Mathematical Modeling in Finance with Stochastic Processes

(Ben Green) #1

32 CHAPTER 1. BACKGROUND IDEAS


1.4 Arbitrage


Rating


Student: contains scenes of mild algebra or calculus that may require guid-
ance.


Section Starter Question


It’s the day of the big game. You know that your rich neighborreallywants
to buy tickets, in fact you know he’s willing to pay $50 a ticket. While on
campus, you see a hand lettered sign offering “two general-admission tickets
at $25 each, inquire immediately at the mathematics department”. You have
your phone with you, what should you do? Discuss whether this is a frequent
occurrence, and why or why not? Is this market efficient? Is there any risk
in this market?


Key Concepts



  1. Anarbitrage opportunityis a circumstance where the simultaneous pur-
    chase and sale of related securities is guaranteed to produce a riskless
    profit. Arbitrage opportunities should be rare, but in a world-wide
    market they can occur.

  2. Prices change as the investors move to take advantage of such an op-
    portunity. As a consequence, the arbitrage opportunity disappears.
    This becomes an economic principle: in an efficient market there are
    no arbitrage opportunities.

  3. The basis ofarbitrage pricingis that any two investments with identical
    payout streams must have the same price.


Vocabulary



  1. Arbitrageis locking in a riskless profit by simultaneously entering into
    transactions in two or more markets, exploiting mismatches in pricing.

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