# How does the Black Scholes Merton model work?

## How does the Black Scholes Merton model work?

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.
- The risk-free rate and volatility of the underlying asset are known and constant.

## What is D1 and D2 in BSM model?

D2 is the probability that the option will expire in the money i.e. spot above strike for a call. N(D2) gives the expected value (i.e. probability adjusted value) of having to pay out the strike price for a call. D1 is a conditional probability.

**What are the assumptions of Black-Scholes model?**

Assumptions about risky assets Constant volatility − The Black Scholes method assumes that the volatility of the options is constant and known beforehand. In the practical world, it is neither possible to find constant volatility and nor can we find a pre-known asset price.

**What is the Black-Scholes mathematical model What is it used for?**

Definition: Black-Scholes is a pricing model used to determine the fair price or theoretical value for a call or a put option based on six variables such as volatility, type of option, underlying stock price, time, strike price, and risk-free rate.

### What is N d1 in BSM?

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. Ke-rt = the present value of the strike price.

### What are D1 and D2 in Black-Scholes?

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.