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7 Things We Understand About FinancePowerPoint Presentation

7 Things We Understand About Finance

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

7 Things We Understand About Finance

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7 Things We Understand About Finance

6: Option Theory

- 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

- 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

- 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

- 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

- 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

- A current price (for itself)

FIN 4250, Dr. Tufte

- 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

- 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

- 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

- 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

- You could buy a share of stock, and a put on the stock

FIN 4250, Dr. Tufte

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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