UNPACKING PROFIT AND LOSS ATTRIBUTION IN OPTIONS: A THEORETICAL PERSPECTIVE

This paper delves into the theoretical foundations of option trading activities, profit and loss attribution, and associated hedging in the presence of market risk. While the Black-Scholes formula is a fundamental tool for pricing European options, it assumes constant volatility. In practice, the volatility surface, characterized by maturity and strike level dimensions, is introduced to match market prices. Investment banks play a pivotal role in options trading, where clients, such as oil producers, airlines, and insurers, manage their risk by trading options. Investment banks, when involved in such transactions, delta hedge the options to balance their risk. This paper demonstrates that the gains from the hedging activity will equate to the option's price, shedding light on the mathematical derivation under the assumptions of flat and sideways market movements. This reformulation of the Black-Scholes formula provides valuable insights into option trading strategies.