Monte Carlo Valuation of a Callable Zero-Coupon Bond

Summary

The document describes a proposed Monte Carlo approach to valuing the termination option embedded in a zero-coupon bond. The setup is a 20-year bond callable after ten years, with a stated zero rate and Z-spread. The author proposes estimating the future borrowing rate from the forward rate plus the spread, modeling future rates as lognormally distributed, simulating outcomes, valuing the option against the contractual repayment amount, and discounting the average payoff.

It gives no valuation results or worked calculation; instead, it asks whether the procedure is correct and why its prices differ from Bloomberg. The proposal raises relevant issues in callable-bond valuation, including how to model rates and credit spreads and how to value and discount exercise payoffs. However, it does not specify a term-structure model, exercise decision rule, calibration inputs, or whether the spread should be treated as constant. Those omissions prevent a conclusion about the method or a reliable comparison with market prices.

Key ideas

• A callable zero-coupon bond embeds an option for the issuer to terminate the debt at the call date.
• The proposed approach simulates future borrowing rates and values the option from the simulated payoff at termination.
• The proposed rate model combines a forward rate with the bond’s Z-spread.
• The document does not establish that the simulation or discounting method is correct, and supplies no market-price comparison details.

Tags

# Pricing a zero coupon callable bond


# Pricing a zero coupon callable bond












Suppose I have a 20-year zero bond with a call date in 10 years and a zero interest rate of 2%, which is currently valued at a Z-spread of 100. Now I would like to evaluate the right of termination and proceed as follows: I calculate the forward interest rate in 10 years, add the Z spread and get the appropriate interest rate at which the debtor could borrow money again at the time of termination. I assume that the interest rate in the future will be logarithmically normally distributed and simulate the 10 annual interest rate with an assumed volatility. I calculate the value of the option from the realizations of the simulation and the agreed repayment rate. After drawing 1000 random numbers, I determine the average and discount it with today's 10-year interest rate plus the Z spread. I take this value as the option value. Is this procedure correct? Unfortunately, I can never get the prices from Bloomberg.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.