Timeline for Why aren't econometric models used more in Quant Finance?
Current License: CC BY-SA 3.0
30 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 21, 2021 at 7:57 | comment | added | Konstantin | GBM is not the analog of log-AR(1). It has exploding variance and isn't mean reverting. | |
| Aug 24, 2017 at 15:18 | comment | added | zer0hedge | @Quantuple We are back at square one. Suppose the real (unknown) model is arithmetic brownian motion and you are pricing an option using geometric brownian motion. Is this price usuful? I don't think so. Noone is trying to pin down Q-world to the reality unfortunately and that is the difference between P and Q worlds. | |
| Aug 24, 2017 at 11:57 | comment | added | Quantuple | Congratulations, you've discovered that while P is the only real measure it remains unknown while on the contrary Q doesn't exist per se but can be pinned down mathematically, by making some assumptions. You should maybe write a book about it since you're the first one. You'll probably then realise that "all models are wrong, some models are useful". | |
| Aug 24, 2017 at 10:37 | comment | added | zer0hedge | @Quantuple When you say "voluntarily over-simplifying" it appears that there is another explanation, which is "complex but correct". In reality, there is no such explanation. Q-world is a pure theory, there are no any logical justifications why, for example, the price of some derivative calculated in Q-world is good for trading, i.e. it is not the 'real' price in any sense. The same even more true for greeks etc. The Q-world in my opinion just don't want to see the inconvenient reality of P-world, so no need to analyze the historical data, to try to forecast the real future etc | |
| Aug 24, 2017 at 7:31 | comment | added | Quantuple | @zer0hedge - Ah I see, so you're basically unhappy with the "voluntarily over-simplifying" part although it's explicitly written. This level of detail is irrelevant for the question at hand but let me make this clear for you. Static replication => 1 price. Dynamic replication in a complete market => 1 price. Dynamic replication in an incomplete market => not 1 price. Of course when I talk about dynamic replication I'm in the theoretical realm of a market with no frictions, continuous trading, spot prices evolve as per your model, AOA etc. which is at the heart of the derivation of $\Bbb{Q}$. | |
| Aug 24, 2017 at 7:06 | comment | added | zer0hedge | @Quantuple Only static replication can be perfect as we all know. So we say either "perfectly statically replicate" or "approximately dynamically replicate". I believe you should state that and then see whether your logic works. | |
| Aug 23, 2017 at 17:13 | comment | added | Quantuple | @zer0hedge I don't understand your point, BS PDE is obtained through a dynamic replication argument. Of course this is purely theoretical but it is what guarantees the existence of a unique pricing measure $\Bbb{Q}$ un that case. | |
| Jun 24, 2017 at 14:39 | comment | added | zer0hedge | Do you mind to replace "perfectly replicate" with "perfectly statically replicate" above? I think that someone shoudn't expect a "perfect dynamic replication" when the actual price process is an Arithmetic Browinan Motion while his model thinks it is GBM? | |
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
|
|
| Mar 3, 2017 at 15:23 | comment | added | vonjd | Funny that you edited it 2 hours ago since I was rereading some of the answers just yesterday evening ;-) | |
| Mar 3, 2017 at 12:48 | history | edited | Quantuple | CC BY-SA 3.0 |
added 10 characters in body
|
| Jul 13, 2016 at 20:52 | history | edited | Quantuple | CC BY-SA 3.0 |
added 35 characters in body
|
| May 22, 2016 at 11:53 | history | edited | Quantuple | CC BY-SA 3.0 |
edited body
|
| May 13, 2016 at 20:18 | vote | accept | vonjd | ||
| May 12, 2016 at 8:56 | comment | added | Quantuple | Thanks for this comment which made me delve back into this interesting topic. | |
| May 12, 2016 at 8:51 | history | edited | Quantuple | CC BY-SA 3.0 |
added 381 characters in body
|
| May 12, 2016 at 6:03 | history | edited | Quantuple | CC BY-SA 3.0 |
added 60 characters in body
|
| May 11, 2016 at 20:38 | history | edited | Quantuple | CC BY-SA 3.0 |
added 3 characters in body
|
| May 11, 2016 at 19:19 | comment | added | Kiwiakos | The limiting behaviour of discrete time processes and their continuous time counterpart is a very tricky subject. As Nelson showed in his famous 1990 paper the limits are not unique and diffusions spring up from nowhere. For example a Garch(1,1) which has one Gaussian source of uncertainty can converge to a Stoch Vol continuous time process driven by two Brownian motions. One of my favourite interview topics. | |
| May 11, 2016 at 18:54 | history | edited | Quantuple | CC BY-SA 3.0 |
added 178 characters in body
|
| May 11, 2016 at 18:39 | history | edited | Quantuple | CC BY-SA 3.0 |
edited body
|
| May 11, 2016 at 14:32 | history | edited | Quantuple | CC BY-SA 3.0 |
added 50 characters in body
|
| May 11, 2016 at 14:22 | history | edited | Quantuple | CC BY-SA 3.0 |
added 50 characters in body
|
| May 11, 2016 at 12:44 | history | edited | Quantuple | CC BY-SA 3.0 |
added 217 characters in body
|
| May 11, 2016 at 12:38 | history | edited | Quantuple | CC BY-SA 3.0 |
added 217 characters in body
|
| May 11, 2016 at 12:27 | comment | added | Quantuple | Thanks Richard, I've added OU as an additional example as you suggested. | |
| May 11, 2016 at 12:27 | history | edited | Quantuple | CC BY-SA 3.0 |
added 217 characters in body
|
| May 11, 2016 at 11:46 | comment | added | Richi Wa | The discretization is a good point. You could add that the Ornstein-Uhlenbeck process in continuous time is an AR(1) in discrete time. There is a question on QSE about this. | |
| May 11, 2016 at 9:22 | history | edited | Quantuple | CC BY-SA 3.0 |
added 202 characters in body
|
| May 11, 2016 at 9:16 | history | answered | Quantuple | CC BY-SA 3.0 |