Bond Future Option
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Bond Future Option Valuation
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A bond future option is an option contract that gives the holder the right but not the
obligation to buy or sell a bond future at a predetermined price.
| 1. Bond Future Option Introduction |
The writer/seller receives a premium from the buyer for undertaking this obligation.
Options are leveraged instruments that allow the owner to control a large amount of the
underlying asset with a smaller amount of money. Bond future options offer significant advantages for reducing costs,
enhancing returns and managing risk. They could be European style or
American style.
Bond futures options are also exchange traded derivatives on treasury instruments. They provide market participants
with the ability to adjust their interest rate exposures. A bond future option is also a good tool for hedging, income
enhancement, duration adjustments, interest rate speculation and spread trading. There are established global markets
for bond futures and future options so they are very liquid. Investors use bond future
options to hedge an existing bond portfolio against adverse interest rate movements or
enhance the long-term performance of a portfolio of assets. Arbitrageurs profit from the price difference between the
spot bonds and the bond futures. Speculators use bond future
option in the hope of making a profit on short-term movements in prices. This presentation provides an overview of
bond future option product and valuation.
| 2. Bond Future Option Valuation: European Style |
The present value of a call bond future option is represented as:
The present value of a put bond future option is represented as:
| 3. Bond Future Option Valuation: American Style |
We use the Cox-Ross-Rubinstein (CRR) binomial tree to price American bond future option.
Build forward bond price tree.
After constructing the tree, valuation is performed backward until the valuation. The option value at node 0 is the present value of the bond future option.
Practical Notes
- First compute the CTD forward bond price first.
- Then determine the volatility of the forward bond price.
- After that, call Black formula for pricing European bond future options.
- Or build binomial tree to value American bond future options.
| 4. Related Topics |
| 4.1. Fixed Rate Bond |
A fixed rate bond pays coupons at a fixed rate over the bond life. An investor who wants to earn a guaranteed interest rate for a specified term can choose fixed rate bonds. Due to the fixed coupon, the market value of a fixed rate bond is susceptible to fluctuation in interest rate and therefore has a significant interest rate risk.
The present value of a fixed rate bond can be expressed as
You can find more details at Bond Calculator
| 4.2. Bond Future |
A bond future is a future contract in which the asset for delivery is a government bond. Any government bonds that meet the maturity specification of a future contract are eligible for delivery. All eligible delivery bonds construct the delivery basket where each bond has its own conversion factor.
The present value of a bond future contract is given by
| References |