## Cheatsheet of Latex Code for Financial Engineering and Quantitative equations

rockingdingo 2022-07-18 #financial engineering #black-sholes 2 0

Cheatsheet of Latex Code for Financial Engineering and Quantitative equations

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

##### 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.