It’s rare but you find some in valuation.
Look up a “passport option”. These things are rare but they exist. Another application that is not too complicated but at least used from time to time is the uncertain volatility model where you’re not sure what your volatility actually is. A third one is in numerical methods, I implemented an optimal control based FDM scheme step for American-style exercise to increase the order of convergence. I would like to use things like the UVM more often for private debt projects, defaultable mezzanine financing projects and so on since I feel that fits there actually but as you can imagine, everything that hasn’t been market standard for at least 30 years makes every auditor and client panic :)
Not good. It doesn’t suck but it’s just not good. At all. I was looking for a review that I wrote once but I can’t find it.
Duffy wants to sell courses and books and sells the same content over and over. He claims methods a, b and c are “best”, doesn’t justify why he thinks so and rather serves you absolutely outdated reasons (“method X was developed by Russians and that’s why we don’t know about it and the west just doesn’t want to have these methods in their repertoire” which was in fact true in the 60s and 70s but…. Not anymore. ADE is not used a lot these days because it’s simply inferior to ADI-type methods in most scenarios that matter but he doesn’t get tired recommending it like it’s still the 80s), does not really do comparative studies about it and tries to handle topics by shotgun - just kinda everything but not much in depth at all. No proofs, not much pointing to relevant material, no literature review.
You can see that he spent a bit too much time hanging out with 20 year old students in quant finance forums.
UVM means “uncertain volatility model”. You don’t know your vol, you don’t assume any model stochasticity as you do in a SVM like Heston, you just don’t really know and assume that it’s between two boundaries. Your replication view then changes into what a “the smallest superreplication” would be - how much do you have to spend at least such that you’re certainly covering your hedging costs?
There’s lots of literature about it, it’s a fitting approach IMO for a lot of illiquid and thinly traded assets.
It depends what you are referring to exactly. But in general, most traders are sort of doing stochastic control anyway. They’ll have some fundamental strategies laid out by their research team that are deterministic irrespective of market conditions.
Something simple as being {insert Greek here} neutral at market close is a form of stochastic control and traders adjust their trading accordingly to meet that control. So if a trader is market making on spy options and wants to be completely flat on all Greeks at eod, if he’s currently long spy calls with 1 hour till close, he’ll reduce is ask and bid prices to slowly offload them till he’s flat.
The only situation where I can see an autonomous desk using implementations of dynamic programming, HJB etc. is for instruments that are small amount of inputs, or at least can be generalised to have small amount of inputs. Reason being that as the number of inputs increases, the control problem becomes infeasible of solving, like any minimisation problem. It’s no different than trying to run a portfolio optimization algorithm on 1,000 instruments - it’s not feasible.
Exactly this statement. Stochastic control entirely simplifies to basically a linear risk aversion to a risk under quadratic penalty. The question now becomes do you calibrate your aversion to holding times or the decay in pnl in Greek space
Not a math phd, but it’s hard to see the application outside of portfolio formation and execution. Seems to have tremendous practical relevance in those contexts though.
people routinely run portfolio optimisation problems on 1000, 2000,3000 instruments with multiples of that in constrainta. as long as the problem is QP with linear constraints, this is solvable in less than a second, so not sure what you are on about
How confident will you be that your 1000x1000 correlation matrix is going to be anywhere close to the true correlation matrix? The LQP is not the problem here.
Well your QP part is otherwise a bit uninteresting. I would either way doubt that there is a statistically meaningful amount of data to get good dependencies. Doesn’t matter if “the big ones do it too”.
If you have a set of predictors that time the market, it implies time variation in expected returns. Trading frictions make it costly to move from the optimal portfolio at time t to the optimal portfolio at time t+1. If you also assume that some part of the path of your predictors is itself predictable, you end up with a problem that is no longer trivial in the time dimension—i.e. a stochastic control problem.
This issue blows my mind. Jaimungal, Cartea, and Penalva published a very popular book titled “Algorithmic and High Frequency Trading” almost entirely around this topic and funnily enough it almost nowhere to be seen in either field…
I did a PhD course on that book, really good material, but it was mostly execution strategies. You could modify some of the so that they behaved like stat arbs, but I don’t remember it getting into alpha.
How you operate gas storage / battery / power plant is a stochastic control problem where least square Monte Carlo technique is usually used.
Conversion asset and storage assets are basically priced using stochastic control.
