In this paper, we examine the price dynamics of on-line art auctions of modern Indian art using functional data analysis. The purpose here is not just to understand what determines the final prices of art objects, but also the price movement during the entire auction. We identify several factors, such as artist characteristics (established or emerging artist; prior sales history), art characteristics (size; painting medium--canvas or paper), competition characteristics (current number of bidders; current number of bids) and auction design characteristics (opening bid; position of the lot in the auction), that explain the dynamics of price movement in an on-line art auction. We find that the effects on price vary over the duration of the auction, with some of these effects being stronger at the beginning of the auction (such as the opening bid and historical prices realized). In some cases, the rate of change in prices (velocity) increases at the end of the auction (for canvas paintings and paintings by established artists). Our analysis suggests that the opening bid is positively related to on-line auction price levels of art at the beginning of the auction, but its effect declines toward the end of the auction. The order in which the lots appear in an art auction is negatively related to the current price level, with this relationship decreasing toward the end of the auction. This implies that lots that appear earlier have higher current prices during the early part of the auction, but that effect diminishes by the end of the auction. Established artists show a positive relationship with the price level at the beginning of the auction. Reputation or popularity of the artists and their investment potential as assessed by previous history of sales are positively related to the price levels at the beginning of the auction. The medium (canvas or paper) of the painting does not show any relationship with art auction price levels, but the size of the painting is negatively related to the current price during the early part of the auction. Important implications for auction design are drawn from the analysis.