Callable and Putable bond: market price & OAS

• An interest rate lattice is constructed to be arbitrage-free.
• However, when an analyst calculates the price of the callable and putable bond (call & put price = 100) using the interest rates in the lattice, the analyst gets a value higher than the market price of the bond.
• The embedded options will be exercised if the option has value(i.e., in-the-money).

The price of the callable and putable bond is likely:

Callable and putable bond

		Market price	OAS
A.		< 100%	Zero
B.		= 100%	Positive
C.		> 100%	Negative

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Answer: B

Market price:
In this case, the bond is callable and putable at the same price(100). Since the embedded options (the issuer's call option and the holder's put option) will be exercised if the option has value (i.e., is in-the-money), the value (=market price, in an ideal world) of the bond must be 100 (plus the interest) at all times.

If rates fall and the computed value goes above 100, the company will call the issue at 100.
Conversely, if rates increase and the computed value goes below 100, the bondholder will "put" the bond back to the issuer for 100.


OAS:
The OAS is a constant spread added to every interest rate in the tree so that the model price of the bond is equal to the market price of the bond. In this case, using the interest rate lattice, the model price of the callable and putable bond is greater than the market price. Hence, a positive spread must be added to every interest rate in the lattice. When a constant spread is added to all the rates such that the model price is equal to the market price, you have found the OAS. The OAS will be positive for the callablle and putable bond.