Risk-neutral versus real-world probability measures in asset pricing

Abstract

This study examines the distinction between risk-neutral and real-world probability measures in asset pricing, highlighting their theoretical foundations, practical applications, and implications for financial modeling. Risk-neutral measures are primarily employed in derivative pricing, reflecting market-implied expectations under a no-arbitrage framework, whereas real-world measures capture actual probabilities derived from historical market data. By analyzing statistical properties, distributional differences, and transformations between the two measures, the research provides insights into the potential mispricing and risk assessment errors that may arise when relying solely on one approach. Empirical results demonstrate the importance of integrating both measures for enhanced accuracy in pricing, portfolio management, and regulatory compliance. The study further underscores the relevance of stochastic volatility models and simulation techniques in bridging the gap between theoretical constructs and real-world applications.