This chapter picks up from where we left off in chapter 20 and explains the valuation of options from the first principles. We start with the simplified version of the binomial method for valuing options. This approach uses option-equivalent portfolios using ownership in stock and borrowing. Alternately, one could the risk-neutral method, which involves computing the probability of stock price changes under the assumption of risk-neutral investors. The two methods are equivalent and give the same valuation. The general binomial method and its applications are presented later. This is followed by the Black and Scholes formula, which is easier and more accurate than the binomial method. The formula is illustrated with a clear worked out example. The chapter also reviews the application of the binomial option-pricing model to American options. Remember that the Black-Scholes model was derived for the European call option. Valuation of American options as well as European options on stocks paying dividends need to be adapted or modified to the specific situation. In some cases, the step-by-step binomial method may the only right approach.