Binomial option pricing model. Comparing prices

A pricing model would yield an inaccurate answer if you used an incorrect input (volatility, time remaining, stock and strike price, carry cost, and dividend if any).

The most likely culprit for the disparity is your volatility input. It's a historical value and the current volatility estimate is the implied volatility which is derived from actual market price.

Consider double checking some other calls on your trading site to see if your valuation is consistently different across the board. Then adjust your volatility input to see if they align, give or take.

Plan B? Any decent broker (and many web sites) will provide the implied volatility for options.