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What is the Black-Scholes Model for Options Pricing?

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The Black-Scholes model is a mathematical model used to estimate the theoretical value of a European-style option. It uses several factors, such as the:

  • Underlying asset price
  • Strike price
  • Time to expiry
  • Volatility
  • Interest rate, and 
  • Dividends.

What is the Black-Scholes Formula in India?

Generally, there are two distinct formulas for both call and put options:

For a European Call OptionFor a European Put Option
C = S0 x N(d1) – Ke-rt x N(d2)P = Ke-rtx N(-d2) -S0 x N(-d1)

Where:

  • S0 = Current price of the underlying asset
  • Ke = Strike price
  • T = Time remaining until expiry
  • r = Risk-free interest rate
  • N(d) = Cumulative standard normal distribution

The Black-Scholes Model for Options Pricing is also used to calculate option Greeks such as Delta, Gamma, Vega, and Theta. It is most directly suited to European-style options. However, the theoretical value produced by the model can differ from the actual market premium.

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