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Options

Andrew B. Martin

IENG 6918

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Definition: Option

• An alternative which puts one in a position where most unexpected events can do limited harm and some unexpected events can provide potentially unlimited benefit.

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Outline

• Characterization and definition

• Examples

• Implications

• Summary

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Example: Party - Option

• “Drop by if you are around”

• Something better comes up we can take advantage of it

• Something unexpected and bad happens all we stand to lose is our night

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Example: Party - not an Option

• “Are you going to be there?”

• Something better comes up, we can take advantage of it but suffer damage

• Something unexpected and bad occurs I lose my night and then some

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Definition: Unbounded

• Y = x2 is unbounded above. Y goes to infinity as x goes to +/- infinity. It is also bounded below as Y can never be less than 0.

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Extending Unboundedness

• Y: outcome; x: conditions

• Unbounded gain: by choosing some possible conditions we can make the outcome as good as we can imagine.

• Bounded loss: regardless of conditions the outcome cannot exceed a known magnitude.

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An option puts you in a position where your potential

gains are unbounded and your potential losses are bounded.

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Example: Rent Controlled Apartments

• Rent can only increase so much

• Housing Market Grows: my rent only increases by known amount

• Housing Market Collapses: I can look for a better, now cheaper, apartment

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Example: Rent Controlled Apartments

• I am insulated from potentially harmful unexpected events.

• I can take advantage of some other unexpected events.

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Definition: Obligation

• A decision alternative that has bounded potential gains and unbounded potential losses.

• The opposite of an option.

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Example: Getting into Debt

• Bounded gain: accomplishing the purpose that motivated taking out a loan.

• Unbounded loss: unquantifiable potential damage can be inflicted on you in having keep up with debt payments.

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An option puts you in a position where some

unexpected events can benefit you, and most other

unexpected events can only do limited harm.

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The Role of the Unexpected

• Unexpected events have a disproportionate impact on our lives

• Consider stock market crashes

• These events have the potential to inflict irrecoverable damage

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We choose alternatives that are options because we do not want to be irrecoverably

damaged by unexpected events, and, on occasion, we

want to benefit from them.

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Where do we find these options?

• We must actively hunt them out!

• Recall Dr. Barzilai’s Dutch friend’s son.

• We need to know the qualities options possess so we can construct them.

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Summary Page 1/3

• Options are alternatives that put us in a position where our potential gains are unbounded and our potential losses are bounded.

• Another way to look at this is to say they place us to take advantage of some unexpected events, and such that most others can only do us limited harm.

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Summary Page 2/3

• Unexpected events can be much more harmful than those we expect. Choosing options insulates us from getting irrecoverably damaged.

• That is, suffering a loss so devastating it compromises the range of decisions we have to consider in the future.

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Summary Page 3/3

• We must look for options!

• They will not always be apparent.

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Cheers