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Lecture Notes 14 Foundations of Finance: Options: an Overview Prof. Alex Shapiro Lecture Notes 14 Options: an Overview I. Readings and Suggested Practice Problems II. Options: Characteristics and Payoffs III. Options Portfolios IV. Options Trading V. Additional Readings Buzz Words: European Options, American Options, Executive Stock Options, Exotic Options, Naked Call/Put, Straddle, Spread, Portfolio Insurance 1 Foundations of Finance: Options: an Overview I. Readings and Suggested Practice Problems BKM, Chapter 20 Suggested Problems, Chapter 20: 2, 4, 6, 8. II. Options: Characteristics and Payoffs A. Introduction • Options, futures and forwards are the basic derivative securities: Their payoffs are closely tied to (“derived from”) the price of an underlying security. • Derivatives are used for Hedging / Risk Management and for Speculation (often Hedgers and Speculators are the counter- parties of a transaction). • Our analysis will concentrate primarily on stock options. (But there are also options traded on bonds, currency, commodities, etc.) 2 Foundations of Finance: Options: an Overview • Our discussion will concentrate primarily on publicly traded options. But many options are nontraded or implicit, and our analysis applies to those as well: For example: options can be used to analyze Levered Equity, Oil fields, Callable Bonds, etc. In recent years, options gained popularity as a tool for employee and executive compensation (see the Economist and the NYT articles in the additional readings), but lately some companies reversed to stock compensation due to incentive problems with options, and due to debates on how to expense option in the financial statements. B. Stock Options • An [American] call option gives the holder the right (but not the obligation) to buy a share of the underlying stock at the prespecified exercise (or strike) price at any time up to the expiration date. • A put option is the right to sell the underlying stock. at the prespecified exercise (or strike) price at any time up to the expiration date. • A European option can be exercised only on the expiration date. 3 Foundations of Finance: Options: an Overview • Exchange-traded puts and calls are standardized as to quantity (e.g., 100 shares per option), price and expiration dates. [For example: See the Chicago Board Options Exchange (CBOE) webpage (www.cboe.com) for more details.] Over-the-counter (OTC) puts and calls are custom contracts sold to clients by brokers. Example: IBM and Microsoft Call and Put Options (Monday 4/3/2000, closing prices) are given on the next page. The first column is the stock price: IBM stock price: 121 Microsoft stock price: 90 7/8 [For option valuation, which we will discuss later, it may be useful to note that Microsoft shares dropped $15 3/8 per share on that day – the day Justice Thomas Penfield Jackson of the U.S. District Court of Washington D.C. ruled that Microsoft violated the antitrust law (the Sherman Act) in the way it preserved its monopoly status. Side Remark: Some see that day as the turning point, which signaled the “beginning of the end” of the Bull market of the 1990s.] 4 Foundations of Finance: Options: an Overview [options quote here] 5 Foundations of Finance: Options: an Overview C. Example: Microsoft call options • The Oct 85 call gives us the right to purchase MSFT at $85/share (through Saturday, Oct 21, 2000, “the Saturday following the 3rd Friday of the month”). • If we owned this call, we could exercise it, and sell the stock. Proceeds = S – X S = stock price X = exercise price • At close, Proceeds = S – X = 90 7/8 - 85 = 5 7/8 (per share) This call is in the money (X < S). • For the Oct 95 call, Proceeds = 90 7/8 - 95 = -4 1/8 This call is out of the money (X > S), It wouldn’t pay to exercise. • The intrinsic value of a call is Maximum[S-X, 0] • The market price of an option is also called the premium. 