subject: What Is Black Scholes Model Option Pricing? [print this page] Black-Scholes formula was articulated in the year 1973 paper by Myron Scholes and Fisher Black with basic insight that the option is perfectly priced is there is stock trading. According to the Black-Scholes Model for option pricing in the financial market, there are several assumptions that are taken into consideration:
-A person trading in the financial market is allowed to borrow or lend cash at a known interest rate that is risk free.
-The prices follow the GBM-Geometric Brownian Motion which is under constant drift and volatility.
-This model for option pricing doesn't involve any type of transaction charges.
-No dividend to be paid for the stock.
-Any security can be exactly divided, which means, a person is allowed to buy any fraction of the share.
-No limitations on short selling.
-Arbitrage opportunity is zero.
These are the ideal conditions that are assumed in the financial market, for equity as well as option on equity. The authors also think that it is practical to make hedged position which includes long position for the stock and short position for calls, on that stock itself. Also the value will never depend on the stock price.
However, the Black-Scholes model disagrees with the fact in several ways and many were significant. It is greatly used as a helpful estimation, however, if you want to apply it practically and properly, it is essential to understand its limitations. The trader can fall into a great risk if he/she blindly follows the model, thus it is necessary to know its limitations as well. It will help to perform accurately and understand the level of risk involved while trading.
Here are a few limitations to Black-Scholes Model Option and are considered as most important limitations:
-The disbelief of acute moves, resulting trail risk that can be hedged using out-of-the-money options.
-It is assumed quick and cost-less trading which results in liquidity risk which is quite difficult to hedge.
-It is also assumed stationary process and this result in volatility risk. This risk can be hedged using volatility hedging.
-It is assumed continuous trading along with continuous time. This results in risk gap and this risk is hedged with Gamma hedging.
The bottom line is that, with the help of Black-Scholes model option trading, it is possible to hedge options by just Delta hedging, but in reality, there are several other risk factors that should be kept in mind while options trading. Moreover, the most significant restriction is, actually the security prices do not agree with stern stationary log normal procedure, nor anyone actually knows the risk free interest rate which is also not constant over a period of time. Thus, once you are aware about the assumptions and the limitations of Black-Scholes model option trading, you will surely trade with minimum risks as well as you will be able to hedge the risk that usually evolve over a period of time.
by: Jamie Hanson
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