Page 115 - DMGT513_DERIVATIVES_AND_RISK_MANAGEMENT

Derivatives & Risk Management

Notes Self Assessment

Fill in the blanks:
6. Put-call is nothing but a relationship that must exist between the prices of ………..put and
call options having same underlying assets, strike price and expiration date.

7. Put-call parity is a classic application of …………….
8. The put-call parity states that the difference in price between a call-option and a put-
option with the same terms should equal the price of the underlying asset less the present
……………..value of the exercise price.
9. If call or put option prices deviated substantially then, transactions in them would drive
prices up or down until the …………… is eliminated.
10. ………..links up the price of a call and the price of a put.

8.3 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:

8.3.1 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.

Notes Assumptions
1. The current selling price of the stock (S) can only take two possible values i.e., an
upper value (Su) and a lower value (Sd).
2. We are operating in a perfect and competitive market, i.e.
(a) There are no transaction costs, taxes or margin requirements.

(b) The investors can lend or borrow at the risk-less rate of interest, r, which is the
only interest rate prevailing.
(c) The securities are tradable in fractions, i.e. they are divisible infinitely.

(d) The interest rate (r) and the upswings/downswings in the stock prices are
predictable.

Contd...

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