Re: Casual Fridays - Black Scholes Assumptions
in response to
by
posted on
Apr 25, 2012 11:00AM
Saskatchewan's SECRET Gold Mining Development.
The Black–Scholes model of the market for a particular stock makes the following explicit assumptions:
From these assumptions, Black and Scholes showed that “it is possible to create a hedged position, consisting of a long position in the stock and a short position in the option, whose value will not depend on the price of the stock.”[4]
Several of these assumptions of the original model have been removed in subsequent extensions of the model. Modern versions account for changing interest rates (Merton, 1976)[citation needed], transaction costs and taxes (Ingersoll, 1976)[citation needed], and dividend payout.[5]
source: http://en.wikipedia.org/wiki/Dynamic_Hedging
While reading about dynamic hedging, if you were to come up with a description of how the market works, you need not go any further than the assumptions of the Black Scholes model.
If anything describes what we've been seeing in GBN.V shares are the above assumptions in practise. A second assumption that I would make is that GBN.V is strongly inversely correlated with the long-dated U.S. Treasury prices. This arbitrage in Treasury options vs. GBN.V share price ultimately determines the price of the GBN.V shares. Not the fundamentals.
But, in some way, the fundamentals are in play, for instance zero interest rate lending to the commercial banking sector. And GBN.V does not pay a dividend. So the treasury prices go up, while GBN.V share prices go down.
You can see why paying a dividend as a gold miner is extremely important in light of dynamic hedging strategies using the Black Scholes options pricing model.
Other Factors
Also, you must remember a number of things have occurred since the collapse of the ABCP in Canada. With the rise of the conservative minority in 2005, we saw further deregulation in the banking sector. Then we have the no down-tick rule abolished last year. This was at the time that the last financing by GBN.V was offered. The stock has pretty much been at the whim of dynamic hedging strategies since that time.
Or a simple way to put it, if long dated U.S. treasuries sell off, then GBN.V stock prices advance. But more than likely U.S. treasury prices will advance during QE. (discounting any currency devaluation against gold)
An obvious minor gap has been filled in the monthly chart, leading to a GBN.V share price low.
supersize: http://www.flickr.com/photos/11747277@N07/7112803189/sizes/l/in/photostream/