This project established a comprehensive, four-phase, quantitative framework for identifying option mispricings in Apple Inc. (AAPL) by comparing market expectations with historical data. The analysis began with Phase 1 (HV Cone), constructing a statistical baseline of realized volatility across multiple time windows over five years, establishing the 30-day historical median at 24.9%. Phase 2 (IV Extraction) inverted the Black-Scholes model to find the market's current expectation, yielding an ATM Implied Volatility (IV) of 10.6%. The most significant finding, derived in Phase 3 (Signal Generation), was the discovery of a persistent and systematic negative volatility premium , where the current IV sat 14.3 percentage points below its historical median. This anomaly contradicts standard financial theory and generated a strong, statistically significant BUY OPTIONS signal.