The prices which IB uses to mark U.S. listed securities options as of the close of business each day (both TWS and statements) originate from the Options Clearing Corporation (OCC). As the sole clearinghouse for these option products, OCC generates a closing price for each option contract in order to calculate the margin required of its members on whose behalf it clears transactions (e.g., IB) and also to supply the risk arrays used by brokers carrying portfolio margin accounts.
Its important to note that the prices generated by OCC are edited and therefore may not reflect the closing price as disseminated by any of its participant exchanges. They are edited primarily due to the fact that there is no consolidated quote provided for options, most of which are multiply listed and fungible across all seven exchanges (i.e., there may be seven different prices to choose from each day). As a result, OCC creates a single price as of the close which is theoretically consistent across all exchanges and reviewed to ensure that there are no arbitrage conditions across strikes or time.
In creating prices, OCC will start by taking the mid-point of the highest bid and lowest ask price across all listing exchanges, determining the implied volatility and then smoothing that implied volatility curve (for a given option class, type and expiration) through an iterative process which, in turn, adjusts the option mark prices. There are also rules enforced to cap volatility for certain deep in and deep out-of-the-money options. The resultant edited price is extended out to six decimal places. Due to the operational overhead of computing edited prices for the complete universe of option series, this process is performed only once per day as of the market close.