Page 90 - DCOM510_FINANCIAL_DERIVATIVES

Unit 6: Valuation and Pricing of Options

Notes

Notes Basic principles of Option valuation.

The two basic principles/rules of option valuation are as follows:
1. If one portfolio of securities gives a higher future payoff than another portfolio in every
possible circumstance, then the first portfolio must have a higher current value than the
second portfolio.
2. If two portfolios of securities give the same future payoff in every possible circumstance,
then they must have the same current value.

Self Assessment

Fill in the blanks:
6. The ……………………… of an option contract is that amount which is paid by the option
buyer to the option seller.

7. The option price is also known as ………………………
8. The option price changes as per changing ……………………… price.
9. The ……………………… interest rate is the interest rate that may be obtained in the
marketplace with virtually no risk.
10. The higher the interest rate, the lower the ……………………… of the exercise price.

6.3 Options Pricing Models

Option pricing theory also called Black-Scholes theory or derivatives pricing theory – traces its
roots to Bachelier (1900) who invented Brownian motion to model options on French government
bonds. This work anticipated Einstein’s independent use of the Brownian motion in physics by
five years.
The following are the key option pricing models:

6.3.1 Binomial Options Pricing Model (BOPM)

In finance, the binomial options pricing model provides a generalisable numerical method for
the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein
(1979). This model is an important technique of pricing a stock option by constructing a binomial
tree. The binomial tree represents different possible paths that may be followed by the stock
price over the life of the option. At the end of the tree i.e., at the expiration of the option, the final
possible stock prices are simply equal to their intrinsic values. This model will consider the time
to expiry of an option as being one-period, two-periods and multiple periods.
The Binomial model is used by the help of probabilities of a stock moving up or down, the risk-
free rate and the time interval of each step (in the binomial tree) till expiry. By use of these
probabilities, a binomial tree is to be constructed and evaluated to finally find the price of a call
option.
Essentially, the model uses a “discrete-time” model of the varying price over time of the
underlying financial instrument. Option valuation is then via application of the risk neutrality
assumption over the life of the option, as the price of the underlying instrument evolves.

LOVELY PROFESSIONAL UNIVERSITY 85