Page 83 - DCOM510_FINANCIAL_DERIVATIVES

Financial Derivatives

Notes Modern option pricing techniques are often considered among the most mathematically complex
of all applied areas of finance. Financial analysts have reached the point where they are able to
calculate, with alarming accuracy, the value of a stock option. Most of the models and techniques
employed by today’s analysts are rooted in a model developed by Fischer Black and Myron
Scholes in 1973.
The price of an option contract is that amount which is paid by the option buyer to the option
seller. This is otherwise, known as option premium. Like, other price mechanism the premium
(option price) on a particular option contract is computed by the demand and supply of the
underlying asset (option). There are two types of option price i.e., intrinsic value and time value.
The intrinsic value of a call option is that amount by which stock price exceeds the strike price,
whenever the option is in-the-money. This intrinsic value will be zero when the stock price is
less than the option strike price. On the other hand, the intrinsic value of put option is that
amount by which strike price exceeds the stock price, whenever the option is in-the-money. This
intrinsic value of put option will be zero when the strike price is less than the stock price. Time
value of an option is the excess of option price over the intrinsic value.

Options trading have been done for many centuries by traders using their instincts to guide the
choice of prices. At the dawn of modern financial economics, researchers faced the challenge of
finding a scientific theory which would yield an explicit solution to the question of how options
can be priced. The identity of the underlying asset impinges upon option pricing via the volatility
of returns on the asset. Options on more volatile assets are more valuable e.g. the insurance
premium would be higher if there was more uncertainty about an outcome. When the volatility
of an asset goes up, options on that asset become more valuable. To understand better the
significance and option pricing techniques, we discuss the two important models of option
valuation like Black-Scholes model and the Binomial model.

6.1 Valuation of Options

In order to understand how options work in practice it is necessary to go back to the most
fundamental financial dynamic: the balance between expected return and risk. The problem for
all investors is that it is only possible to receive a higher expected return if one also is prepared
to take on more risk. But what is acceptable risk – and how should it be managed?

For a financial player the risk is that one a position never guarantees a return. This uncertainty
about the future value of an asset is a central issue within all investment decisions. A measure of
an asset’s risk in this context is price movements or volatility, which refers to the average
deviation from the asset’s historical average value change. In other words, the risk of a stock is
dependent on how much and how fast the price moves on the exchange. The problem is that risk
is not entirely uniform. A stock portfolio is usually connected to three different types of risks;
company risk, industry risk and market risk. The company and industry specific risks – basically
all those factors that can affect the unique company or its whole industry negatively – can be
eliminated through diversification, achieved mainly by including stocks from several companies
from different industries in the portfolio. The third risk, the market risk, is common for all
assets on the market and cannot be diversified away.
For options the situation is different, since options do not imply the purchasing of assets.
Instead, one invests in the opportunity to share the future price change of a stock. Thereby
completely new rules are introduced in comparison with trading stocks only – rules that for an
outsider just may seem risky and complicated, but which the initiated find as logical as any
other mathematical dynamics.
The value of an option is determined by its chance to be exercised with profit on the expiry day.
This consists of two parts: the real value and the time value. The real value is the value that is
possible to ‘touch’. A call option has a real value if the underlying stock’s price exceeds the

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