OM Session 2

AndrewS

Member
B&S assumes by default that a fully hedged position should only yield the risk-free rate. An interesting concept when the risk-free rate in much of the world is now a negative number.
 

Bruno

Member
There are a few ways to interpret that statement. B&S is not always right considering its hypotheses but one shouldn't throw it away either. B&S is still prevalent so one shouldn't be worse off than the vast majority of traders who would err in a similar fashion.
Secondly,the goal yesterday was to highlight some Greeks equivalence and maybe look beyond simple Delta rules, in other words, whether you're into Delta hedging or not, one should keep an eye on Gamma, and that is not restricted to short term weekly traders.
The demonstration assumed small moves of the underlying. I shall cover possible corrections to the model (e.g. jump-diffusion) in future presentations. The point was to highlight "local" hedging only. Extending it to global hedging becomes theoretically very complex and to some extent also pointless considering a zero sum game is not attractive at all. Controlling Gamma is already a good start.

Anyway, if my short topics get you thinking then I'm happy. Complacency is our worst enemy...
 

AndrewS

Member
My comment was (slightly) tongue-in-cheek but, as you said, it does make one think. The B&S world is to the real world the way Euclidean geometry is to the real world; close enough, most of the time. Really great presentations!
 

Bruno

Member
Andrew,
You could hardly find a better analogy ! Euclidean geometry is about perfect in a vast majority of cases, where Riemann geometry extends (some would say distort) it to cover odd geodesic projections as well chaos (e.g. fractals) and markets are fractal by nature.

WRT these presentations: I want to remain as humble as possible as modelling options can become hair-raising!
At the same time, dealing with an imperfect world should never be an excuse not to learn and think. I have no ambition of becoming popular with my unconventional way of thinking; I just hope we'll manage to form a small group of like-minded practitioners eventually and push the can down the road together.
 
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