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Unit 6: Valuation and Pricing of Options

option’s strike price. For put options it is the other way around, in that they have real value if the Notes
strike price instead exceeds the value of the stock. Conversely the time value is the value of the
possibility that good news will occur during the time to maturity in order for an option to have
a real value on the expiry day. Time value changes during the maturity period and will always
be zero on the expiry day. Options that have a real value are said to be ‘in the money’ and are
called plus options by professionals, while options that completely miss real value are ‘out-of-
the-money’ and are referred to as minus options. Options where the strike price and stock price
corresponds are ‘at-the-money’ and are called “pari” options.
The value of the option can be estimated with a mathematical formula named Black & Scholes
after its inventors. In the formula the price is calculated as a function of the underlying stock
value, the strike price, the time to maturity and the level of the risk free interest rate, among
others. All terms in the equation can be determined relatively easy except one: the stock’s
volatility. The risk measure that is interesting when one deal with options is the so called
‘implied volatility’, which contains the premium that the market has set on the option. Contrary
to historical volatility, implied volatility measures the market’s expectations on the future
changes in the stock price. This is crucial, as it is when an investor has a different opinion to the
general market about the future risk of a stock that it becomes possible to enter and make
money from an option, since its premium then will be different than what it ‘should’ be.
There are a large number of strategies that one can use in order to profit from the possibilities
of options. Learning the differences and advantages between different options is critical to
success, as options can appear superficially similar. It is seldom enough just to look at the
option’s premium and the strike price. Real professionals also look at how sensitive the options
are for the market climate.

Did u know? By using Black & Scholes’ formula one can derive several important sensitivity
measures – commonly mentioned as ‘the Greeks’ since they have been provided with
Greek letters – that can clearly tell how an option will react from different market conditions.

6.1.1 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.
If (1) and (2) did not hold, then it would be possible for a professional trader to make an
arbitrage profit by simultaneously selling the relatively overpriced portfolio and buying the
relatively under priced portfolio. We will use these rules to construct positions that offer the
identical payoff as the option. If we can price the position with the same payoff as the option,
then we have the price of the option.

Notes Another point to note is that the modern valuation of exchange-traded options
ignores margin requirements, transactions costs, and taxes because it focuses on market
pricing relations that are enforced by the arbitrage activities of professional traders. The
margin requirements and transactions costs of these traders are very low. Furthermore,
taxes usually reduce the level of arbitrage profits but do not change the circumstances in
which they occur.

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