Election contracts with a dominated Pennsylvania bet
Question
Four binary contracts on the 2020 US presidential election each pay $1 if their event happens and $0 otherwise. Buying costs the quoted price; shorting one credits you the quoted price and costs you $1 if the event happens. Quotes (first outcome, second outcome):
- National result, Trump wins (yes / no): $0.17 / $0.83
- Arizona winner (Democrat / Republican): $0.80 / $0.20
- Georgia winner (Democrat / Republican): $0.56 / $0.44
- Pennsylvania winner (Democrat / Republican): $0.84 / $0.16
Assume Trump wins nationally only if Republicans carry all three of Arizona, Georgia and Pennsylvania. Construct an arbitrage and report the size (absolute value, in dollars) of the net credit received when the position is opened.
Short answer
$0.01. A Trump national win implies a Republican win in Pennsylvania, so the Pennsylvania-Republican contract pays at least as much as the Trump-wins contract in every state of the world, yet it is cheaper. Buy Pennsylvania-Republican at $0.16 and short Trump-wins at $0.17: you pocket $0.01 and the terminal payoff is never negative.
Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.
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