Black-Scholes Formula Discussion | Forum

Thread starter TSC
Start date Apr 14, 2014
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In summary, The Black-Scholes formula is a mathematical equation used to calculate the theoretical value of European-style stock options. It was developed by Fischer Black and Myron Scholes in 1973, with the assistance of Robert Merton. The formula makes assumptions such as a lognormal distribution for the underlying asset, no transaction costs or taxes, and a constant risk-free interest rate. It is not suitable for valuing options on assets that do not follow a lognormal distribution and does not account for market volatility changes or other factors. However, it is widely used in practice for pricing options, managing risk, and identifying trading opportunities.

Apr 14, 2014

TSC

If I want to discuss Black–Scholes formula, where should I post?

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Apr 14, 2014

AMenendez

Post it in the "Differential Equations" forum, as the Black-Scholes Model is an extremely popular PDE. As a reminder, the BSM is:
[itex] \frac{\partial V}{\partial t} + \frac{1}{2} \sigma^2 S^2 \frac{\partial^2V}{\partial S^2} + rS \frac{\partial V}{\partial S} - rV = 0 [/itex]

What is the Black-Scholes formula?

The Black-Scholes formula is a mathematical equation used to calculate the theoretical value of European-style stock options. It takes into account factors such as the current price of the underlying asset, the strike price, the time until expiration, and the volatility of the asset.

Who developed the Black-Scholes formula?

The Black-Scholes formula was developed by Fischer Black and Myron Scholes in 1973, with the assistance of Robert Merton. They were awarded the Nobel Prize in Economics in 1997 for their groundbreaking work.

What are the assumptions of the Black-Scholes formula?

The Black-Scholes formula makes several key assumptions, including that the underlying asset follows a lognormal distribution, there are no transaction costs or taxes, and the risk-free interest rate is constant. It also assumes that the option can only be exercised at its expiration date and that the market is efficient.

What are the limitations of the Black-Scholes formula?

The Black-Scholes formula is not suitable for valuing options on assets that do not follow a lognormal distribution, such as commodities or currencies. It also does not account for market volatility changes, which can greatly affect the value of options. Additionally, the formula does not consider factors such as dividends and early exercise of options.

How is the Black-Scholes formula used in practice?

The Black-Scholes formula is used by investors and financial institutions to price options and manage risk. It is also commonly used as a benchmark for comparing the value of options in the market. Traders may also use the formula to identify mispriced options and execute profitable trades.