Market Probability of Interest Rate Tick Movements

Abstract

This paper introduces an analytically tractable model for modelling interest-rate tick movements and pricing interest-rate options in closed forms. We derive all higher-order moments analytically, and also equivalent martingale measures and their unique optimal measure in an incomplete market. It is applied to options on loan prime rates (LPR), the foremost benchmark interest rates that matter to almost all businesses and households in China. Empirically, by reverse engineering, our new option-pricing model is flexible enough to extract the market's forward-looking information from option prices, and reveals the evolution of market's views on future interest rate movements with tick effect.

Keywords: Policy rate, China's markets, Loan prime rate (LPR), Loan prime rate option, Delta negative binomial models, Delta negative binomial (DNB) distribution, Risk-neutral probability mass distribution, Incomplete market, Optimal martingale measure, Minimal entropy measure, Convexity adjustment

JEL Classification: G13, G12, E43, C51, C58