Cheatsheet of Latex Code for Financial Engineering and Quantitative equations

rockingdingo 2022-07-18 #financial engineering #black-sholes


Cheatsheet of Latex Code for Financial Engineering and Quantitative equations

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In this blog, we will summarize the latex code of most popular equations for financial engineering. We will cover important topics, including Black-Scholes formula, Value at Risk(VaR), etc.

1. Black-Scholes Formula

  • Black-Scholes Formula

    Equation

    1.1 Call Formula

    1.2 Put Formula

    Parameters

    Latex Code
                C(S_{t},K,t)=S_{t}\Phi (d_{1})-Ke^{-r(T-t)}\Phi (d_{2})
            
                P(S_{t},K,t)=Ke^{-r(T-t)}\Phi (-d_{2})-S_{t}\Phi (-d_{1})
            
                d_{1}=\frac{\ln \frac{S_{t}}{K} + (r + \frac{\sigma^2}{2})\tau}{\sigma\sqrt{\tau}}
            
                d_{2}=d_{1}-\sigma\sqrt{\tau}
            
    Explanation

    Latex code for Black-Scholes Formula. I will briefly introduce the notations in this formulation.

    • : The spot price at time t for dividend stock.
    • K: Strike price
    • T: Maturity Time, T-t equals to time to maturity
    • : constant volatility of the asset
    • r: risk-free rate of interest
    Detailed explanation can be found in this document Four Derivations of the Black-Scholes Formula.

  • 2. Value at Risk(VaR)

    • Value at Risk(VaR) Formula

      Equation


      Latex Code
                  \text{prob}(\Delta P < -\text{VaR})=1-\alpha
              
      Explanation

      Latex code for Value at Risk Formula. I will briefly introduce the notations in this formulation.

      • VaR: Value at Risk
      • : Confidence level that asset price will fall below the target
      • : Price at time t
      • : The difference in price from time t to t+1
      Detailed explanation can be found in this document Four Derivations of the Black-Scholes Formula.