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Option pricing: an empirical evaluation of higher-moment and risk-neutral approaches
(2025-10-06) Tasioudis, Diamantis; Τασιούδης, Διαμαντής; Demos, Antonios; Varthalitis, Petros; Topaloglou, Nikolaos
This thesis examines discrete distribution–based approaches to option pricing, focusing on the comparative performance of three methodologies: the Black–Scholes (BS) model, the Corrado–Su (CS) approach incorporating higher moments such as skewness and kurtosis, and a Risk–Neutral (RN) approach implemented through scenario generation and constrained optimization. The study is motivated by the limitations of the BS model, particularly its assumptions of lognormal asset prices and constant volatility, which have been repeatedly challenged by empirical evidence. By extending the analysis to approaches that incorporate higher moments or risk neutral probabilities, the thesis seeks to assess whether these alternatives provide more accurate and robust pricing methods. The empirical application considers European-style options on the S&P 500 index across two distinct market environments: September 30, 2022, representing a bearish environment characterized by prolonged downturns, and October 31, 2024, reflecting a bullish environment marked by consecutive recovery and optimism. For each regime, estimated prices from the three models were compared against observed market prices for multiple strike prices spanning ITM, ATM, and OTM regions. Model performance was evaluated using mean absolute error (MAE), root mean squared error (RMSE) and mean absolute percentage error (MAPE). The results confirm the limitations of the BS framework. While it provides a solid benchmark and performs reasonably well for ITM options, it systematically underprices OTM options and fails to capture higher-moment effects, particularly in bearish conditions. The CS approach improves pricing accuracy across both regimes, especially near the ATM region, by incorporating skewness and kurtosis. Its effectiveness is most evident under the bearish environment, where return distributions exhibit heavy left tails. However, in the bullish environment, CS occasionally mispriced OTM options, particularly overpricing ITM puts and OTM calls. The RN approach displayed mixed performance, where it underpriced options and delivered higher errors in the bearish environment compared to the other approaches but performed comparatively better in the bullish environment, especially for deep OTM calls and deep ITM puts, where it provided valuations close to market prices. Overall, the findings demonstrate that model choice depends on both market conditions and option moneyness. CS emerges as the most consistent alternative to BS, offering more accurate pricing with modest computational complexity, while the RN approach contributes valuable insights at the extremes of the distribution. The study underscores the need for option pricing models that go beyond the restrictive assumptions of BS and incorporate empirical features of asset returns. By providing a comparative evaluation of discrete distribution–based methodologies, this thesis contributes to the ongoing discussion in both academia and practice regarding optimal approaches for pricing options under different market environments.