Options, futures and other derivatives

Type :

Presentation

Pages :

9 pages

Format :

.doc

Published date :

01/16/2009

Category :

Economics & finance

Sub category :

Finance

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Summary :

Evaluation of the two IBM's options (one call and one put).
1. The Black-Scholes model.
2. The Monte Carlo simulation.
Comparision between the stock volatility to the volatility implied by the Black-Scholes Model.
Interpret the values of the Greeks as given by the binomial tree.
1. Delta.
2. Gamma.
3. Theta.
4. Vega.
5. Rho.
Appendices.
Bibliography.

Abstract

The binomial model is used to describe stock price movements through consecutive periods of time over the life of the option and to determine the actual price of this derivative. Each period is an independent trial. The binomial formula describes a process in which stock return volatility is constant through time (= 23.64% in our example). Thus, the stock can move up with constant probability p, called the up transition probability (p = 49.77 % in our example). If it moves up, u is equal to 1 plus the rate of return for an upward movement (u = 1.0403 in our example). Or, the stock can move down with constant probability (1-p), called the down transition probability (1-p = 50.23 % in our example). If it moves down, d is equal to 1 plus the rate of return for a downward movement (d = 0.9613 in our example). Thus, the variable p and (1-p) can be interpreted as the risk-neutral probabilities of an upward and downward movement in the stock price. Graphically, by taking into account all of these movements we obtain a binomial tree. Each boxed value from which there are successive moves (two branches) is called a node. Each node gives us the potential value for the stock and option price at a specified time.