Option Pricing Theory

TABLE OF CONTENTS

1. INTRODUCTION................................................................................................2

2. THE FUNCTIONING OF OPTION MARKETS.............................................3

2.1. Parties in Options..........................................................................................3

2.2. Call Options...................................................................................................4

2.3. Put Options....................................................................................................4

2.4. Exercise Price................................................................................................5

2.5. American vs. European Options..................................................................5

3. OPTION PRICING.............................................................................................6

3.1. Option Pricing Principles............................................................................6

3.1.1. Factors Affecting Option Pricing.....................................................6

3.1.2. The Value of An Option....................................................................7

3.1.3. Boundary Conditions for Option Prices..........................................8

3.1.4. Put - Call Parity.............................................................................. 10

4. OPTION PRICING MODELS..........................................................................11

4.1. Black-Scholes Model...................................................................................11

4.1.1. Advantages and Limitations of Black-Scholes Model..................15

4.1.2. The Holes in Black - Scholes Model...............................................15

4.2. Binomial Model...........................................................................................16

4.2.1. Advantages and Limitations of the Binomial Tree Model............19

4.2.2. Relationship to the Black-Scholes Model.......................................19

REFERENCES.................................................................................................... 21

1. INTRODUCTION

The most popular example of a derivative securities is options, which represent a contract allowing one side to buy (in the case of a call option) or to sell (the case of a put option) a security on or before some specified maturity date in the future for a price which is set today.

The buyer (holder) of the option contract pays the seller of the option, a premium which is also called the option price. On the other hand, the seller (writer) of the option, with this contract, undertakes the obligation to deliver the asset at the understood price whenever the the buyer claims for.

In this study, the functioning of option markets, option types and option pricing methods are examined, respectively.

2. THE FUNCTIONING OF OPTION MARKETS

Options are traded in the over the counter market (OTC) and on organized exchanges. OTC markets are markets conducted via phones and computers between various commercial and investment banks. In contrast, organized exchanges have physical location at which trades take place.

The first time options traded on an organized exchange occurred

in 1973 at the Chicago Board Options Exchange (CBOE). Today there are organized option markets in all the major financial centers of the world.

Option contracts traded on an organized exchange are standardized as to:

1- the exercise prices available

2- the maturity dates

3- the number of units of the asset which can be purchased or sold per option contract,

4- the procedures dealing with stock splits and dividends.

On OTC markets, however, items such as exercise price or maturity dates are determined by mutual agreements.

2.1. Parties in Options

There are two basic types of option contracts as call options and put options and there are two parties in options as buyer (holder) and seller (writer).

A call option buyer, has a right to buy an asset at a preset price until a preset date. In other words, the buyer can prefer not to buy the asset. However, a call option seller, has an obligation to sell the asset stated in the option contract whenever it is asked to do so.

A put option buyer, has a right to sell an asset at a preset price until a preset date whereas a put option seller has an obligation to buy the asset whenever the buyer asks him/her to do so.

CALL PUT

BUYER Right to buy Right to sell

SELLER Obligation to sell Obligation to buy

Option Types

Parties in Options

Table 1: "Rights and Obligations in Call and Put Options"; NurgÑŒl R. Chambers,