Understanding-Delta

This project explores the concept of Delta, a key sensitivity measure in options pricing and risk management. It begins with a formal definition of Delta and an interpretation of its values across different levels of moneyness. The relationship between Delta and the Black Scholes model is examined to understand its theoretical foundation. A detailed analysis is presented on how Delta evolves with changes in the underlying asset price, followed by a discussion of Delta in the context of the Taylor expansion, offering intuition on how small price changes affect option value and how this insight supports dynamic hedging strategies. A practical case study on delta neutral hedging is developed to illustrate the implementation and effectiveness of hedging under real world conditions, including the role of time decay (Theta) and volatility. Theoretical explanations are supported by Python based visualizations and simulations, including Delta approximation graphs and the impact of other Greeks. This work aims to bridge the gap between mathematical theory and trading practice, highlighting Delta’s role in both pricing and hedging.