["International Journal of Finance &Economics, Volume 31, Issue 2, Page 2396-2416, April 2026. ", "\nABSTRACT\nThis paper implements the deterministic volatility function (DVF) in the context of the truncated Black‐Scholes (TBS) model, which is identified as the truncated practitioners' Black‐Scholes (PTBS) model, and compares the pricing and hedging performance with the Black‐Scholes (BS), TBS, practitioners' BS (PBS) models. Using the S&P500 index call options data, we find that the PTBS model outperforms all in‐sample and out‐of‐sample regardless of moneyness. On weekly counts, the success rates of the PTBS model are significantly higher for both the in‐the‐money (ITM) and out‐of‐the‐money (OTM) options. The weekly approximation errors of delta and delta‐gamma approximations against full valuation for the PTBS model are lower than those of other models, and the PTBS model is more accurate and stable. The findings are robust to alternative sample variations.\n"]