Edit Content
Edit Content
Edit Content
  1. Home
  2. »
  3. Recommendations
  4. »
  5. Black-Scholes Model

Black-Scholes Model

Black-Scholes Model

The Black-Scholes model, also known as the Black-Scholes-Merton (BSM) model, is one of the most important concepts in modern financial theory. It provides a mathematical formula that calculates the theoretical value of derivatives based on investment vehicles, taking into account the effect of time and other risk factors.

From the parabolic partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price given the risk of the security and its expected return (instead replacing the security’s expected return with the risk-neutral rate).

The Black-Scholes model requires five input variables: the strike price of an option, the current stock price, the time to expiration, the risk-free rate, and the volatility.


  • C = call option price
  • S = current stock price
  • K = strike price
  • r = risk free interest rate
  • t = time to maturity
  • N = normal distribution

With these variables, it is theoretically possible for options sellers to set reasonable prices for the options they sell.

When was the Black-Scholes model developed?

The Black-Sholes model has been in development since 1973. It is still the best method for pricing options contracts.

How Accurate Is Black-Scholes Pricing?

Although it is usually accurate, the Black-Scholl model makes certain assumptions that may cause prices to deviate from real market results.

Why not use the Black-Scholes model in pricing US options?

The standard BSM Black-Scholes model is used only for pricing European options. This is because it does not take into account the possibility of exercising US options before the expiration date.

What are the assumptions of the Black-Scholes model?

The Black-Scholes model is based on several assumptions: no dividends are paid during the life of the option, and there are no transaction costs when purchasing the option. Also, the returns of the underlying assets are distributed normally. And prices move in random markets (market movements cannot be predicted). On the other hand, the risk-free rate and volatility of the underlying assets are known and stable. Finally, the option can only be exercised upon expiration.

If you would like to know more about Black-Scholes model, you can visit Exfor website. For the first time ever, we offer traders direct prices from a liquidity provider. Don’t miss your chance to subscribe for just $300 per year and ensure your trading success!

Recommended for you
5 Essential Money Management Skills

5 Essential Money Management Skills

How to Budget Without “Budgeting” Only a third of families actually organize a detailed household budget. This is crucial behavior especially if basic goals have not been met – such as paying off an emergency

What is the inverted yield curve?
For novice traders

What is the inverted yield curve?

If we compare 10-year and 30-year bonds, nobody doubts that unfavorable things can happen in a 30-year period with a higher statistical probability than in a 10-year period. For this reason, typically the yield on

Currency exchange commission: what is it?
Financial markets news

Currency exchange commission: what is it?

One of the commissions that has the greatest impact on the profitability of investors in the stock market or traders and in turn one of the most unknown is the commission for currency exchange. What

Forex Trading vs Stock Trading - The Most Notable Differences
For novice traders

Forex Trading vs Stock Trading – The Most Notable Differences

Despite the great popularity of cryptocurrency trading in recent times, the foreign exchange (forex) and stock markets are still the most popular. While trading in these markets looks somewhat similar, there are several important differences