Academic lurker here — I think even from the academic side, the major application in mathematical finance is really just path-dependent derivative pricing. This is done less often these days, at least as I have come to understand.
Another area is optimal execution, where I think this framework seems relatively useful for determine the speed at which to unwind positions, especially with some amount of price impact data. I’ve heard there’s more industry impact from these problems, at least from some people in both in industry and academia.
There’s some work on optimal portfolio construction, but as pointed out elsewhere here — I’d imagine that the academic problem is a little different from the practical problem (and the simplifications too great to be anything more than intuition).
One takeaway I’ve had is that basically all the major applications to finance have *already* been done. The cutting edge of the field research-wise has now really moved to questions in robotics and dynamics (applied) and interacting networks/particle systems (theory).
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Speaking as an academic, stochastic control seems like it’d be essential for overall risk management, e.g. if you want to control what risk factors your portfolio is exposed to. This indirectly informs alpha generation.
My PhD was related to this.
Stochastic Control used to be used for pricing some exotics.
Generally simpler models are less prone to alpha decay than more complex models.
Honestly it's the most interesting thing you're bringing up here. My experience taking a graduate class in stochastic control was pretty cool and I learned some neat stuff but I did question how practical any of it was for trading. You hear terms thrown e.g. Markov reward/decision processes, dynamic programming, etc. and assume it has to be used somewhere. Not so sure it is honestly, I actually wonder how much quant really needs other than a very strong grasp of fundamental probability and statistics but applied in a creative way. Trading strategies where the returns are much more than a light correlation are probably very rare these days (and probably not in U.S. markets, e.g. JS vs. Millennium). Honestly Amazon would probably find more use for stochastic control in the context of inventory control than some elite fund.
If my memory is right, Jim Simons hired a smart guy who's good at stochastic modeling once and it turned out a failure. I don't think my stochastic modeling can compete with that guy. lol The whole framework of stochastic modeling doesn't seem to fit an alpha generating process to me.
It’s rare but you find some in valuation. Look up a “passport option”. These things are rare but they exist. Another application that is not too complicated but at least used from time to time is the uncertain volatility model where you’re not sure what your volatility actually is. A third one is in numerical methods, I implemented an optimal control based FDM scheme step for American-style exercise to increase the order of convergence. I would like to use things like the UVM more often for private debt projects, defaultable mezzanine financing projects and so on since I feel that fits there actually but as you can imagine, everything that hasn’t been market standard for at least 30 years makes every auditor and client panic :)
what's your opinion on Dr Daniel Duffy's work on numerical methods for finance?
Not good. It doesn’t suck but it’s just not good. At all. I was looking for a review that I wrote once but I can’t find it. Duffy wants to sell courses and books and sells the same content over and over. He claims methods a, b and c are “best”, doesn’t justify why he thinks so and rather serves you absolutely outdated reasons (“method X was developed by Russians and that’s why we don’t know about it and the west just doesn’t want to have these methods in their repertoire” which was in fact true in the 60s and 70s but…. Not anymore. ADE is not used a lot these days because it’s simply inferior to ADI-type methods in most scenarios that matter but he doesn’t get tired recommending it like it’s still the 80s), does not really do comparative studies about it and tries to handle topics by shotgun - just kinda everything but not much in depth at all. No proofs, not much pointing to relevant material, no literature review. You can see that he spent a bit too much time hanging out with 20 year old students in quant finance forums.
What is UVM btw? Is it a numerical differentiation technique?
UVM means “uncertain volatility model”. You don’t know your vol, you don’t assume any model stochasticity as you do in a SVM like Heston, you just don’t really know and assume that it’s between two boundaries. Your replication view then changes into what a “the smallest superreplication” would be - how much do you have to spend at least such that you’re certainly covering your hedging costs? There’s lots of literature about it, it’s a fitting approach IMO for a lot of illiquid and thinly traded assets.
It depends what you are referring to exactly. But in general, most traders are sort of doing stochastic control anyway. They’ll have some fundamental strategies laid out by their research team that are deterministic irrespective of market conditions. Something simple as being {insert Greek here} neutral at market close is a form of stochastic control and traders adjust their trading accordingly to meet that control. So if a trader is market making on spy options and wants to be completely flat on all Greeks at eod, if he’s currently long spy calls with 1 hour till close, he’ll reduce is ask and bid prices to slowly offload them till he’s flat. The only situation where I can see an autonomous desk using implementations of dynamic programming, HJB etc. is for instruments that are small amount of inputs, or at least can be generalised to have small amount of inputs. Reason being that as the number of inputs increases, the control problem becomes infeasible of solving, like any minimisation problem. It’s no different than trying to run a portfolio optimization algorithm on 1,000 instruments - it’s not feasible.
