关键词: 晶格场理论, 不完全相关性, 动态规划, 国债期货定价

Abstract: The main purpose of this paper is to establish a more accurate pricing model for treasury bond futures. The difficulty in pricing treasury bond futures is how to build a more realistic forward rate model and price a series of embedded options based on the futures transaction delivery rules. However,the traditional Treasury bond futures prices are usually obtained by pricing the forward price and the quality option separately with different models, resulting to the model-error problem caused by the inconsistency of the pricing model.
In this paper, a more realistic field theory model of treasury forward rate is constructed by using the QFT (Quantum Field Theory) method in financial physics that can effectively incorporate the incomplete correlation between calendar time and expiration time on treasury bond forward rates. Based on the optimal field theory model of forward interest rate constructed, a theoretical lattice field model of the forward interest rate is obtained by discretizing the two-dimensional quantum field A(t,T). Then the dynamic programming method is utilized to model the transaction and trade rules to construct the pricing model of treasury bond futures and its embedded options within a unified framework.For example, if the rules of "a basket of deliverable bonds" was modified as "only the standard notes can be delivered", the optimal settlement price of Treasury bond futures without quality options can be obtained; By changing the terms of "the delivery date choices within the last delivery month" to "only the final delivery date be delivered", the optimal settlement price of the Treasury future without timing options can be found;Finally, the value of the quality option and timing option are got by subtractingthe optimal settlement price calculated by the original rule from the above two prices.
In the empirical study, based on the daily data of treasury forward rates with 115 maturities, from June 1, 2012 to May 31,2016, the QFT model constructed provides a goodness of fit of 95.16% to the actual treasury forward rate, which is better than the case that traditional mainstream two-factor HJM model's fitting accuracy of 66.85%. In addition,the pricing effect of the Treasury bond futures pricing model based on lattice field theory and dynamic programming are confirmed to be far superior to the mainstream two-factor HJM model commonly used in financial industry,employing the data with the 5-year treasury futures and 10-year treasury futures in 2017; The results show that Treasury bond futures pricing model constructed in this paper fits well with the settlement price of the real market; Its average pricing errors are all within 3%, and the values of quality option are about 2% to 6% of its corresponding treasury bond futures par value; The timing option value of all contracts is significantly less than the value of quality option and mostly hovers around 0, but both show a rapid upward trend before the close of the delivery date.
The research work done in this paper not only provides the pricing foundation and theoretical support for new Treasury futures products development and design, but also has some reference value for the interest-rate risk management.

Key words: latticefield theory, incomplete correlations, dynamic programming, treasury-bond futures pricing