Assumptions behind the Black-Scholes Model

The famous options pricing model known as the Black-Scholes model or Black-Scholes-Merton, can help it’s users deduce the correct price for European Style Options. The model came first came to prominence in the 1970’s and is now widely used within the world of Options trading. The Black-Scholes model has become somewhat infamous after the collapse of gigantic hedge fund Long Term Capital Management who put to play the model they themselves had created. Behind the Black-Scholes model lies several assumptions, today we are going to go through and examine each of the assumptions. 

There is no arbitrage opportunity 
An arbitrage opportunity is an opportunity to make a risk-less profit by Buying and Selling in two different market places. Back when the Black-Scholes Model came onto the scene there were plenty of arbitrage opportunities in the financial markets. For example commodity traders were able to set up arbitrage desks trading price discrepancies present in two different open outcry markets. While the majority of arbitrage opportunities of the kind mentioned above have disappeared, it is not impossible to exploit arbitrage opportunities for risk-less profit.  
 
It is possible to borrow and lend at a constant risk free rate 
A important part of the model relies on the idea that at any moment in time there is a riskless rate which one can both borrow and lend at. Firstly it’s clear that such a risk free rate wouldn’t remain constant and would be subject to change. This issue for the Black-Scholes Model was overcome by more complex versions that can account for changing interest rates. But it can also be seen that the idea there is a riskless rate which can both borrow and lend at is questionable. When taking about a risk free rate of return one is normally talking about short term government bonds or LIBOR. But since the financial crisis of 2008 the idea that these represent a truly risk less proposition has become more dubious with bonds being seen in a somewhat different light.  In times of turmoil it is difficult to see whether this assumption really does hold true. 
 
It is possible to both buy and sell any amount, even fractional of stock,(including short selling). 
This is also a very questionable assumption there will be times when you will not be able to buy or sell stock including short selling. As there may not be the liquidity or people willing to loan the stock in order for you to be able to short sell it. Again this another assumption that seems problematic for those who wish to use the Black-Scholes model. Again during the 2008 financial crisis there were periods where certain stocks were totally unavailable for short sale as there was more demand to short sell the stock than there was stock to be short sold.  
 
The Black-Scholes models also contains other assumptions more expanded versions of the model can avoid or account for these assumptions. While these assumptions and the questions surrounding them are some cause for concern don’t rule out using the Black-Scholes as tool in your trading arsenal. Just remember to becareful not to accept Black-Scholes or any other model as trading law. 

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