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Sizing a cross-book arbitrage lock

MediumMarket Making & Betting Games~4m

A two-outcome event is offered by two books: Book A quotes decimal odds 2.402.40 on outcome XX; Book B quotes decimal odds 2.002.00 on outcome not-XX. You will stake $100 in total, split across the two sides so that your payout is identical whichever outcome occurs (a true lock). What is your guaranteed profit (in dollars, to two places)?

Show hints (2)+
  1. The lock condition is 2.40a=2.00b2.40a = 2.00b with a+b=100a+b=100 - the split is not 50/50.
  2. Equal-lock return =S/(1/2.40+1/2.00)= S / (1/2.40 + 1/2.00); profit is the excess over the $100 stake.

Answer

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9.09 (± 0.02)

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Asked at: Options Market-Making, ETF Market-Making

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