A Skellam Market Model for Loan Prime Rate Options

Abstract

This paper documents vanilla interest-rate options (caps, floors and swaptions) 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 at predetermined monthly announcement times. Although the current literature on interest-rate options is vast, these unique stylised features bring a new challenge for interest-rate option pricing. We propose a novel continuous-time discrete-state market model built upon the integer-valued Skellam distribution, named Skellam market model. It is parsimonious and analytically tractable, which leads to arbitrage-free pricing formulas in closed forms. We advocate that it is more meaningful to quote the LPR option prices in terms of implied intensity rather than the conventional implied volatility. Our preliminary empirical work finds intensity frown implied from cap prices and intensity skew implied from swaption prices.

Keywords: Loan prime rate (LPR), Loan prime rate option, Skellam market model, Implied intensity, Intensity smile, Intensity frown, Intensity skew, Prescheduled macroeconomic announcements, China's markets

JEL Classification: G13, G12, C51, E43