F303 Class 18

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Information about F303 Class 18
Product-Training-Manuals

Published on August 30, 2007

Author: Clown

Source: authorstream.com

F303 – Intermediate Investments:  F303 – Intermediate Investments Class 18, Oct 30 Options and Put-Call Parity Andrey Ukhov Kelley School of Business Indiana University Outline of This Subject:  Outline of This Subject Profits from options. Different types of options. Factors affecting option prices. Put-call parity. Option trading strategies. Profits from Buying a Call:  Profits from Buying a Call Stock Price Profit X 0 Premium Profits From Writing a Call:  Profits From Writing a Call Stock Price Profit X 0 Premium Profits From Buying a Put:  Profits From Buying a Put Stock Price Profit X 0 Profits From Writing a Put:  Profits From Writing a Put Stock Price Profit X 0 Types of Options:  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. Factors Affecting Option Prices:  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 asset’s price Risk-free interest rate Dividends expected during life of the option Stock Price and Strike Price:  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 way…they become less valuable as the stock price increases and more valuable as the exercise price increases. Time to Maturity:  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… Volatility of the Underlying Asset:  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… Risk-free Interest Rate:  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. The Six Factors…:  The Six Factors… Call Exercise:  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. Put Exercise:  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. Put-Call Parity:  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 Put-Call Parity:  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. Put-Call Parity:  Put-Call Parity Put-Call Parity: An Example:  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? Put-Call Parity: An Example:  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. Trading Strategies With Options:  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. The Straddle:  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. The Straddle:  The Straddle Stock Price Profit Buy a Call Buy a Put The Butterfly Spread:  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. The Butterfly Spread:  The Butterfly Spread Stock Price Profit X1 X2 X3 Net Payoff Selling two call options at X2 Buy 1 call at X1 Buy 1 call at X3 Key Points to Remember:  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.

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