OAS for putable bond

Volatility used in generating the interest rate tree is less than the true volatility, which of the following most accurately describes the impact on the value of bond B (with embedded with put option) and the estimated OAS of the bond

anwser: Value of bond is underestimated and estimated OAS of bond is too low

I dont know why estimated OAS of bond is too low :frowning: can you help

When interest rate volatility is high, putable bonds have higher OAS compare to comparable callable bonds. Thus, when the volatility is too low in a interest rate tree, it underestimates putable bonds and OAS for putable bond is too low.

Think of OAS as attractiveness of a bond , the higher the OAS, the more attractive the bond.

The first part of the answer is stupid; you’re using the market price of the bond to estimate OAS, so the value of the bond is estimated exactly right.

The second part is explained thus:

  • Lower volatility (in the tree) means lower high interest rates and higher low interest rates
  • Lower high interest rates means higher high bond prices
  • Higher bond prices means it’s less likely that the bond will be put
  • When the bond is put, cash flows are higher, so when it’s less likely that the bond will be put, the average cash flow will be lower
  • Lower average cash flows means lower discount rates to get to the same (i.e., today’s market) price
  • Lower discount rates means lower OAS

Can I use the formulas: z spread = OAS - put premium spread to explain?

I dont know which induction is wrong

Low volatility => Value put option underestimate => Put premium spread overestimate

z spread constant => OAS overestimate (too high)