Market Probability of Interest Rate Tick Movements

Abstract

This paper introduces a highly analytically tractable parametric model for modelling interest-rate tick movements and arbitrage-free pricing interest-rate options. We apply it to loan prime rates (LPR), the foremost benchmark interest rates that matter to almost all businesses and households in China, and evaluate the associated vanilla options in closed forms. We derive all higher-order moments analytically, and obtain equivalent martingale measures and their unique optimal measure for option pricing in an incomplete market. By reverse engineering, our new option-pricing model is flexible enough to extract the forward-looking information embedded in the market, and reveals the evolution of market's views on future interest rate movements with tick effect. Empirically, a simple index for measuring the consensus of market's views is constructed, and the time series of risk-neutral probability mass distributions and moments of future interest-rate tick movements are implied from market option prices. They are found to be time-varying, highly fluctuated and largely shaped by macroeconomic announcements even when there was no any change in the underlying interest rate.

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

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