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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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7 things we understand about finance l.jpg

7 Things We Understand About Finance

6: Option Theory


History l.jpg

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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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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