Comments on: The Black Swan http://leduc998.wordpress.com/2008/03/28/the-black-swan/ Just another WordPress.com weblog Mon, 16 Nov 2009 05:36:31 +0000 http://wordpress.com/ hourly 1 By: Nick http://leduc998.wordpress.com/2008/03/28/the-black-swan/#comment-584 Nick Sun, 20 Apr 2008 21:32:05 +0000 http://leduc998.wordpress.com/2008/03/28/the-black-swan/#comment-584 Calibration is usually the method of fitting a risk-neutral model to today's data. Yesterday's data is discarded. So, for instance in plain-old Black-Scholes you might fit ATM vol every day. This allows you to reprice your ATM options. The problem there is, in the original derivation, vol was never meant to be changed--the drift was, not the vol. You should really have the same vol in both the physical and risk-neutral measures. Anyhow, calibrators are not bothered by their lack of self-consistency. Models though can refer to the not particularly realistic SDEs of the financial engineering risk-neutral types or statistical models of all sorts which can be fit to historic data (i.e., by MLE) and "tested" or used to find posteriors and (model-error adjusted) predictive densities in a Bayesian way. The statistical models, unlike the SDEs, have metrics associated with them and make reference to history and out-of-sample prediction. Calibration is usually the method of fitting a risk-neutral model to today’s data. Yesterday’s data is discarded. So, for instance in plain-old Black-Scholes you might fit ATM vol every day. This allows you to reprice your ATM options. The problem there is, in the original derivation, vol was never meant to be changed–the drift was, not the vol. You should really have the same vol in both the physical and risk-neutral measures.

Anyhow, calibrators are not bothered by their lack of self-consistency.

Models though can refer to the not particularly realistic SDEs of the financial engineering risk-neutral types or statistical models of all sorts which can be fit to historic data (i.e., by MLE) and “tested” or used to find posteriors and (model-error adjusted) predictive densities in a Bayesian way. The statistical models, unlike the SDEs, have metrics associated with them and make reference to history and out-of-sample prediction.

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