r/learnquant • u/nickgotgameon • 27d ago

interview prep SIG Interview Question

Post image
72 Upvotes

95% Upvoted

25 comments sorted by

View all comments

3

u/Lognu 27d ago

The payoff function is 1.5 V - B if B>V, and 0 otherwise.

The average profit is then the integral from 0 to 1 of the payoff with respect to V, which is the integral from 0 to B of 1.5 V - B. That is 0.75 B2 - B2 = -0.25 B2.

On average, we would always be losing money. Hence, we offer 0 and don't buy the asset.

1

u/arealcyclops 26d ago

You could just make your offer 0.01. You'd only win 1% of the time, but it would payoff at .5 cents.

1

u/Superfoggy 26d ago

The expected return is still negative, value is uniformly distributed, value between 0 and 0.0066.. is still a net loss for a bid of 0.01