
Black-Scholes Model calculators
New Category!
Thinking of a Best Practice which could fit in this category? Tell us
What is the Black Scholes Model?
The Black Scholes model was the first widely used model for option pricing. It is used to calculate the theoretical value of European-style options by using current stock prices, expected dividends, expected interest rates, the option’s strike price, time to expiration and expected volatility.
The model makes certain assumptions:
The option is European and can only be exercised at expiration.
No dividend is paid out during the life of the option.
Markets are efficient and cannot be predicted.
No transaction costs are incurred when buying an option.
The risk-free rate and volatility of the underlying are known and constant.
The returns on the underlying are normally distributed.
The Black-Scholes Formula
The Black Scholes formula is calculated by multiplying the stock price by the cumulative standard normal probability distribution function. Then, the net present value (NPV) of the strike price multiplied by the cumulative standard normal distribution is subtracted from the resulting value of the previous calculation. C = SN(d1) - Ke^(-rT)*N(d2).
Conversely, the value of a put option could be calculated using the formula: P = Ke^(-rT)N(-d2) - S*N(-d1). In both of these formulas, S is the stock price, K is the strike price, r is the risk-free interest rate and T is the time to maturity. The formula for d1 is: (ln(S/K) + (r + (annualized volatility)^2 / 2)*T) / (annualized volatility * (T^(0.5))). The formula for d2 is: d1 - (annualized volatility)*(T^(0.5)).
Criticisms of the Model
Tail-risk fragility or other extreme randomness: Generally, returns do not follow a normal distribution. The p-value on the Normality Test is 0.0 when applied to S&P returns meaning market returns are leptokurtic.
The structure does not reflect present realities: it assumes a market is using European options. It also does not allow for dividends.
Assumes the interest rate is risk-free.
Assumption of cost-less trading: there are usually trading fees such as the cost to buy or sell stocks and options, cost of time etc. These costs are not included in the model.
Gap-Risk: the model assumes that trading continues continuously, unlike reality, where markets close overnight and then reopen with different prices to reflect new information.
For more on the Black Scholes Formula:
Last downloaded
- 24 seconds agoFind the value of puts, calls, and combinations of options using the Black-Scholes formula.1,9531add_shopping_cart
- 30 minutes ago
Black-Scholes Excel Pricing Model
A mini Black-Scholes Excel model, just hit and go!2,604Discussadd_shopping_cartfreeby Gia Hy Le Pham
- 1 day ago
Black-Scholes Option Pricing Models
This document comprises of 4 incredibly useful Black-Scholes option pricing models.1,520Discussadd_shopping_cartfreeby Michael Ho
- 1 day ago
Black-Scholes converted for Binomial Tree
Converts the standard deviation input in the Black-Scholes model to up and down movements in the binomial tree.916Discussadd_shopping_cart - 1 day ago
Black-Scholes Option Pricing Excel Model (with add-on for Privately Held Companies)
An Excel Black-Scholes option pricing model with volatility estimator for privately held companies481Discussadd_shopping_cart$5.00by Jhett Koo
- 3 days ago
Black-Scholes Option Price Excel Calculator
Call and put options price calculator that uses the Black-Scholes model for option pricing560Discussadd_shopping_cart - Earlier
Black-Scholes Options & Warrant Pricing Model
A simple Black-Scholes Model in Excel. Input your own data!96Discussadd_shopping_cart$5.00by Prather Financial
Full catalog
Black-Scholes Options & Warrant Pricing Model
A simple Black-Scholes Model in Excel. Input your own data!96Discussadd_shopping_cart$5.00by Prather Financial
Black-Scholes converted for Binomial Tree
Converts the standard deviation input in the Black-Scholes model to up and down movements in the binomial tree.916Discussadd_shopping_cartBlack-Scholes Option Price Excel Calculator
Call and put options price calculator that uses the Black-Scholes model for option pricing561Discussadd_shopping_cartBlack-Scholes Option Pricing Models
This document comprises of 4 incredibly useful Black-Scholes option pricing models.1,521Discussadd_shopping_cartfreeby Michael Ho
Black-Scholes Option Pricing Excel Model (with add-on for Privately Held Companies)
An Excel Black-Scholes option pricing model with volatility estimator for privately held companies481Discussadd_shopping_cart$5.00by Jhett Koo
Black-Scholes Excel Pricing Model
A mini Black-Scholes Excel model, just hit and go!2,605Discussadd_shopping_cartfreeby Gia Hy Le Pham
Option Value with Black-Scholes formula
Find the value of puts, calls, and combinations of options using the Black-Scholes formula.1,9551add_shopping_cart- Have a Black-Scholes Excel Model to Share?
Your Black-Scholes Excel Model
Publish your model
Learn more about digital publishing