# How should the spread be determined after calculation of expected value?

Suppose I am willing to buy a contract which I believe has a 15% chance to settle to \$100 and 0 otherwise. The EV of this contract is therefore 15. How much should I buy this for?

I would answer at most 15 (in order to ensure I make money on this contract). But going beyond this, how can the price on (0, 15) be determined? Is it arbitrary? Should the price be altered until other people are willing to make a trade with me? How can we make a better answer to this than "at most 15"? Suppose that we are trading against other people who do not necessarily agree on how much this contract may be worth.

To make this more concrete, we were playing a trading game which was a toy model of a real trading scenario. I believed the scenario above, and I did not know which price on (0, 15) to quote, so I just quoted a pretty much arbitrary price until someone was willing to trade. How can I do better?

• If you are convinced that it is at most 15 for you. What do you think the rational seller should be convinced of ? Apr 15, 2022 at 19:30

Say I'm a person with current utility $$u(x,y)$$ (where $$x$$ is money and $$y$$ is everything else). Paying $$p$$ for this contract leaves me in only two possible states. I lose so end up with utility $$u(x-p,y)$$ or I win and end up with utility $$u(x-p+100,y)$$. So the shape of $$u$$ is going to determine my answer. Since each of us has different utility functions, we will each give our own answer. So sampling seems like all you can do.