F303 Intermediate Investments

1
F303 Intermediate Investments

• Class 18, Oct 30
• Options and Put-Call Parity
• Andrey Ukhov
• Kelley School of Business
• Indiana University

2
Outline of This Subject

• Profits from options.
• Different types of options.
• Factors affecting option prices.
• Put-call parity.
• Option trading strategies.

3
Profits from Buying a Call
Profit
X
0
Stock Price
Premium
4
Profits From Writing a Call
Profit
Premium
0
X
Stock Price
5
Profits From Buying a Put
Profit
0
X
Stock Price
6
Profits From Writing a Put
Profit
0
X
Stock Price
7
Types of Options

• American options can be exercised at any time up
  to the expiration date.
• European options can only be exercised on the
  expiration date.
• Most of the options that are traded on exchanges
  are American options. However, European options
  are generally easier to analyze than American
  options.

8
Factors Affecting Option Prices

• We have six factors that influence the price of a
  stock option
• The current security price
• The exercise price
• Time to maturity
• Volatility of the underlying assets price
• Risk-free interest rate
• Dividends expected during life of the option

9
Stock Price and Strike Price

• Remember the payoff of a call
• Maximum 0, S-X
• This means that a call becomes more valuable as
  the stock price increases and less valuable as
  the exercise price increases.
• Put options will behave in the opposite waythey
  become less valuable as the stock price increases
  and more valuable as the exercise price increases.

10
Time to Maturity

• American put and call options become more
  valuable as the time to expiration increases.
• Consider two identical options except for their
  time to maturity (a) one has a short term
  maturity, and (b) the other has a longer term to
  maturity.
• The owner of the long-life option has many more
  exercise opportunities open to him/her than the
  owner of the short term option.
• A longer time to maturity is like a form of
  insurance

11
Volatility of the Underlying Asset

• As the volatility of the underlying asset
  increases, the chances that the stock will do
  very badly or very well increase.
• For the owner of a call or put, this is good
  news. The call owner will benefit from price
  increases but has limited downside risk
• The owner of a put benefits from price decreases
  but has limited downside risk

12
Risk-free Interest Rate

• To understand this effect, you must assume that
  all other variables remain fixed when interest
  rates change.
• Consider a rise in interest rates. In this case,
  you have (a) a rise in the expected growth rate
  of the stock price, and (b) a decline in the
  present value of the future cash flows received
  by the option holder.
• In the case of puts these two effects decrease
  the value of puts
• In the case of calls value of calls increase.

13
The Six Factors
14
Call Exercise

• Does it make sense to exercise an American call
  option on a non-dividend stock early?
• No!!
• A call provides a kind of insurance. A call
  option, when held instead of the stock itself, in
  effect insures the holder against the stock price
  falling below the exercise price.
• Once the option has been exercised and the
  exercise price has been exchanged for the stock
  price, this insurance disappears.

15
Put Exercise

• Does it make sense to exercise an American put
  option on a non-dividend stock early?
• Yes, but only if it is sufficiently deep in the
  money!!
• A put option also provides a kind of insurance.
  But, the investor may, in certain circumstances,
  forgo this insurance and exercise early in order
  to realize the strike price immediately.
• The early exercise of a put option becomes more
  attractive as (a) the security price decreases,
  (b) risk-free rate increases and (c) volatility
  decreases.

16
Put-Call Parity

• We can obtain an important relationship between
  the prices of calls and puts. This relationship
  will allow us to price a call or put, and see
  whether there are arbitrage opportunities.
• The relationship is given by
• Call P.V. of Exercise Price Put Security
  Price

17
Put-Call Parity

• Where does the put-call parity come from?
• Consider two portfolios
• Portfolio A One European call option plus an
  amount of cash equal to Present Value of X
• Portfolio B One European put option plus one
  share.
• If these two portfolios produce the same pay-offs
  under all states of nature, then they should have
  the same price.

18
Put-Call Parity
19
Put-Call Parity An Example

• If the Put-Call Parity does not hold, then
  arbitrage opportunities will arise.
• Example Suppose that the security price is 31,
  the exercise price is 30, the risk-free rate is
  10 per annum, the price of a 3-month European
  call option is 3, and the price of a 3-month
  European put option is 2.25.
• Do we have mispricing?
• If yes, could we make arbitrage profits?

20
Put-Call Parity An Example

• Value of Portfolio A
• Value of Portfolio B
• Portfolio B is overpriced relative to portfolio
  A.
• What is the arbitrage strategy?
• Buy securities in Portfolio A and short the
  securities in Portfolio B.

21
Trading Strategies With Options

• Options can be used with a position in the stock
  to form specific payoffs.
• Example 1 Long position in the stock and short
  position in a call
• Example 2 Short position in the stock and a long
  position in a call.
• Options can also be combined together to create a
  wide range of different payoff functions.

22
The Straddle

• One possible combination is a straddle.
• How to create a straddle?
• Buy a call and put options on the same stock with
  the same exercise price and expiration date.
• The straddle is appropriate when the investor
  expects a large move in the stock price but is
  unsure in which direction the price will move.

23
The Straddle
Profit
Buy a Put
Buy a Call
Stock Price
24
The Butterfly Spread

• Another possible combination is a butterfly
  spread.
• How to create a butterfly spread?
• Buying a call option with a relatively low
  strike price, X1
• Buying a call option with a relatively high
  strike price, X3
• Selling two call options with a strike price,
  X2, halfway between X1 and X3.

25
The Butterfly Spread
Profit
Selling two call options at X2
Net Payoff
Stock Price
X1
X2
X3
Buy 1 call at X3
Buy 1 call at X1
26
Key Points to Remember

• Profit diagrams from Call and Put options.
• Factors affecting option prices.
• Put-call parity formula.
• The uses of put-call parity.
• Option trading strategies.