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
• 1.1 Call Formula
• 1.2 Put Formula
• 2. Value at Risk(VaR)

• 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.