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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

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history
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

what do we mean by options
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

options and obligations
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

financial options
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

specifics
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

european vs american
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

the option viewpoint is more applicable than you think
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

the option viewpoint is way more applicable than you think
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

put call parity
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

the importance of put call parity
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

limited liability means that bonds are options too
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

the hockey stick diagram for a firm
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

pinning down a call option value
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

variables that effect call option values
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

why present value calculations aren t useful for call options
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

risk neutral valuation of a call
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

the black scholes formula
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

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