Page 239 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Security Analysis and Portfolio Management

Notes generally require six inputs: underlying price, strike price, time to expiration, interest rates,
dividend amount and volatility.
The term ‘fair value’ (also ‘theoretical value’) refers to a theoretical option price generated by an
option pricing model. Because pricing models require an assumption about an underlying stock
or index’s future volatility as input, values produced by these formulas are ultimately subjective.

Volatility is fluctuation, not direction, of stock price movement. It represents the standard
deviation of day-to-day price changes, expressed as an annualized percentage.
Option traders are generally interested in two types of volatility: historical and implied.

1. An underlying stock’s historical volatility represents its actual price fluctuation as observed
over a specific period in the past.
2. An option’s implied volatility (as derived from an option pricing calculator or displayed
on many option chains) represents a forecast of the underlying stock’s volatility as implied
by the option’s price in the marketplace. In other words, it is the volatility measurement
that would be needed as input into a pricing model to generate a theoretical value the
same as the options current market price.

It is often asked why an option change in price didn’t change as much as the underlying stock. You
should expect only deep in-the-money calls and puts to change in price as much as the underlying
stock. A theoretical sensitivity of option value to underlying stock price movement can be
quantified by an option’s “delta,” generated by an option pricing model, which can range from
0 to 1.00. At-the-money calls and puts have deltas around 0.50, which implies an expected change
in option price by 0.50 (or 50%) of underlying stock price change. Deep-in-the-money options
may have deltas up to 1.00, implying an expected change in option price of up to 100% the
change in stock price. Out-of-the-money calls and puts have deltas less than 0.50, down to a low
of 0. An option pricing calculator may generate deltas.
Lets not forget about liquidity. Liquidity is a trading environment characterized by high trading
volume. Liquid markets commonly have narrow spreads between the bid and ask prices, and
the ability to accept larger orders without significant price changes. Always keep in mind that
Index and Equity Options with poor liquidity will serve as a disadvantage to the trader due to
wider bid ask spreads and less favourable fills. We should always consider the liquidity issue
prior to getting involved in the trading of options in these areas.

The Black-Scholes model and the Cox, Ross and Rubinstein binomial model are the primary
option pricing models. Both models are based on the same theoretical foundations and
assumptions (such as the geometric Brownian motion theory of stock price behaviour and risk-
neutral valuation). However, there are also some important differences between the two models
and these are highlighted below.
Black Scholes Model: The Black-Scholes model is used to calculate a theoretical call price (ignoring
dividends paid during the life of the option) using the five key determinants of an option’s price:
stock price, strike price, volatility, time to expiration, and short-term (risk free) interest rate.
The original formula for calculating the theoretical option price (OP) is as follows:
OP = SM(d ) – Xe N(d )
-rt
1 2
S v 2
ln r t
X 2
Where: d =
1 v t
d = d – v t
2 1

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