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Chinese Journal of Management Science ›› 2020, Vol. 28 ›› Issue (3): 132-141.doi: 10.16381/j.cnki.issn1003-207x.2020.03.014

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“Pricing of CMS Digital Range Notes” Based on Multi-factor LIBOR Model

WU Ping1, YUN Jun-chao2, DONG Bin2   

  1. 1. School of Business, Nanjing University of Information Science and Technology, Nanjing 210044, China;
    2. School of Economics and Management, Southeast University, Nanjing 211189, China
  • Received:2017-10-13 Revised:2018-03-22 Online:2020-03-20 Published:2020-04-08

Abstract: Nowadays, CMS derivatives have become a very important financial tool. It plays an essential role for investors to make profits and hedging risks. The pricing of CMS derivatives will also become more and more important as the demand increases. Due to the increase in usage, the use of the past hundreds of data to simulate the method is more and more cumbersome, and it will also consume a lot of time, is not conducive to the timeliness of the information. Calculating the analytical solution of CMS derivative pricing becomes an important issue.
In the past, pricing for CMS derivatives was mostly calculated using Monte Carlo simulations. Thousands of data have greatly reduced efficiency. Moreover, investors prefer closed-form formulas because they are more convenient to calculate and are more conducive to calculating hedging risk parameters (Delta, Gamma, Vega).
Using the multi-factor LIBOR market model as a framework to price CMS derivative products is a suitable method. It avoids the problem of insufficient one-factor model fitting, avoids the situation of big data simulation, and can solve the problem that CMS interest rates are not satisfied. The problem of normal distribution of numbers greatly simplifies the derivation process. In the later application, the model can be better promoted.
In the first chapter, the analytical formula of the CMS interest rate is derived through derivation, and incorporates the formula into the framework of the multi-factor LIBOR market model. The second chapter derives the analytical solution of the CMS digital range bond. This is also the focus and innovation of the paper. At the same time, in order to test the results, the model was tested in the third chapter.
The approximate formula of CMS interest rate is introduced gradually through the derivation of LIBOR market model, and the second-order variation method is used to obtain the approximate distribution of CMS interest rate and bring it into the subsequent model. The second-order variation method makes the pricing of the CMS interest rate closer to that of Monte Carlo, and the use of the LIBOR market model makes the simulation of the CMS interest rate not negative, making the CMS interest rate distribution more realistic. This provides good income expectations for investors investing or hedging. Solved the problem of effectiveness due to Monte Carlo data simulation. It solves the problem that the arithmetic mean of the lognormal distribution is not a lognormal distribution. At the same time, due to the introduction of the LIBOR market model, the negative swap rate is avoided.
CMS interest rate derivatives are products that are traded in the OTC market and there is no price to look up. Unlike actual stock data, it is traded through the counter, so there are very few actual commodity prices that can be queried, which makes the actual product. The simulation becomes difficult to carry out. The third chapter data inspection is mainly done by comparing with the results of the Monte Carlo simulation.
In practical applications, obtaining the analytical formula of the CMS interest rate is beneficial to the pricing of derivative products. The formula is in many ways similar to the BLACK classic pricing formula. The pricing of European bonds has a very good effect. Similarly, similar derivatives can be priced through the LIBOR market model to facilitate future research. The key is not to consider the big data simulation problem in the pricing process, avoiding a large amount of computing time, and providing investors with greater benefits.

Key words: LIBOR market model, CMS interest rate, CMS digital range notes

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