Introduction

Understanding how to hedge an option position is crucial for managing risk in fixed income portfolios. In this chapter, we’ll explore the concept of using the DV01 (Dollar Value of 01) to calculate the face amount of bonds required to hedge an option position effectively. This technique allows investors to offset the price risk associated with options, ensuring a more stable portfolio in changing interest rate environments.

Hedging with DV01

When you hold an option position, your portfolio is exposed to changes in interest rates, which can impact the value of your options. To protect against this risk, you can use bonds to offset the price movements of your options. The key to this hedging strategy is understanding the DV01, which represents the change in the value of a bond for a 1-basis point (0.01%) change in yield.

Calculating the Face Amount

To calculate the face amount of bonds required to hedge an option position, follow these steps:

1) Determine DV01: Start by calculating the DV01 for your option position. This is done by multiplying the option’s duration (measured in years) by the option’s notional amount.

• Formula: $DV01 = \text{Option Duration} \times \text{Option Notional}$

For example, if you have an interest rate option with a duration of 0.05 years and a notional amount of USD 1,000,000, the DV01 would be: (0.05 $\times$ USD 1,000,000) = USD 50,000.

2) Identify Bonds for Hedging: Choose suitable bonds for hedging. These bonds should have a DV01 that matches the DV01 of your options as closely as possible. You can use government bonds, corporate bonds, or other fixed income securities with similar characteristics.

3) Calculate Face Amount: Calculate the face amount of bonds required for hedging by dividing the DV01 of your options by the DV01 of the selected bonds.

• Formula: $\text{Face Amount of Bonds} = \left(\frac{\text{Option DV01}}{\text{Bond DV01}}\right) \times \text{Option Notional}$

For instance, if the DV01 of your options is USD 50,000, and you select a bond with a DV01 of USD 10,000, you would need $\left(\frac{\text{USD 50,000}}{\text{USD 10,000}}\right) \times \text {USD 1,000,000}= \text{USD 5,000,000}$ face amount of the selected bonds to hedge your option position.

Example: Let’s say you hold interest rate call options with a DV01 of USD 40,000 and total worth of USD 1,000,000. You decide to hedge this position with 10-year government bonds, which have a DV01 of USD 8,000. To calculate the face amount of bonds needed:

$$\text{Face Amount of Bonds} = \left(\frac{\text{USD 40,000}}{\text{USD 8,000}}\right) \times \text{1,000,000} = \text{USD 5,000,000}$$

Therefore, you would need USD 5,000,000 worth of 10-year government bonds to hedge your call option position effectively.