Black-Scholes Formula: Objective or Risk-Neutral?

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In summary, the normal distribution is commonly used to model stock returns in the Black-Scholes formula. However, there is a debate on whether this distribution represents the subjective or risk-neutral probability distribution. Some academic sources suggest that implied volatility, which is an estimate of the variance of asset return, may be based on the subjective probability rather than the risk-neutral one.
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pkxt
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Hello,

I understand that the normal distribution is used to model stock returns in the Black-Scholes formula.

Can someone please tell me whether this is meant to be the subjective probability distribution or the risk-neutral probability distribution?

Thank you!
 
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risk neutral (assuming prices are continuous & the underlying can be sold short without limit)
 
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Thank you for your response! Can you perhaps point me to some academic sources?

I read something that claims the implied volatility is an estimate of the variance of the subjective probability of asset return -- is that just because they are not drawing the distinction between subjective and risk-neutral?
 

1. What is the Black-Scholes Formula?

The Black-Scholes Formula is a mathematical model used to calculate the theoretical value of European-style options. It takes into account factors such as the current stock price, strike price, time to expiration, volatility, and risk-free interest rate to determine the fair price of an option.

2. Is the Black-Scholes Formula objective or risk-neutral?

The Black-Scholes Formula is considered to be risk-neutral, meaning that it assumes investors are indifferent to risk and make decisions based solely on expected returns. This assumption allows for a simpler and more efficient calculation of option prices.

3. Who developed the Black-Scholes Formula?

The Black-Scholes Formula was developed by Fischer Black, Myron Scholes, and Robert Merton in 1973. They were awarded the Nobel Prize in Economics in 1997 for their contribution to the understanding of financial markets with their groundbreaking formula.

4. What are the limitations of the Black-Scholes Formula?

While the Black-Scholes Formula is a widely used and respected model, it does have some limitations. It assumes that the market is efficient, which may not always be the case. It also does not account for factors such as dividends, transaction costs, and market volatility.

5. How is the Black-Scholes Formula used in practice?

The Black-Scholes Formula is used by investors and financial institutions to determine the fair price of options and to make informed trading decisions. It is also used in risk management to assess the risk exposure of portfolios containing options. However, it is important to note that the Black-Scholes Formula is just one tool and should not be the sole basis for making investment decisions.

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