December 21st, 2020, 7:02 pm

Girsanov isn't particularly useful, in my opinion.

Change of measure = change of variables. The latter you do in high school. The former is just a complicated presentation of the latter in a very narrow field to make it palatable for university professor probabilists to teach.

Assumptions hint at a model.

Randomness in model makes people worried about how to value risky things. E.g. expectations might not play a simple role.

Assumptions +model +hedging + no arbitrage => BS PDE, Binomial model, ...

Trivial observation about BS PDE or binomial model shows that there is a role for simple expectations.

That role is to pretend that assets all have the same rate of return. Even though they don't. This is risk neutrality.

Probabilists get all aroused. Trivial things gets messy.

As to derivation of BS formulae, there are many ways that are equally simple.

The role of expectations also has the result that values can be found by simulations, Monte Carlo. Very useful.

But risk neutrality distracts from reality. It's a very tempting dead end, but with lots of drink, drugs, free love.