A Skellam market model for loan prime rate options

This paper documents vanilla interest‐rate options newly introduced in China. The underlying rates are the RMB loan prime rates (LPRs), the foremost interest rates that matter to almost all businesses and households in China. They are digital with a tick size of five basis points, and the changes only occur monthly at predetermined announcement times. We propose a novel continuous‐time discrete‐state market model based on the integer‐valued Skellam distribution, and derive arbitrage‐free pricing formulas in closed forms. We advocate that it is more meaningful to quote LPR option prices in terms of implied intensity rather than implied volatility.