Options and their Applications

1. Options and their Applications

2. Some Details about Option Contracts • Options – Grants its owner the right, but not the obligation, to buy (if purchasing a “call” option) or sell (if purchasing a “put” option) a given asset on a specified date at a specified price (the “strike price”) at the origination of the contract. • Key Features: • Calls allow you to bet on increases in the asset’s value. • Puts allow you to bet on decreases in the asset’s value. • The option buyer pays a premium to acquire the option. • The seller of the option does have an obligation to buy/sell the asset. Much riskier than buying the option. • Options can be: “in-the-money”, “at-the-money”, and “out-of-the-money”. • An option is a portfolio of forward contract and a riskless bond. Also, can create forwards from options!

3. Option Details (cont.) • Call owner has the right to buy an asset at a strike price specified today at some time in the future. • Put owner has the right to sell an asset at a strike price specified today at some time in the future. • Call seller/writer has the obligation to sell an asset at a strike price specified today. • Put seller/writer has the obligation to buy an asset at a strike price specified today. • Two main types of options: European and American. • American option value always greater than/equal to a European option’s value.

4. Why Use Options? • Allows you to protect against adverse price movements but still allows for upside potential. • Easy to buy protection you need and sell off the coverage you don’t need (e.g., buy a put at X = 50 and sell a put at X = 20). • Options can be purchased on exchanges or in the OTC market (thus giving users a wider choice of markets). • You can sell options and earn the premium to boost income or cushion losses.

5. Option Payoffs • Option payoffs are non-linear. • Owner’s Net Payoffs are similar to that of a portfolio of a forward contract and a riskless bond. • Call owner = C = max[0, (S – X)] - Premium • Put owner = P = max[0, (X – S)] - Premium • Main incentive of call/put selleris to earn the premium. • Call seller = Premium + min[0, (X – S)] • Put seller = Premium + min[0, (S – X)]

6. Put-Call Parity Relation • Portfolio 1 – own a Call (C) and a riskless bond (X*D, where D = a TVM discount factor). • Portfolio 2 – own a Put (P) and a share of stock at the current spot price (S). • Note: Both portfolios have identical payoffs, thus they must have the same value (assuming “no arbitrage”). • Can use the above relation to price a put option based on the call’s price: P = C – (S – X*D)

7. Inter-relationships between Options and Forwards • Recall that there are six building blocks (two linear and four non-linear). • We can use the non-linear payoffs of options to construct linear payoffs that are identical to a forward contract’s payoffs: • (1) Long Call and Short Put = Long Forward: C – P = F • (2) Short Call and Long Put = Short Forward: -C + P = -F

8. Factors affecting an Option’s Value

9. The Black-Scholes Option Pricing Model In the limit, the binomial method becomes the Black-Scholes OPM: C = S*[N(d1)] - Xe –rfT*[N(d2)] d1 = d2 = d1 - s t See Spreadsheet File. ln(S/X) + [rf + (s2/2)]*T s t

10. Assumptions underlying the Black-Scholes OPM • Option is European-style. • Stock pays no dividend during the option’s term. • Interest rates are constant. • No restrictions on short sales of stock. • Trading is done continuously and share prices follow a continuous Ito process. • The distribution of terminal stock prices is lognormal

11. American Options • Differ from European options because American options can be exercised at any time (not just at expiration). • If the stock pays no dividend, it is never optimal to exercise the option early (i.e., can sell it for S – X*D which is always greater than S – X). • For a dividend-paying stock, early exercise will be optimal only if the dividend is sufficiently large: Exercise early when Dividend > C – (S – X).

12. Using Options to Hedge Interest Rate Risk • Interest Rate Cap: this contract represents a call option on an interest rate (rather than a bond price). • Interest Rate Floor: this contract represents a put option on an interest rate (betting that rates will fall). • Interest Rate Collar: created by buying a cap and selling a floor (at different strike prices). You can use this when you want to lock in a range of interest rates.

13. Uses of FX Rate Options • Used to protect against adverse movements in currencies that can affect the value of a firm’s international receivables, fixed assets, liabilities, etc. • Typically used to hedge “firm commitments” and, increasingly, anticipated cash flows. • Protection (and its cost) will vary depending on whether the option is at- or out-of-the money. • Puts and calls can be bought/sold to create combined payoffs that lock in a range of “acceptable” prices.

14. Uses of FX Rate Options (cont.) • Hedge Overseas Revenues/Assets against a weakening foreign currency (buy puts on the foreign currency and/or sell calls). • Hedge Overseas Costs/Liabilities against a strengthening foreign currency (buy calls on the foreign currency and/or sell puts). • Use the above strategies to protect cash flows and, more broadly, protect operating margins, gain a competitive advantage, and provide greater customer satisfaction.

15. Uses of Commodity Options • Options on commodities such as metals can protect against adverse price movements that can affect basic inputs and outputs of the production process. • Hedging with commodity options can: • protect operating margins, • ensure cash flow is available for new investments, • facilitate long-term planning and budgeting, and • give the firm a pricing / service advantage. • Option Spreads can be used to target the RANGE and/or COST of the commodity price protection. (See Spreadsheet File).

16. Uses of Equity Options • Traditionally used by institutional equity investors and investment banks/dealers. • Growing use of equity options by non-financial firms related to: • Stock repurchase programs, • Mergers, acquisitions, and divestitures, • Managing employee stock option programs, • Protecting an investment portfolio or enhancing yields.