Monday, May 18, 2015

1st theorem of equivalent MG pricing, precisely(%%best effort

Despite my best effort, I think this write-up will have
* mistakes
* unclear, ambiguous points

, but first step is to write it down. This is first phase of thin->thick->thin.

Version 1: under RN measure [1], all traded asset [2] prices follows a GBM [4] with growth rate [5] similar to the riskfree money market account. The variance parameter of the GBM is unique to each asset.

Version 2: under RN measure [1], all traded asset [2] prices discounted to PV [3] by the riskfree money market account are martingales. In fact they are 0-drift GBM with individual volatilities.

Version 3: under RN measure [1], all traded asset [2] prices show an expected [3] return equal to the riskfree rate.

[2] many things are not really traded asset prices. See post on "so-called tradable"

[3] why we need to discount to present, and why "expected" return? because we are "predicting" the level of random walker /towards/ a target time later than the last revelation.  The value before the revelation is "realized", "frozen" and has no uncertainty, no volatility, no diffusion, and no bell-shaped distribution.

[4] no BM here. All models are GBM.

[5] see post on drift ^ grow rate

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New York (Time Square), NY, United States
http://www.linkedin.com/in/tanbin