Why does Black-Scholes assume normal distribution?

Why does Black-Scholes assume normal distribution?

Assumptions of the Black-Scholes-Merton Model Lognormal distribution: The Black-Scholes-Merton model assumes that stock prices follow a lognormal distribution based on the principle that asset prices cannot take a negative value; they are bounded by zero.

Which of the following is an assumption on the returns distribution in Black-Scholes model?

Black-Scholes Assumptions The Black-Scholes model makes certain assumptions: No dividends are paid out during the life of the option. Markets are random (i.e., market movements cannot be predicted). There are no transaction costs in buying the option.

Are log returns normally distributed?

Therefore log returns have a normal distribution. That applies to individual assets. The returns of an index — which is the weighted average of a number of assets — has even more reason to be normal.

What is N d1 n d2 in Black Scholes?

N(d1) = a statistical measure (normal distribution) corresponding to the call option’s delta. d2 = d1 – (σ√T) N(d2) = a statistical measure (normal distribution) corresponding to the probability that the call option will be exercised at expiration.

Why are returns log normal?

While the returns for stocks usually have a normal distribution, the stock price itself is often log-normally distributed. This is because extreme moves become less likely as the stock’s price approaches zero. Cheap stocks, also known as penny stocks, exhibit few large moves and become stagnant.

How do I know if my data is Lognormally distributed?

The usual way to test for lognormality would be to take logs and test for normality. Then any suitable test of normality would do; a Shapiro Wilk would be a reasonable choice.

What is Ln in Black Scholes model?

s = instantaneous standard deviation of the return on the underlying asset. t = time remaining until maturity (in years) and ln = Naperian logarithm.

What is d1 and d2 in Black-Scholes model?

The Black-Scholes formula expresses the value of a call option by taking the current stock prices multiplied by a probability factor (D1) and subtracting the discounted exercise payment times a second probability factor (D2).

What is the difference between n d1 and n d2?

Cox and Rubinstein (1985) state that the stock price times N(d1) is the present value of receiving the stock if and only if the option finishes in the money, and the discounted exer- cise payment times N(d2) is the present value of paying the exercise price in that event.

Are returns normally distributed?

We all know that stock market returns are not normally distributed. Instead, we think of them as having fat tails (i.e. extreme events happen more frequently than expected).

Are the log returns normally distributed?