1. Black-Scholes Formula and Python Implementation

    The Black-Scholes model was first introduced by Fischer Black and Myron Scholes in 1973 in the paper "The Pricing of Options and Corporate Liabilities". Since being published, the model has become a widely used tool by investors and is still regarded as one of the best ways to determine fair prices of options.

    Tagged as : Python finance mathematics
  2. Implied Volatility Calculations with Python

    Implied volatility $\sigma_{imp}$ is the volatility value $\sigma$ that makes the Black-Scholes value of the option equal to the traded price of the option.

    Recall that in the Black-Scholes model, the volatility parameter $\sigma$ is the only parameter that can't be directly observed. All other parameters can be determined through market data (in the case of the risk-free rate $r$ and dividend yield $q$ and when the option is quoted. This being the case, the volatility parameter is the result of a numerical optimization technique given the Black-Scholes model.

    Tagged as : Python finance mathematics

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