The Black–Scholes or Black–Scholes–Merton model is a mathematical model of a financial market containing derivative investment instruments. From the model, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options. The formula led to a boom in options trading and legitimised scientifically the activities of the Chicago Board Options Exchange and other options markets around the world. lt is widely used, although often with adjustments and corrections, by options market participants. Many empirical tests have shown that the Black–Scholes price is "fairly close" to the observed prices.
The app calculates theoretical price and option greeks (Delta, Gamma, Vega, Theta, Rho) using black-scholes model with the most accurate calculations around d1, d2, call and put prices with 16 decimal accuracy using cumulative distribution and standard normal distribution. For display purpose, we later round these values to 3 decimal places.
Assumptions of the Black and Scholes Model are as follows -
1. The stock pays no dividends during the option's life
2. European exercise terms are used
3. Markets are efficient
4. No commissions are charged
5. Interest rates remain constant and known
6. Returns are lognormally distributed
The Black Scholes Formula -
c= S + p – Xe – r(T-t)
p = c – S + Xe – r(T-t)
c = call value
S = current stock price
p = put price
X = exercise price
e = Euler's constant (exponential function on a financial calculator equal to approximately 2.71828)
r = continuously compounded risk free rate of interest
T = Expiration date
t = Current value date
The Option Greeks taken into account along with their meaning are as follows -
1. Delta - measures the rate of change of option value with respect to changes in the underlying asset's price. Measures the exposure of option price to movement of underlying stock price
2. Vega - measures sensitivity to volatility. Measures the exposure of the option price to changes in volatility of the underlying
3. Theta - measures the sensitivity of the value of the derivative to the passage of time. Measures the exposure of the option price to the passage of time
4. Rho - measures sensitivity to the interest rate: it is the derivative of the option value with respect to the risk free interest rate
5. Gamma - measures the rate of change in the delta with respect to changes in the underlying price. Measures the exposure of the option delta to the movement of the underlying stock price
We have added the above definitions!
You can easily switch for Call and Put calculations and you can also use the reset button to clear all the values. It is a simple one page application without any complexity for quick calculations and analysis around option pricing.
DISCLAIMER: Although we try really hard to list out all the nitty-gritty around our option greeks calculator and give you accurate output, we cannot be held responsible for any resulting loss from inaccuracies or via any other means. All information provided via Option Greeks Calculator must be used for information purpose only and not investment advice.
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