Tài liệu Option pricing theory and models

OPTION PRICING THEORY AND MODELS


In general, the value of any asset is the present value of the expected cash flows on


that asset. In this section, we will consider an exception to that rule when we will look at


assets with two specific characteristics:


They derive their value from the values of other assets.


The cash flows on the assets are contingent on the occurrence of specific events.


These assets are called options and the present value of the expected cash flows on these


assets will understate their true value. In this section, we will describe the cash flow


characteristics of options, consider the factors that determine their value and examine how


best to value them.


Basics of Option Pricing


An option provides the holder with the right to buy or sell a specified quantity of


an underlying asset at a fixed price (called a strike price or an exercise price) at or before


the expiration date of the option. Since it is a right and not an obligation, the holder can


choose not to exercise the right and allow the option to expire. There are two types of


options: call options and put options.


Call and Put Options: Description and Payoff Diagrams


A call option gives the buyer of the option the right to buy the underlying asset at


a fixed price, called the strike or the exercise price, at any time prior to the expiration date


of the option. The buyer pays a price for this right. If at expiration, the value of the asset


is less than the strike price, the option is not exercised and expires worthless. If, on the


other hand, the value of the asset is greater than the strike price, the option is exercised -


the buyer of the option buys the asset [stock] at the exercise price. And the difference


between the asset value and the exercise price comprises the gross profit on the option


investment. The net profit on the investment is the difference between the gross profit


and the price paid for the call initially.


A payoff diagram illustrates the cash payoff on an option at expiration. For a call,


the net payoff is negative (and equal to the price paid for the call) if the value of the