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It seems like the field has become stagnant in the decades following the enormously successful and influential Black Scholes model. (The original paper has been cited a staggering 25,000 times - more than ANY economics paper, by far.) There is also the CAPM and GARCH models, but those were decades ago. Now we have Black Scholes type models for every type of option under every conceivable condition. We have multiple derivations of these formulas (forier series, closed form, etc) . So what is next? The only new idea is http://en.wikipedia.org/wiki/User:Stockequation/sandbox which makes the jump from the stock market being a statistical system to a mechanical/physical one, like general relativity. It's essentially a 1-d ADS/CFT applied to the stock market and it generates fat tail option prices and vol. smile

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    $\begingroup$ What about those compex term structure interest rates model? Credit? Incomplete markets? Stochastic volatility models? $\endgroup$ – Tulio Carnelossi Jan 15 '15 at 14:17
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    $\begingroup$ I could see the answers being interesting if they discuss new developments. I would like to change the phrasing of the question though. This can be an old-style Community Wiki post with one development per answer. $\endgroup$ – Bob Jansen Jan 15 '15 at 14:36
  • $\begingroup$ In this sweeping question, it would help your credibility a little if your spelling was actually correct. $\endgroup$ – Dirk Eddelbuettel Jan 17 '15 at 3:01
  • $\begingroup$ Was this question just about options (i.e. the only tag), or all of quantitative finance? (I.e. it'd be good if either the tags or title were updated.) $\endgroup$ – Darren Cook Jan 20 '15 at 21:24
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    $\begingroup$ The field is not stagnant; HJM/BGM models were huge advances. CVA->XVA is a big deal, and funding issues in general. Local volatility was a brilliant derivation. Replication with market impact is ongoing. There's tons of stuff happening, but I don't think that "Scalar" model is a part of it, at all. EDIT: In fact, I'm a little suspicious that this entire post is to drive traffic to that wiki "user" page. $\endgroup$ – experquisite Jan 23 '15 at 19:37
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Ross had an interesting paper thats making the rounds: The Recovery Theorem. He claims that the physical measure can be recovered from option prices under certain conditions. I think that's getting a lot of academic interest recently.

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These years, The new frontier has been around optimal trading, market impact and orderbook dynamics. They are plenty of sources around, one of them being this bi-yearly conference. You have all the slides on the web site: Market Microstructure: Confronting many Viewpoints.

The next challenge is to link previous quant and economic knowledge with micristructure.

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http://www.algorithmicfinance.org/

It's a free peer reviewed journal, depending on your definition of discovery you might find interesting tidbits there.

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  • $\begingroup$ I guess the downvoters wanted this to be a comment, not an answer... but as they kept quiet we might never know :-) (downvote-without-comment is one of my pet hates.) $\endgroup$ – Darren Cook Jan 20 '15 at 21:27
  • $\begingroup$ I wasn't really sure what OP defined as discovery, so I linked to a journal I read for new ideas $\endgroup$ – Kyle Balkissoon Jan 20 '15 at 21:42

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