the holder maintains. How to fairly price options is the topic of this reading note.

A previous note by the same authors, “Basic Option Properties,”¹ covered the fundamentals of options, including their payoff schemes, the parameters that influenced their value (stock price, strike price, volatility, time-to-maturity, interest rate and dividends), the put-call parity, and also bounds of options prices. This note builds on these concepts, applying them to option valuation: How do you price an option, given all we now know about its influencing factors and relationships? We will in this note cover two pricing methods: the binominal tree and the Black-Scholes/Merton formula.

THE BINOMIAL MODEL

Say you want to price an equity-based option. Perhaps you want to sell one that you own; perhaps you are looking to buy one. A common approach is to construct a binomial tree, which follows the price of the underlying stock during the lifespan of the option. Figure ...