6 Foundations of Finance: Options: an Overview • The premia (last sale prices) for the Oct 85 and Oct 95 calls exceed their intrinsic values: Int Val Premium Oct 85 5 7/8 17 1/4 Oct 95 0 12 1/2 • A call option is created when someone “writes” the option. This means: – The writer is “short” the call. – For everyone who owns (is “long”) the call, someone is short. – The net amount outstanding of the call is zero. – Options are “zero-sum” games. D. Example: Option Writing • To sell (write) the Oct 85 call, we simply communicate this intention this to our broker. The call is sold and we receive the premium (last sale price = 17 1/4) We do not necessarily have to own the stock. (But if we don’t, we will have to post margin.) • Writing a call is like selling short: our liability is potentially unlimited. • If the MSFT price rises, we can avoid further loss by repurchasing the Oct 85 call. 7 Foundations of Finance: Options: an Overview E. Example: Microsoft put options • The Oct 95 put option gives the holder the right to sell the stock at 95 per share (through Saturday, Oct 21). • If we buy MSFT in the market and exercise the put, Proceeds = X - S = 95 - 90 7/8 = 4 1/8 This put is in the money (X >S). • The Oct 85 put is out of the money (X < S). If we bought MSFT and exercised this option, Proceeds = 85 - 90 7/8 = - 5 7/8 • For a put option, Intrinsic value = Max[X-S, 0] 8 Foundations of Finance: Options: an Overview III. Options Portfolios We now use a spreadsheet to analyze costs, payoffs and profits of portfolios that involve options. The portfolios may consist of puts, calls, stock, bonds (riskless borrowing or lending). [Market prices for the options are Black-Scholes values for European options. Market price for a $1 par bond is (with continuous compounding) e-rT, where T is time to maturity.] A. Long one share of stock Stock Price 15 ($ per share) 35 Std. Dev. 20% per year 30 Risk-free rate 8% per year 25 20 Maturity (years) 1/2 15 10 Security Amt Price Cash Flow 5 Stock 1 $15.000 -$15.000 0 Portfolio -5 Bond ($1 par) 0 $0.961 Value -10 Call: X= 15 0 $1.156 Profits Call: X= 20 0 $0.039 -15 -20 Put: X= 10 0 $0.000 0 10203040 Put: X= 20 0 $4.254 Stock Price at Expiration(ST) Total: -$15.000 B. Long one call Stock Price 15 ($ per share) 20 Std. Dev. 20% per year Risk-free rate 8% per year 15 Maturity (years) 1/2 10 Security Amt Price Cash Flow 5 Stock 0 $15.000 Portfolio Value Bond ($1 par) 0 $0.961 0 Call: X= 15 1 $1.156 -$1.156 Profits Call: X= 20 0 $0.039 -5 Put: X= 15 0 $0.568 010203040 Put: X= 20 0 $4.254 Stock Price at Expiration (S T) Total: -$1.156 9 Foundations of Finance: Options: an Overview C. Long one put Stock Price 15 ($ per share) 20 Std. Dev. 20% per year Risk-free rate 8% per year 15 Maturity (years) 1/2 10 Security Amt Price Cash Flow 5 Stock 0 $15.000 Portfolio Value Bond ($1 par) 0 $0.961 0 Call: X= 15 0 $1.156 Profits Call: X= 20 0 $0.039 -5 Put: X= 15 1 $0.568 -$0.568 0 10203040 Put: X= 20 0 $4.254 Stock Price at Expiration(ST) Total: -$0.568 D. Writing an uncovered (“naked”) call Stock Price 15 ($ per share) 5 Std. Dev. 20% per year Risk-free rate 8% per year 0 Maturity (years) 1/2 -5 Security Amt Price Cash Flow -10 Stock 0 $15.000 Portfolio Bond ($1 par) $0.961 Value 0 -15 Call: X= 15 -1 $1.156 $1.156 Profits Call: X= 20 0 $0.039 -20 Put: X= 15 0 $0.568 010203040 Put: X= 20 0 $4.254 Stock Price at Expiration (S T) Total: $1.156 10 Foundations of Finance: Options: an Overview E. Writing and uncovered (“naked”) put Stock Price 15 ($ per share) 5 Std. Dev. 20% per year Risk-free rate 8% per year 0 Maturity (years) 1/2 -5 Security Amt Price Cash Flow -10 Stock 0 $15.000 Portfolio Value Bond ($1 par) 0 $0.961 -15 Call: X= 15 0 $1.156 Profits Call: X= 20 0 $0.039 -20 Put: X= 15 -1 $0.568 $0.568 0 10203040 Put: X= 20 0 $4.254 Stock Price at Expiration (ST) Total: $0.568 F. Straddle: long one call, one put Stock Price 15 ($ per share) 20 Std. Dev. 20% per year Risk-free rate 8% per year 15 Maturity (years) 1/2 10 Security Amt Price Cash Flow 5 Stock 0 $15.000 Portfolio Value Bond ($1 par) 0 $0.961 0 Call: X= 15 1 $1.156 -$1.156 Profits Call: X= 20 0 $0.039 -5 Put: X= 15 1 $0.568 -$0.568 010203040 Put: X= 20 0 $4.254 Stock Price at Expiration(ST) Total: -$1.724 The Components of the Straddle: + = Straddle X S X S Long Call Long Put 11 Foundations of Finance: Options: an Overview G. A spread: short call (X=15), long call (X=20) Stock Price 15 ($ per share) 5 Std. Dev. 20% per year Risk-free rate 8% per year Maturity (years) 1/2 0 Security Amt Price Cash Flow Stock 0 $15.000 -5 Portfolio Bond ($1 par) 0 $0.961 Value Call: X= 15 -1 $1.156 $1.156 Profits Call: X= 20 1 $0.039 -$0.039 -10 Put: X= 15 0 $0.568 010203040 Put: X= 20 0 $4.254 Stock Price at Expiration (ST) Total: $1.117 The components of the spread: 15 20 + 15 20 15 20 = S S S Short call X=15 Long call X=20 Spread 12 Foundations of Finance: Options: an Overview H.
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