Why do we need a characteristic function and how does it relate to Options?\nOptions + probability are deeply related. If you know characteristic function of the option, you can compute the option price.
\nBenefit of characteristic functions: Allows for more flexibility in pricing risk, volatility. Increases flexibility with regards to pricing.\n“Correlation structure is easier to work with in characteristic function” - Prof Resnick
\nMotivation: This stuff can be calculated on chain using Fast Fourier Transform if we have a characteristic function\nCharacteristic function: Alternative way to express info about random variable
\nRecall cumulative density function (Probability that random variable is less than a given value)\nE[e^(itX)] - corresponds to the fourier transform, which is a good way to model things
\nCan express characteristic function as sum of the moments? E[X^n] term ~ price of a power future with power n.\nThe price of a power perpetual implies something? <- not sure what it implies
\nSum of two random variables => product of characteristic functions\n^ What’s the use case here?
\nDelta is useful for market makers - If we can compute delta easily, we can check things on chain?\n^Spoiler alert, we can using fast fourier transform
\nTwo sides: uninformed flow + market makers on options(PhD physicist/math/stats)
\nDerivative that is settled in a different reference currency.
\nWhy isn’t there another instrument that could close the gap in premiums between these products?\nYou are paying for more protection
\nWhen the euro collapsed, greece, italy, spain defaulted. Two types of cds, one denominated in euros and one denominated in usd. The usd premiums are much more expensive than the cds premiums denominated in euros because if greece defaulted on their loans, the euro is more likely to collapse as well
\nEffect of lower price of euros
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