Options & Put-Call
Parity (Page 1 of 2)
Date Added: June 9th, 2004
By Dan Schuster
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So you want to start investing? It seems like a great
idea: the sooner you start making gains, the more they compound;
and before you know it, you're sitting on some exotic beach. However,
there is one major problem facing young investors: where
to begin when there are millions of choices to allocate your money.
Like any analyst, do you simply march into a CEO's office and begin
discussing how the slowdown in Chinese economic growth will affect
future earnings growth of the firm? Of course not, which shows
the problem is that young investors don't have access to the kinds
of information that Wall Street analysts do. To compromise,
most beginning investors turn to TV and magazines for a little advice,
but many sound investments fly under the media's radar. One
such example is options. Options can be used for either speculative
purposes or to hedge against potential losses in the underlying
asset. Both are extremely practical, but for some reason,
they never seem to get much attention.
Types of Options
Options are one type of derivatives, meaning they derive
their price from the price of some underlying asset. There
are basically two types of options: calls and puts.
When an investor buys a call, they are given the right, but not
the obligation, to buy a particular quantity of the underlying asset
at a predetermined price (called the exercise or strike price) at
some date in the future. On the other hand, a put gives an
investor the right, but not the obligation, to sell a particular
quantity of an asset. Again, the price, quantity, and future
date are determined when the put is purchased. So you are
probably thinking, why doesn't everyone just buy options and why
haven't I heard of them before? In exchange for the luxury
of being able to buy or sell at a preset price in the future, investors
must pay a fee for the option. Also, if not used carefully,
options can lead to big losses.
Using Options for
Hedging Purposes
Because options allow investors to buy or sell an asset
at a future date at a predetermined price, options can be used to
hedge against possible losses from investing directly in the underlying
asset. Let's start by discussing the use of put options.
If an investor is long on the asset, he or she is worried that its
price will fall in the future; however, by combining this long position
with a put option, the investor can set a price floor on the asset.
This price floor is the exercise price of the option because if
the price of the stock is below the exercise price, the investor
simply exercises the put and sells the asset at the exercise price.
In this case, his or her gain from buying the put is equal to the
exercise price (E) minus the current market price of the asset when
the option is exercised (S) minus the fee paid for the put (P).
If the market price is greater than the exercise price, clearly
the investor would simply sell the asset on the open market.
Now, the loss from buying the put is the fee paid for the put.
To review, just remember that any sensible investor always wants
to see at the higher price:
E
> S
E
< S
Investor
exercises the put Investor doesn't exercise
the put
Gain:
E - S - P
Gain: - P
A graphical representation of the relationship between
E and S may help readers to further understand this situation.
Now, let's
look at the use of put options. If an investor is short on
the asset, he or she is worried that its price will rise in the
future, but by combining this short position with a call option,
the investor can set a price-ceiling floor on the asset for when
he or she needs to cover the short. This price ceiling is
the exercise price of the option. If the price of the stock is below
the exercise price, the investor will not exercise the call because
he or she can cover the short cheaper in the open market.
In this case, his or her loss from buying the call is equal to the
fee paid for the call (C). If the market price is greater
than the exercise price, then the investor would exercise the call
to get the cheaper price. In this case, the gain from buying
the call is the current market price of the asset when the option
is exercised (S) minus the exercise price (E) minus the fee paid
for the call (C). To review, just remember that you always
want to buy at the lower price:
E > S
E > S
Investor doesn't
exercise the call Investor exercises the call
Gain: -C
Gain: S - E - C
Again, a graph can be very helpful.
Pricing Options
for Speculative Purposes
Options can not only be used to help investors reduce
their risk, but they can also make investors a lot of money in their
own right. As stated before, the value of the option changes
as the does the value of the underlying asset. Thus, most
options traded aren't even held till expiration; rather, they are
used to solely for speculative purposes. As we always do on
this site (see Chris's article on intrinsic value or mine on CAPM),
I need to stress the importance of finding the value of the option
before trading them, and thanks to Nobel Prize winners Myron Scholes
and Fischer Black, European options can easily be priced using the
following Black-Scholes Option Pricing Model.
European Call: C = S *N(d1) -Ee^(-dn) * N(d2)
European Put: P = Ee^(-dn) * [1- N(d2)]
- S[1-N(d1)]
Now it becomes clear why options fly under most of
the media's radar. Even as a math minor, I will admit that
these formulas are so ugly that it practically requires a computer
to use them. Thankfully there is an easier way to price options.
If you can find a European put and a European call on the same underlying
asset with the same expiration date, you can apply what is called
put-call parity equation. According to put-call parity:
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