經濟,財務,統計學,數理科學與政治評論

Heelo there:

  這裡專門談的是有Embedded options的債券評價!!

  幾個重要的名詞認知:Yield curve, Spot rate curve

 I. Spread Measures:

 (1) The nominal spread:用在Treasury yield corve上面,其spread為債券的到期殖利率扣除掉可比較相同到期期間Treasury benchmark債券.對Treasury yield rate curve來說,反應credit risk,option risk與liquidity risk.

 (2) The Zero-volatility spread(the Z-spread):用在Treasury spot rate curve,其spread為將Z-spread值加入每一個spot rate上面,以求取滿足目前市價的債券現值!!對Treasury spot rate curve來說,反應credit risk,option risk與liquidity risk.

 (3) The OAS(Option-Adjusted spread):其為Z-spread扣除option cost!!對Treasury spot rate curve來說,反應credit risk與liquidity risk

 II. 一般債券價值的算法,均配合每期不同的利率,用backward-induction來求算!!不論是Callable/Putable Bond,在backward induction的計算過程中,都會將其與Threshold value做比較,callable是當其市價超過threshold value時,發行人用threshold value將其債券買回;而putable是當其市價低於threshold value時,債券持有人用threshold value賣回債券給發行人!!

III.Convertible Bond

  conversion ratio:可轉換債券轉換成普通股的股數

  conversion price = 可轉換債券發行價格/conversion ratio

  conversion value = 普通股市價 * conversion ratio

  straight value

  = 可轉換債券不轉換成普通股時的市價

  = the present value of bond's cash flow discounted at the requred return on a comparable option-free bond

  a. the minimum value of convertible bond = Max(conversion value,straight value) 

  market conversion price = market price of convertible bond/conversion ratio

  b. market conversion premium per share = market conversion price - market price of common stock

  c. market conversion premium ratio = market conversion premium per share/market price of common stock

  favorable income difference per share

   = [coupon interest - conversion ratio * dividends per share]/conversion ratio

  d. premium payback period = market conversion premium pershare/favorable income difference per share

  e. premium over straight value = [market price of convertible bond/straight value] - 1