## Black–Scholes Model for Trading

Blach-Scholes model is term in the binary trader’s dictionary widely used to describe a mathematical model of the financial marked, which is used to deduce the future market price. Underling of it, is the Back-Scholes formula, which provides a theoretical estimate of the price in European-style options. The model is widely used around the world and in time it has received numerous plethora of models, used in derivative pricing and risk management. There are numerous insights of Black-Scholes formula that are regularly used by market players, including the no-arbitrage bounds and neutral risk pricing.

The only parameter that can’t be seen in the market is the average future volatility of the examined asset. The Black-Scholes formula increases in this parameter and the creation of volatility surface can be produced that can be used for calibrating other models. The nature of the formula disagrees with reality in couple of ways. Also it is widely used as approximation, but for the use of its full extend a good grasp of its limitations is needed. Blind following of the model exposes the trader to risk.

Some examples include the good understanding of extreme moves and respectively the yielding tail risk, which can be hedged using out of the money options. Another example is the assumption of cost-less trading, liquidity risk which is almost impossible to hedge. Theoretically put Black-Scholes model can hedge any position via Gamma hedging, but in reality there are other factors at play.

In reality the results in using the Black-Scholes model differs greatly from the real world prices, due to the simplification caused by the model. For example: security prices don’t follow a stationary log-normal process, nether the risk-free interest is actually know. Observations have shown that the variance is not constant and as a result lead to the use of models such as GARCH in order model change in volatility.

Another problem is the price discrepancies between Black-Scholes model for binary options trading and the empirical model, can be found in options that are far out of the money, as a result to extreme price change. Theoretically speaking such events should be very rare if returns are normally distributed, but in practice it’s exactly the opposite.

On the other hand, the Black-Scholes pricing is very easy to calculate, it is very useful as an approximation, when analyzing the price move between two points and it is very easy to robust. This is what makes the model so widely spread in the trading world.