1,059 reputation
423
bio website dcsc.tudelft.nl/~itkachev
location Leiden, Netherlands
age 27
visits member for 3 years, 10 months
seen Dec 8 at 8:33

I am a PhD student at TU Delft, working in applied probability and stochastic optimal control. My current focus is on approximate model-checking of stochastic systems via bisimulations (a part of computer science). I am interested in a wide field of applications, in particular in some areas of finance, such as risk theory.


Nov
9
comment Stochastic Differential
Like any other differential, this differential is defined in terms of its integral - that's a bit of an overstatement. It certainly is the case for most of stochastic differentials, but in real analysis the basic differential on a real line is often defined formally way before integrals.
Nov
9
comment What is the best source (book or article) to learn pair trading from for the layman?
The book "Pairs trading" by Vidyamurthy is a standard reference
Apr
14
comment How can the Wiener process be nowhere differentiable but still continuous?
I would be careful with such explanation, though. For example, a straight line is extremely self-similar on various scales, however it is perfectly smooth. Also, one can say that smoothness is exactly local similarity to straight lines, isn't it?
Apr
14
comment How can the Wiener process be nowhere differentiable but still continuous?
@Probilitator The gif actually looks like some old-school flight simulator in the mountain area :)
Apr
11
comment Convolution copula?
There is no need or requirement for the two copulas above to be the same. Do you mean here that $$ \mathbb{P}(X\leq x,y_{1}\leq Y\leq y_{2})=C_1(F_{X}(x),F_{Y}(y_{2}))-C_2(F_{X}(x),F_{Y}(y_{1})) $$ with $C_1\neq C_2$ in general?
Apr
10
comment How can the Wiener process be nowhere differentiable but still continuous?
@Probilitator: thanks. 3d - is some quant joke I fail to understand?
Apr
9
comment unique equivalent martingale measure in incomplete markets
Sure :) also, what does these square mean? That you take an expectation/integral of squared R-N derivative?
Apr
8
comment unique equivalent martingale measure in incomplete markets
Are you missing come expectations in the right-hand side?
Apr
8
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?
Apr
7
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
Apr
4
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.
Apr
4
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.
Apr
4
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.
Apr
4
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?
Apr
4
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?
Apr
4
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?
Apr
1
comment Fundamental Theorem of Asset Pricing (FTAP)
Hi, you may be interested in this question of mine
Mar
27
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.
Mar
26
comment Does risk-neutral measure have anything to deal with risk-neutrality in utility theory?
@Probilitator: indeed, I've modified this part - better now?
Jan
27
comment Why banks borrow from each other
Thanks - I can see some reasons why bank may be short for cash: too much withdrawal, small capital inflow at exactly that moment etc. I also understand that it may happen that the bank has much more cash above the required level and it wants money to work. However, why would such a bank lend it to another bank rather than investing this money at a better return rate?