Letters in Economic Research Updates
Put Call Duality for the Truncated Normal Distribution Model in Option Pricing
Abstract
Alex Nyonga Onsoti
This study explored the put-call duality under the Truncated Normal Distribution (TND) model in option pricing, which assumed that the log-prices of the underlying assets were bounded above and below. The model was compared with the famous Black-Scholes Model, which has consistently been considered the benchmark model for option pricing. Using the model, we derived a model-consistent put-call duality identity. We applied it to construct an objective function to improve the accuracy and consistency of option pricing. This is in conjunction with the various modifications put forward to “improve” the pricing of options. This study extended Zhu & He’s work by incorporating the put-call duality relation in the proposed model and compared the results to those obtained using the classical Black & Scholes (BS) Model. Similarly, this study investigated the implied volatility of the proposed model and compared it with the BS model. From the duality constraint calibration, the proposed model performed significantly better than the traditional Black-Scholes model. A numerical analysis was done using S&P 500 options data retrieved on June 27, 2025. Model performance checks, such as AIC, BIC, and pricing errors, indicated the outstanding performance of the TND model. From the methodology and numerical analysis, there was evidence that the duality relation holds for the Truncated Normal Distribution model, as is the case with the Black & Scholes model. The implied volatility indicated that the TND model was sensitive to in-and-out-of-the-money options. Therefore, enforcing the duality constraint in the pricing of European options improved the market consistency, ensuring that no arbitrage opportunities exist in the market that can provide enormous risk-free earnings.