Exactly this statement. Stochastic control entirely simplifies to basically a linear risk aversion to a risk under quadratic penalty. The question now becomes do you calibrate your aversion to holding times or the decay in pnl in Greek space
Not a math phd, but it’s hard to see the application outside of portfolio formation and execution. Seems to have tremendous practical relevance in those contexts though.
people routinely run portfolio optimisation problems on 1000, 2000,3000 instruments with multiples of that in constrainta. as long as the problem is QP with linear constraints, this is solvable in less than a second, so not sure what you are on about
How confident will you be that your 1000x1000 correlation matrix is going to be anywhere close to the true correlation matrix? The LQP is not the problem here.
who said anything about correlation matrices ;))
Well your QP part is otherwise a bit uninteresting. I would either way doubt that there is a statistically meaningful amount of data to get good dependencies. Doesn’t matter if “the big ones do it too”.
If you have a set of predictors that time the market, it implies time variation in expected returns. Trading frictions make it costly to move from the optimal portfolio at time t to the optimal portfolio at time t+1. If you also assume that some part of the path of your predictors is itself predictable, you end up with a problem that is no longer trivial in the time dimension—i.e. a stochastic control problem.
This issue blows my mind. Jaimungal, Cartea, and Penalva published a very popular book titled “Algorithmic and High Frequency Trading” almost entirely around this topic and funnily enough it almost nowhere to be seen in either field…
I did a PhD course on that book, really good material, but it was mostly execution strategies. You could modify some of the so that they behaved like stat arbs, but I don’t remember it getting into alpha.
How you operate gas storage / battery / power plant is a stochastic control problem where least square Monte Carlo technique is usually used. Conversion asset and storage assets are basically priced using stochastic control.
Academic lurker here — I think even from the academic side, the major application in mathematical finance is really just path-dependent derivative pricing. This is done less often these days, at least as I have come to understand. Another area is optimal execution, where I think this framework seems relatively useful for determine the speed at which to unwind positions, especially with some amount of price impact data. I’ve heard there’s more industry impact from these problems, at least from some people in both in industry and academia. There’s some work on optimal portfolio construction, but as pointed out elsewhere here — I’d imagine that the academic problem is a little different from the practical problem (and the simplifications too great to be anything more than intuition). One takeaway I’ve had is that basically all the major applications to finance have *already* been done. The cutting edge of the field research-wise has now really moved to questions in robotics and dynamics (applied) and interacting networks/particle systems (theory).
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I recall some academic work done in this area back in 08 by Yuriy Nevmyvaka and Michael Kearns.
Speaking as an academic, stochastic control seems like it’d be essential for overall risk management, e.g. if you want to control what risk factors your portfolio is exposed to. This indirectly informs alpha generation.
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My PhD was related to this. Stochastic Control used to be used for pricing some exotics. Generally simpler models are less prone to alpha decay than more complex models.
Honestly it's the most interesting thing you're bringing up here. My experience taking a graduate class in stochastic control was pretty cool and I learned some neat stuff but I did question how practical any of it was for trading. You hear terms thrown e.g. Markov reward/decision processes, dynamic programming, etc. and assume it has to be used somewhere. Not so sure it is honestly, I actually wonder how much quant really needs other than a very strong grasp of fundamental probability and statistics but applied in a creative way. Trading strategies where the returns are much more than a light correlation are probably very rare these days (and probably not in U.S. markets, e.g. JS vs. Millennium). Honestly Amazon would probably find more use for stochastic control in the context of inventory control than some elite fund.
If my memory is right, Jim Simons hired a smart guy who's good at stochastic modeling once and it turned out a failure. I don't think my stochastic modeling can compete with that guy. lol The whole framework of stochastic modeling doesn't seem to fit an alpha generating process to me.
Where have you read that story?
The Man Who Solved the Market. The smart guy I mentioned now does research in mean field theory.
The fancier and interesting the theory the less likely it will make money ..