# Binomial Tree & OAS interpretation

Binomial Tree , OAS calculation & Market Value of Bond with embedded option. Step A.) When we calculate the price of callable bond using Binomial Tree, we adjust price at each node with lesser of calculated value at that node or call price. So price at V0 is the value of bond with embedded option. Step B) Now, when we calculate OAS - we add OAS spread to interest rate at each node so that “market value of Bond” is equal to our calculated value. 1. Why is the “market value of Bond with embedded option” not equal to value calcuated in Step A? I understand we adjusted CF at each node to account for embedded option. 2. Isn’t value calculated in Step B is the value of bond without option? Why a bond with embedded option has it’s market value equal to “option removed theoretical value”? AG

1. It is equal. Investors just prefer to talk about a bond being cheap or expensive in terms of a yield spread instead of dollar terms. So there is basically two different approaches to arrive at the same answer. 2. No. The OAS just removes option risk from the nominal spread. So the OAS is still positive. So you have to add this “nominal spread with the option cost removed” to each node to arrive at the price of the callable bond.