Bond Price Calculator
Estimate a bond's theoretical clean price by discounting its coupon payments and face value at a given yield.
輸入資料
計算結果
重點速覽：Bond price is the present value of a bond's future coupon payments plus its face value at maturity, discounted at the market yield. Formula: price = sum(coupon per period / (1 + r)^t) + face value / (1 + r)^n, where r = annual yield / frequency and n = years x frequency. Example: face value HK$100, coupon 5%, 10 years, annual, at a 4% yield gives about HK$108.18. WARNING: This is the clean price (excluding accrued interest); the actual traded dirty price = clean price + accrued interest. The model assumes a single flat yield and ignores credit risk, call features and reinvestment risk.
計算公式
每期票息 = 面值 × 票面利率 ÷ 每年派息次數。
每期殖利率 r = 年殖利率 ÷ 每年派息次數；總期數 n = 年期 × 每年派息次數。
價格 = 每期票息 × [1 − (1 + r)^−n] ÷ r + 面值 ÷ (1 + r)^n。
$$P = C \times \dfrac{1 - (1 + r)^{-n}}{r} + \dfrac{F}{(1 + r)^{n}}$$$$r = \dfrac{\text{年殖利率}}{m}, \quad n = \text{年期} \times m, \quad C = \dfrac{F \times \text{票面利率}}{m}$$使用說明
- Enter the face value, coupon rate, market yield, years to maturity and coupon frequency.
- View the estimated clean price, coupon per period and total periods.
- To estimate the actual settlement amount, add accrued interest based on the trade date.
面值 HK$1,000、票面利率 5%、10 年期、半年付時，不同市場殖利率對應的債券價格
| 市場殖利率 | 債券價格 | 相對面值 | 狀態 |
|---|---|---|---|
| 4% | HK$1,081.76 | 高於面值 | 溢價 (殖利率 < 票面) |
| 5% | HK$1,000.00 | 等於面值 | 平價 (殖利率 = 票面) |
| 6% | HK$925.61 | 低於面值 | 折價 (殖利率 > 票面) |
| 7% | HK$857.88 | 更低 | 折價擴大 |
| 8% | HK$796.15 | 最低 | 殖利率越高、價格越低 |
理財情境案例
案例一：殖利率高於票面，債券折價
一張面值 HK$1,000、票面利率 5%、每年半年付 (每期票息 HK$25) 的 10 年期債券，市場要求殖利率 6%。每期殖利率 = 6% ÷ 2 = 3%，總期數 = 10 × 2 = 20 期。
代入折現公式：價格 = 25 × [1 − 1.03⁻²⁰] ÷ 0.03 + 1,000 ÷ 1.03²⁰ ≈ HK$925.61，低於面值 HK$1,000。
結論：因為市場殖利率 (6%) 高於票面利率 (5%)，票息相對市場偏低，須靠折價 (低於面值) 交易來補償買家，使實際收益率追上市場水平。
案例二：利率下跌，債券由折價轉溢價
同一張債券，若市場殖利率由 6% 回落到 4%，價格會由 HK$925.61 升到 HK$1,081.76 — 因為它 5% 的票息比市場新發債券 (只派 4%) 更優厚，買家願意多付一點搶購，形成溢價。
反之，若殖利率升到 8%，價格會再跌到 HK$796.15。利率每變動，價格就沿反方向調整。
結論：既有債券的資本利得/損失，主要由市場利率的升降驅動。持有中長期債券者要留意利率風險 — 加息時帳面價格下跌，減息時上升。
常見問題
Is this the clean price or the dirty price?
The calculator gives the clean price — the theoretical price excluding accrued interest, as if on a coupon date. In the market you usually pay the dirty price = clean price + accrued interest, because the seller has accrued part of the next coupon. Accrued interest = coupon per period x days held / days in the coupon period.
Does a higher coupon frequency change the price?
With the same coupon, face value, yield and term, a higher frequency changes the price only slightly, because you receive coupons earlier and can reinvest. The difference is usually small; the dominant driver is the yield relative to the coupon rate.
Are longer bonds more sensitive to rate changes?
Yes. Longer maturities have more of their cash flows (especially the face value) far in the future, so they are more sensitive to yield changes — a 1% rise in yield drops a long bond's price much more than a short bond's. Duration quantifies this sensitivity.
相關工具
參考資料
內容審核：香港計算器財經團隊。計算邏輯與公式參考香港金融管理局（HKMA）及投資者及理財教育委員會（IFEC）之個人理財計算指引，結果僅供參考，實際以相關機構公佈為準。