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Actually, financial markets have employed non-Gaussian Levy processes in modelling derivatives for a long time (it is a bit different from the Levy distribution

Actually, financial markets have employed non-Gaussian Levy processes in modelling derivatives for a long time (it is a bit different from the Levy distribution, I agree - but nothing stops the processes from having non-finite moments). For example, a very widely used process for modelling information-driven timeseries (like stock returns) is the jump-diffusion model where the diffusion component is a Brownian motion while the jump component is a Poisson process. The underlying volatility is often modelled using a different process - e.g. the SABR model, the Heston model etc. There are similar cases for interest-rate processes (Hull-White/BDT etc) which have to satisfy conditions of mean-reversion and no-arbitrage across the yield curve. See, it's not as if we don't realize that the underlying processes are mathematically inadequate to fully explain all market movements. But for a model to be useful, it has to satisfy two conditions: 1. Be able to produce a non-arbitrageable "mid"-price for making a market (ie if someone asks a trader to quote the bid-ask for an option, e.g.) 2. Be able to reproduce the current market prices of an asset/its derivatives. This requires model calibration. Models are chosen based on how easily and how fast they can satisfy 1 &2. Do they produce risk numbers that are believable? Probably yes, if the model has been calibrated and has been tested against out-of-sample inputs. Do they guard adequately against event-risk (the thing you would try to signify using your "infinite" variance distributions)? Probably not - but then again, nothing does. How would you go ahead and calibrate the Levy distribution so that the sampling process can explain currently tradeable market prices? Would be it a "do once, leave forever" calibration? Or would it change from day-to-day (ie "local" calibration)?

joe_the_user 14y ago
Well more interesting stuff. My Googling yielding woefully incomplete references for your keywords. So "a long time" means what here? Some pointers would be useful here. I'm interested, help me out here. I know there was a book giving long reworking of Black-Scholes for Levi-Stable distributions in the early 2000's. Of course, while you described the sophisticated approach, from Black-Scholes to the Gaussian "coupela" to the OP, the unsophisticated approach has a lot of traction still. If we're ranging around all our interests in the market, I'd offer what I might hope would be the Minsky comment; "the fault, dear Brutus, lies not with our models but in our selves". Gaussian models reappear because they have "predictiveness". The problematic sides of the more sophisticated models are tolerated for the same reason. Greed tempts us always to irrationality jump from what Keynes called uncertainty to mere probability. Btw, what do you think of Doug Noland of prudentbear.com?

joe_the_user 14y ago

Well more interesting stuff. My Googling yielding woefully incomplete references for your keywords. So "a long time" means what here? Some pointers would be useful here. I'm interested, help me out here. I know there was a book giving long reworking of Black-Scholes for Levi-Stable distributions in the early 2000's. Of course, while you described the sophisticated approach, from Black-Scholes to the Gaussian "coupela" to the OP, the unsophisticated approach has a lot of traction still. If we're ranging around all our interests in the market, I'd offer what I might hope would be the Minsky comment; "the fault, dear Brutus, lies not with our models but in our selves". Gaussian models reappear because they have "predictiveness". The problematic sides of the more sophisticated models are tolerated for the same reason. Greed tempts us always to irrationality jump from what Keynes called uncertainty to mere probability. Btw, what do you think of Doug Noland of prudentbear.com?