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| bio | website | dcsc.tudelft.nl/~itkachev |
|---|---|---|
| location | Leiden, Netherlands | |
| age | 25 | |
| visits | member for | 2 years, 3 months |
| seen | 4 hours ago | |
| stats | profile views | 137 |
I am a PhD student at TU Delft, working in applied probability. My current topic is "Approximate abstractions of stochastic processes" which is on the border of computer science, and the theory of systems and control. I am interested in a wide field of applications, in particular in some areas of finance, such as risk theory.
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Replicating strategy in the Black-Scholes model sorry, I've been away. Nice that you realize it yourself. Anyways, this is a common method of finding a replicating portfolio. |
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2d |
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Parameter estimation of Ornstein–Uhlenbeck and CIR processes edited title |
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2d |
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Parameter estimation of Ornstein–Uhlenbeck and CIR processes Well, you can find $\beta$ and $\sigma$ by using the quadratic variation of a process - no filtering is needed in such a case. W.r.t. $\alpha$ and $\theta$ you can use the UKF as Veeken suggested, or perhaps some particle filters. I am not an expert on filtering, but I'm pretty sure that both methods have their own advantages in your case. |
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Replicating strategy in the Black-Scholes model yes, I mean that if you replication portfolio is of the form $$ \mathrm dX_t = \beta_t\mathrm dB_t + \gamma_t\mathrm dS_t $$ and it is self-financing, then $\frac{X_t}{B_t}$ has to be a martingale. |
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2d |
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Distribution of profit/loss for retail traders in FX +1, but unlikely such statistics exist due to the reasons mentioned by @user2183336. What I've seen is mostly purely empirical estimates in introductions of books on technical analysis, together with reasons why so many people fail. In such a case, perhaps Taleb's book is worth reading. |
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awarded | Organizer |
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2d |
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How to simulate a Geometric Binomial Process with state/tie dependent increments? I can write a sketch of a MATLAB code, would it help you? |
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characterization of coherent risk measures added 38 characters in body |
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characterization of coherent risk measures added 24 characters in body |
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Exact value of mean reversion rate knowing terminal value of the process @quasi: perhaps, you can put this comment as an answer (I would upvote) |
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2d |
answered | What's the first time-integral of price called? |
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2d |
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What is a martingale? Which definition of a random walk are you using here? |
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2d |
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Replicating strategy in the Black-Scholes model In this special case, can't you just use the fact that $\xi = \eta +K$ where $\eta = \max(0,S_T - K)$ is a claim for European call? Also, computing the Ito differential of the discounted portfolio can lead you to the strategy (just take a look on the martingale term). |
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May 17 |
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Desired portfolio volume thanks, I'll try and get back to you. |
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May 17 |
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Desired portfolio volume thanks a lot for the answer, however I am more interested in case when the capital $X$ matters. Shall I look into power utility functions? |
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May 17 |
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Desired portfolio volume @quasi: I am not very familiar with utility theory, so can you elaborate on how to apply your advice? |
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May 17 |
asked | Desired portfolio volume |
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May 17 |
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How to prove that markets are incomplete under the Stochastic Volatility model? It might have been discussed in "Foundation of Stochastic Financial Mathematics" by A. Shiryaev |
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Apr 25 |
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Is statistical arbitrage on FX possible? @maximus_m: google Modern Portfolio theory, and start with a wikipedia page. Also, depending on your technical affinity, you may want to check out that book |
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Apr 4 |
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Stochastic modeling of stock price process I flagged that such question shall be moved to quant.SE |
