How do I value a putable bond and why is it worth more than a straight bond?

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AcadiFi · Accepted Answer

A putable bond gives the holder the right to sell the bond back to the issuer at a specified price, usually par. This is valuable to the holder because it provides downside protection if rates rise (bond price would fall below par, but the holder can still put at 100). Therefore V_putable = V_straight + V_put_option. Valuation via backward induction mirrors the callable procedure but with floor rather than cap. Steps: (1) At year 4 every node pays 103.60. (2) Work backward computing V_t = [0.5*(V_up + C) + 0.5*(V_down + C)] / (1 + r_t). (3) At putable nodes (year 2 and year 3), apply the put rule: if computed value is below the put price (100), floor it at 100 — the holder will put. If computed value is above 100, hold. Example: at a year-3 node with rate 5.8%, if V_up at year 4 is 103.60 and V_down is 103.60, backward value = [0.5*103.60 + 0.5*103.60] / 1.058 = 97.92. This is below 100, so the holder puts and the node value becomes 100. A callable bond at the same node would not change because the issuer would not call when value is below par. (4) Continue to year 0. The put option is more valuable when rates are expected to rise and volatility is high, because more future paths will cross below par. A straight 4-year 3.6% bond at a 4.2% flat yield might price at 97.85; add 1.40 for the put option and you get V_putable = 99.25. The exact amount depends on volatility and rate tree calibration. Key intuition: putable protects the holder; callable protects the issuer.

How do I value a putable bond and why is it worth more than a straight bond?

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