How to evaluate the quality of the yield curve

I just partially agree... fitting reflects the real situation. If it is not true, what is the significance of fitting it out?

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North Star Company Mo Xiaokang Wu Haisheng

Quantitative analysis of financial securities is both a science and an art. Taking bond analysis as an example, the method for calculating certain indicators (such as yield upon expiration, durable period, and convex) is fixed. Only basic data can be provided to calculate the results. There is only one correct answer, and there is no subjective component.

However, just like playing chess, accurate computing is only a basic skill. The ability to defeat opponents depends on the experience, wisdom, and global judgment of the players. In financial analysis, in addition to the calculation of basic indicators, more in-depth analysis involves complex and subtle models (such as the yield curve model ). These models do not have only one correct answer like the calculation of basic indicators, but need to contain certain subjective judgments. That is to say, both the model creator and the user need to evaluate the model quality with their own experience, intuitive judgment on the data, and the knowledge of financial analysis.

The model builder needs to use a large amount of market data to test, test, and adjust the model to achieve more and more satisfactory results. Users of the model also need to use market data for similar tests and compare them with their own investment analysis experience, so as to have a good understanding of the accuracy, advantages and disadvantages of the model. Only through this process can we make full use of the practicality of the model.

This article describes several methods to measure the quality of the national debt yield curve model. Readers can use these methods to analyze and test the yield curve model (or other models) provided by the Alpha-bond analysis system.

1. Can we correctly reflect the basic changes in the short-term, medium-term, and long-term interest rates of the national debt market?

Reflecting the basic trend of short-term, medium-term, and long-term interest rates in the national debt market is the most basic function of the yield curve. Even if you do not use the Rate of Return curve for any calculation, you can view the chart and intuitively feel the rate change trend depicted by the rate of return curve.

Now there are 15-year government bonds on the market, and there will be longer-term government bonds in the future. In this way, the short, medium, and long-term interest rates are different and changing trends, and the performance will become more and more obvious.

When we look at the chart, we can first observe the trend of interest rate changes shown in the scatter chart of the maturity rate of each bond variety, and then compare it with the yield curve, check whether it correctly reflects the basic trend of the scatter chart: rising, falling, raised, concave and so on.

At present, the international and domestic interest rates are relatively low, so the yield curve will certainly show a relatively low short-term interest rate. However, if the market believes that the average interest rate in the next 15 years will be higher than the present, then the yield curve will certainly have an upward trend. If you think that the market is wrong about future interest rate trends, you will have a "time arbitrage" opportunity.

2. Can we take into account the smoothness of the curve and the accuracy of Bond Pricing?

The yield curve represents the overall interest rate level of the market. It should be able to filter the occasional fluctuations in market prices and reflect the real interest rate level. Therefore, curves need to be smooth enough, rather than showing excessive wave fluctuations, especially sudden fluctuations and turns. Otherwise, the model may not be ready.

The yield curve is calculated from the price data of all bond varieties (or a representative variety group) in the entire market. With the yield curve, you can price each bond type in turn. This pricing should be as close as possible to the actual market price. If smoothness is not considered at all, we can make all prices equal to the market price. However, this curve is meaningless.

A good model should be able to take into account smoothness and pricing accuracy. That is to say, the model pricing made with it is generally very close to the market price, and when there is some unexpected deviation in the market price, or the deviation caused by non-market factors, the model should be able to reflect this deviation, give users the necessary tips and even capture important arbitrage opportunities.

Grasping the relationship between smoothness and accurate pricing is the key to measuring the quality of the model. If it is too smooth, it cannot reflect the ups and downs of short, medium, and long-term interest rate changes. Over-precise pricing will cause too many fluctuations in the curve and the function of reflecting the overall situation will be lost.

3. What is the stability of the model?

Stability is a touchstone to measure whether the model is mature. Many inexperienced researchers simply use the formulas in textbooks to create models. when the results are calculated using actual data, unexpected problems may occur, and the results may be good or bad. If there is a small change in the data, there may be an undefinable big jump or a big tilt in the curve. But there seems to be no reason for this.

In fact, the problem lies in some technical aspects of modeling. Because textbooks mainly discuss principles, they generally do not involve too many in-depth technical links. To ensure model stability, you need a lot of experience and skills in analyzing and processing actual data. After a model is created, a large amount of data tests are required, including some data that greatly deviates from the normal range, to ensure the stability of the model. Even if there are some significant fluctuations in the market, the model can still give reasonable results.

4. Is it capable of processing incomplete data?

In mature financial markets, there are a wide variety of bonds, active transactions, and good liquidity. Therefore, the market data is rich, the performance is good, and the yield curve is easy to construct. There are relatively few varieties in the Chinese market, and many types of transactions are not active. In addition, some non-market factors often cause data point exceptions. From the perspective of modeling, it may cause special computing difficulties. Under the existing data conditions in the Chinese market, whether to overcome these difficulties and make a yield curve with good performance and practical value is a test of the modeler's technical level.

For the alpha-bond analysis system, you can intentionally select a period of time when transaction data is incomplete to test the system's ability to process incomplete data.

5. Relationship between the Curve Based on the spot interest rate and the scatter plot

Because the Rate of Return curve depicts the trend of spot interest rates, it should be different from the trend of the rate of return on expiration. When the interest rate is on the rise, the spot interest rate is higher than the rate of return on expiration. Therefore, we will see that the yield curve is higher than the scatter plot, not completely consistent with the scatter plot. The closer the end of a long term, the more obvious the difference. This is not because of the inaccuracy of the model, but a mark of the correctness of the model.

On some foreign product terminals, some yield curves do not reflect the above differences. The reason for this is that the system uses an approximate method such as "Expiration rate" instead of "spot rate. For the U.S. bond market, there are a large number of Strip products, which is equivalent to a long-lived zero-interest coupon. For zero-interest coupons, the rate of return on expiration is equal to the spot interest rate. Therefore, this method is feasible.

However, for the Chinese market, long-term products are provided with interest coupons, and the "yield upon expiration" and "spot interest rate" are obviously different. Of course, the curve made of "yield upon expiration" is an intuitive illustration and has reference value. However, this curve cannot be used for pricing analysis or other precise calculations. The rate of return curve model of foreign specialization generally does not adopt this approximate method.