# Calculating DV01 for Treasury Futures with CTD switch risk

## Introduction

When trading Treasury futures, it is important for traders to understand and manage the risks associated with changes in the cheapest-to-deliver (CTD) bond. One such risk is the CTD switch risk, which can impact the calculation of DV01. In this blog post, we will discuss how to calculate DV01 for Treasury futures with CTD switch risk.

## Understanding DV01

DV01, also known as dollar value of 01, is a measure of the change in the price of a bond or a bond portfolio for a 1 basis point (0.01%) change in yield. It is an important metric for fixed income traders and helps them quantify the interest rate risk associated with their positions.

## Calculating DV01

To calculate DV01 for Treasury futures, traders need to consider the notional value of the futures contract, the modified duration of the CTD bond, and the yield of the CTD bond.

The first step is to determine the notional value of the futures contract. This is the contract size multiplied by the current futures price. For example, if the contract size is $100,000 and the current futures price is 101.25, the notional value would be $101,250.

Next, traders need to calculate the modified duration of the CTD bond. Modified duration measures the sensitivity of the bond’s price to changes in yield. It takes into account the bond’s coupon rate, time to maturity, and yield to maturity. Traders can use bond pricing models or financial calculators to calculate the modified duration.

Finally, traders need to determine the yield of the CTD bond. This can be obtained from the bond market or through financial data providers.

Once the notional value, modified duration, and yield of the CTD bond are known, traders can calculate DV01 using the following formula:

DV01 = (notional value * modified duration) / 100

For example, if the notional value is $101,250 and the modified duration is 7.5, the DV01 would be:

DV01 = (101250 * 7.5) / 100 = $7,593.75

## CTD Switch Risk

CTD switch risk arises when the CTD bond changes during the life of the futures contract. This can happen due to changes in the yield curve or changes in the characteristics of the underlying bonds. When a CTD switch occurs, the DV01 calculation needs to be adjusted to reflect the new CTD bond.

To calculate DV01 with CTD switch risk, traders need to repeat the DV01 calculation using the new CTD bond’s notional value, modified duration, and yield. The adjusted DV01 can then be compared to the original DV01 to assess the impact of the CTD switch on the position’s interest rate risk.

## Conclusion

Calculating DV01 for Treasury futures is an important aspect of managing interest rate risk. Traders need to consider the notional value, modified duration, and yield of the CTD bond to accurately calculate DV01. Additionally, they should be aware of the CTD switch risk and adjust the DV01 calculation accordingly when a CTD switch occurs. By understanding and managing these risks, traders can make informed decisions and effectively manage their Treasury futures positions.

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