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## Friday, April 11, 2014

### risk neutral measure, a beginner's personal view

Risk neutral measure permeates derivative pricing but is not clearly understood. I believe RN measure is very useful to mathematicians. Maybe that's why they build a complete foundation with lots of big assumptions.

Like other branches of applied math, there are drastic simplifying assumptions....

I think the two foundation building block are 1) arbitrage and 2) replication. In many textbook contexts, the prices of underliers and derivatives are related and restrained by arbitrage. From these prices we can back out or imply RN probabilities, but these are simplistic illustrations rather than serious definitions of RN measure.

On top of these and other concepts, we have Martingale and numeraire concepts.

Like Game programming for kids and for professionals, there are 2 vastly different levels of sophistication:
A) simplified -- RN probabilities implied from live prices of underliers and derivatives
B) sophisticated -- RN infrastructure and machinery, based on measure theory