[SC 7727] Greeks tests for option pricer model

[AnilSorathiya]

Internal Notes for Reviewers

[github-actions]

PR Summary

This pull request introduces significant enhancements to the option pricing models by adding calculations for the Greeks, which are essential for understanding the sensitivity of option prices to various factors. The following changes have been made:

1. Addition of Greeks Calculations:

   • Delta: Measures the sensitivity of the option's price to a change in the price of the underlying asset.
   • Gamma: Measures the rate of change of Delta with respect to changes in the underlying asset's price.
   • Theta: Measures the sensitivity of the option's price to the passage of time, also known as time decay.
   • Vega: Measures the sensitivity of the option's price to changes in the volatility of the underlying asset.
   • Rho: Measures the sensitivity of the option's price to changes in the interest rate.

2. Code Enhancements:

   • Introduced new functions to calculate each Greek using the finite difference method.
   • Added test cases for each Greek to ensure the correctness of the calculations.
   • Updated the notebook to include sections for each Greek, providing explanations and code examples.

3. Documentation Updates:

   • Updated the table of contents to include new sections for Greeks.
   • Added markdown cells explaining the significance of each Greek in the context of option pricing and risk management.

Test Suggestions

• Verify the correctness of Delta calculation by comparing with known analytical solutions.
• Test Gamma calculation for different underlying asset prices and ensure consistency.
• Check Theta calculation over different time intervals to validate time decay effects.
• Validate Vega calculation by comparing with market data for volatility changes.
• Ensure Rho calculation accurately reflects changes in interest rates.
• Run the entire notebook to ensure all new code cells execute without errors.
• Test edge cases where input parameters are at their minimum or maximum values.

[johnwalz97]

Nice!