7 Things We Understand About Finance

1. 7 Things We Understand About Finance 6: Option Theory

2. History • Options have been around since ancient times • They weren’t popular because people couldn’t figure out how to price them • Bachelier [1900] introduced the position (or hockey stick) diagram • Black-Scholes [1973] first came up with a pricing formula • CBOE started up in 1973 FIN 4250, Dr. Tufte

3. What Do We Mean By Options? • When we speak of options we mean locking in today opportunities to potentially make trades in the future • This is a buyer’s perspective (although there is a seller’s or writer’s perspective that you shouldn’t forget about). • This is not the same as colloquial understanding of options as a suite of possible choices FIN 4250, Dr. Tufte

4. Options and Obligations • Most financial discussion is about the buying of options. But someone has to sell them – this is called writing. • The writer of an option is imposing an obligation on themselves (to honor the option if it is exercised) • They get paid up front for this obligation when the buyer obtains the option FIN 4250, Dr. Tufte

5. Financial Options • Call • An option to buy in the future at a price that is fixed today • More practically, you pay a fixed price today to selectively buy upside potential • Put • An option to sell in the future at a price that is fixed today • More practically, you pay someone a fixed price to selectively avoid downside potential FIN 4250, Dr. Tufte

6. Specifics • An option has: • A current price (for itself) • This can change after issue • An exercise or strike price on the underlying asset • This doesn’t change after issue • An exercise or strike date • This doesn’t change after issue FIN 4250, Dr. Tufte

7. European vs. American • European options can only be exercised on a specific date. • This makes them simpler to understand (and more common in textbooks) • American options can be exercised any time up to a specific date FIN 4250, Dr. Tufte

8. The Option Viewpoint Is More Applicable Than You Think! • For example, buying a share of stock is a form of call option. • You pay a fixed price today (which because of limited liability is the most you can lose) to acquire upside potential • This makes what we refer to as a call, a form of “call on a call” FIN 4250, Dr. Tufte

9. The Option Viewpoint Is Way More Applicable Than You Think! • Real options is the field of applying option theory to decisions not normally thought of as options (or even as decisions on which a financial perspective would be useful) • A movie ticket is a call option – you pay a fixed price in advance for the option to get as much enjoyment out of the movie as you can. FIN 4250, Dr. Tufte

10. Put-Call Parity • Let’s use avoiding downside risk as an example • You could buy a share of stock, and a put on the stock • You get the upside and downside potential from the stock, and you get rid of the latter with the put • Alternatively, you could put your money in the bank and buy a call • The money in the bank has negligible upside or downside potential, but you add upside with your call FIN 4250, Dr. Tufte

11. The Importance of Put-Call Parity? • It implies that we don’t have to be able to value option, and even that we can usually choose to value the simplest option • Value of a Put = (Value of a Call) + (Present Value of the Exercise Price) – (Current Value of the Share Price) FIN 4250, Dr. Tufte

12. Limited Liability Means That Bonds Are Options Too • Equity has limited downside risk, and that risk is adopted by bondholders • That’s why you make regular payments to them for this obligation they’ve assumed • For a lender, selling a bond to a firm is like buying a risk free bond on which you sell a put FIN 4250, Dr. Tufte

13. The “Hockey Stick” Diagram for a Firm • The value of the firm and the value of the financial assets backing it must be the same • But, those financial assets are broken down into • A call owned by equityholders • A risk-free bond owned by debtholders • A put sold by debtholders to equityholders FIN 4250, Dr. Tufte

14. Pinning Down a (Call) Option Value? • The lower bound on the value of a call is the “hockey stick” • The upper bound on the value of the underlying asset • The actual value of the call lies between those two • Closest to the “hockey stick” at its ends • Furthest from the “hockey stick” at its kink • The risk of the call is reflected by how close you are to the “hockey stick” FIN 4250, Dr. Tufte

15. Variables that Effect (Call) Option Values • Stock price – positively related • Exercise price – negatively related • Interest rate – positively related • Because buying an option lets you avoid paying full price today • Stock price volatility – positively related • A more volatile stock has a better chance of being in-the-money • Time to Expiration – positively related • This increases the chances that the option will ultimately be in-the-money FIN 4250, Dr. Tufte

16. Why Present Value Calculations Aren’t Useful for (Call) Options? • With a stock, discounting cash flow yields value as an answer • But the risk of the stock doesn’t change • With an option, suppose you changed the discount rate. This would: • Change the value of the stock • Which would change the value and risk of the call • Because you move in the “hockey stick” diagram • But changing the risk means that the discount rate you just used isn’t correct any more. FIN 4250, Dr. Tufte

17. Risk-Neutral Valuation (of a Call) • This is a way to value a call by showing that its cash flows are equivalent to those provided by a set of other assets • Conservation of value then says that the sum of the value of those assets must equal the value of the call • This works best for a small number of possible outcomes • Often a binomial is assumed FIN 4250, Dr. Tufte

18. The Black-Scholes Formula • This is the extension of risk neutral valuation to the case of infinite possible outcomes • It only yields the value of a call • We get values of other assets using put-call parity FIN 4250, Dr. Tufte