Microsoft

Topics: Options, Option, Mathematical finance Pages: 24 (5020 words) Published: December 9, 2013
﻿Outline

1 Introduction
2 Overview of One -Step Binomial Model, Black-Scholes Merton Model and Put Call Parity: 2.1. One -Step Binomial Model
2.2. Black-Scholes Merton Model
2.3. Put Call Parity
3 Limitations of Analysis
4 Research Process: Microsoft
5 Research Process: Apple
6 Results and Conclusion
7 Reference List
8 Attachments

1. Introduction
The most common definition of an option is an agreement between two parties, the option seller and the option buyer, whereby the option buyer is granted a right (but not an obligation), secured by the option seller, to carry out some operation (or exercise the option) at some moment in the future. Options come in several varieties:

A call option grants its holder the right to buy the underlying asset at a strike price at some moment in the future. A put option gives its holder the right to sell the underlying asset at a strike price at some moment in the future. There are several types of options, mostly depending on when the option can be exercised. As we know the European options can be exercised only on the expiration date. American-style options are more flexible as they may be exercised at any time up to and including expiration date and as such, they are generally priced at least as high as corresponding European options1. For a call option, the profit made at exercise date is the difference between the price of the asset on that date and the strike price, minus the option price paid. For a put option, the profit made at exercise date is the difference between the strike price and the price of the asset on that date, minus the option price paid. The price of the asset at expiration date and the strike price therefore strongly influence how much one would be willing to pay for an option2. 2. Overview of One -Step Binomial Model, Black-Scholes Merton Model and Put Call Parity:

2.1 Black Sholes Model
As we know the formula options pricing models was first derived by Fisher Black and Myron Scholes in 1973 in the article "Assessment of options and commercial bonds» (The Pricing of Options and Corporate Liabilities). Their research was based on previous work of Jack Treynor, Paul Samuelson, James Boness, Sheen T. Kassouf and Edward Thorp and developed in a period of rapid growth in options trading. There are six assumptions of the theory3.

To get their model of option pricing, Black and Scholes made the following assumptions: • The underlying asset call option not to pay dividends throughout the life of the option. • No transaction costs associated with buying or selling shares or options are exercised. • Short-term risk-free interest rate is known and is constant during the entire term of the option. • Any buyer of the securities may receive loans for short-term risk-free rate to pay for any part of its price. • Short selling is permitted without restriction, while the seller receives immediate cash sum for all sold without covering security at today's price. • Securities trading is a continuous process, and the stock price moves continuously and randomly. Beginning of the model is based on the concept of risk-free hedge. Buying stock and simultaneously selling call options on these shares, the investor can construct a riskless position, where the profit on the shares will be exactly offset losses on options, and vice versa. No risk hedge positions to be repaid at a rate equal to the risk-free interest rate, otherwise there would exist a possibility of extracting arbitrage profits, and investors, trying to take advantage of this capability, would lead the price of an option to an equilibrium level which is determined by the model. 2.2 Binomial Option Pricing

Long years, financial analysts have difficulty in developing a valuable method for estimate options. This is until Fisher Black and Myron Scholes published the article "The Pricing of Options and Corporate Liabilities" in 1973 to describe a model for valuing options. This model is initially...