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Black-Scholes

The Black-Scholes model was published in 1973 by Fischer Black and Myron Scholes. This model is used to calculate the theoretical price of options using five key determinants of an option’s price, that is stock price, strike price, volatility, expiration time and risk-free rate.

Black-Scholes formula for call options is as follows:

https://lh4.googleusercontent.com/kcygTIAWJ7UU-Hv1-2GNnry5dBR-S-_zThnWD9LdMT4IpNPXmucEzY4xSI2bMsjCx0tdxgNNBmS0_VyR7wYHDK-vOV_ErWL4q4dTTXd42YeCqWWCwLWN_VztwpHsCdu6qI_89G1r

 

Where,

r  = Risk-free Rate

t = Expiration Date

X = Strike Price of the option

S = Price of the Stock

σ= standard deviation

https://lh6.googleusercontent.com/DpiTrrhjbIrThh-8PCP2Ro4cFCuuz-mQCOwXOCxWtKiKD-menugW-HNVTZIZzm2C6vGS7QpPV0zqvPShE0-2R1JD8AGWoWdwE0clwPJ0gJjJJ_JlxbliBMBrc6YzqBrcZRD8JVaX

https://lh4.googleusercontent.com/d-JT90wN-fwTL0e36j6qvAoaNVjJPMLYfLbuwSPyU9-U4NABB83jB98FSRjZF2cGppuJhpnE0fT_dc6xS6TX0J1O9h6RtYaFr4er6W30LXOPKDXhtyOS25eH5oehM0Dh6053DR3d https://lh3.googleusercontent.com/UWw-ejZrh4myP-rYKvvx9kLuHnZIJelB1KJUmaAurSdHjlE3YqdGKFZb_PDGObC8WKSpF2fkaOAN2iCNlOoqIlCw3A_72EugStBdN79Iz611E2BWjEtPsLqHzVtH7BhDT_avL0iO

https://lh3.googleusercontent.com/CCfZBW0qMksIq9Tpzq3W98DS5JhaiB-bHz68IWjOn_K_YtZ_-3TwJO3o8FYcGRTlm8FWt__z8QoueW4Qtnega0jpW8-hy4oPDdo7uRXhhj1MvFXp9Ubg9JD5HDontPiij2ZDx4ZR

 

Assumptions underlying the Black Scholes formula

  1. The stock pays no dividend during the option’s life

  2. European style options

  3. Interest rate is constant

  4. Volatility is constant

  5. Infinite liquidity and depth in the market

  6. No commissions and transaction costs

  7. Stock returns follow normal distribution