Ilya
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 Apr8 comment How to choose a risk-neutral measure when the market is incomplete? What is the reason to pick up $\Bbb Q$ to be closest to $\Bbb P$ w.r.t. some metric? Apr7 accepted Simple pricing example confusion Apr7 comment Simple pricing example confusion I think I see your point: when we are making an equivalent change of measure, we have to restrict ourselves to finite intervals of time, otherwise changing the drift changes the null events. Thanks Apr7 asked Simple pricing example confusion Apr4 comment PDE pricing of barrier options in BS Regarding PDE approach, I'd say Wilmott follows it everywhere in his books. Actually that's the same as martingale approach + Markovian structure, but without mentioning the latter two things too often (as Shreve does, in contrast) and using instead $\Delta$-hedging-like arguments, which of course leads to the same PDE as the martingale approach does. So I'd be interested in a book with a similar approach, but slightly more formal on the PDE side (not necessarily on a stochastic side). Maybe there are some known textbooks of that kind, if not - nevermind. Apr4 comment PDE pricing of barrier options in BS Thanks for your answer. I actually didn't mean solution of PDEs, especially an analytic one, just a PDE formulation. At least one advantage it gives is useful formulas for Greeks. My point is that the PDE for barriers in BS is "derived" using arguments like "value of option satisfies BS before hitting the barrier", so obviously we need to solve BS equation with an additional boundary condition on the barrier. As usual, it is this obvious step that can make the whole result being incorrect - so I just wondered whether there is a detailed explanation of this. Apr4 comment Why use implied volatility For your second argument: I've only traded on FX a couple of years ago, and there the frequency of data seemed quite enough to make good estimates of volatility just based on a 5-minute-wide window. Of course, the market is quite dynamical, but even for such a fast market 5 minutes did not seem to be such a big window. Although that's a historical data, it seems to be more relevant to "current volatility" given the latter is continuous, than the IV. Apr4 comment Why use implied volatility I see a point in your first argument - but as in my comment to @Richard, isn't that argument only true given that a lot of people on the market are using BS model for vanilla, or at least using IV? It seems, that IV is of the following feature: if everybody uses it, then it is also of value to you as you are playing against others. If nobody uses it, it does not give you a lot of information, though. Am I correct? Apr4 comment Why use implied volatility In that case, don't we completely exclude from our glance the situation when "market prices derivatives incorrectly" which we may think of taking advantage of? Apr4 comment Why use implied volatility Thanks for the answer. Can you clarify a couple of points? 1. It is useful: yes. Do you mean here, that people in fact use BS to price simple contracts often enough? Cause in that case, I'd agree that it is interesting to take a look at implied volatility. 2. BS-implied vol of the prices calculated by these models fits the BS-implied vol that can be observed on the market. Isn't that equivalent to saying that model prices coincide with market ones? Apr3 asked PDE pricing of barrier options in BS Apr3 asked Why use implied volatility Apr1 comment Fundamental Theorem of Asset Pricing (FTAP) Hi, you may be interested in this question of mine Apr1 asked FTAP a-la Harrison, Kreps and Pliska Mar27 revised Does risk-neutral measure have anything to deal with risk-neutrality in utility theory? added 1099 characters in body Mar27 revised Does risk-neutral measure have anything to deal with risk-neutrality in utility theory? added 88 characters in body Mar27 comment Does risk-neutral measure have anything to deal with risk-neutrality in utility theory? Thanks, I'm assuming in your case $E = E_P$: the expectation over a market measure. In such case, the map $X_T \mapsto \mathsf E_P[X_T]$ is linear as well, so nothing distincts it from the case of a martingale measure. Mar26 comment Does risk-neutral measure have anything to deal with risk-neutrality in utility theory? @Probilitator: indeed, I've modified this part - better now? Mar26 revised Does risk-neutral measure have anything to deal with risk-neutrality in utility theory? added 58 characters in body Mar26 asked Does risk-neutral measure have anything to deal with risk-neutrality in utility theory?