固定收益证券第四章

a. Suppose that market interest rates decline by 100 basis
points (i.e., 1%). Contrast the effect of this decline on the price of each bond. b. Should Kerr prefer the Colina over the Sentinal bond when rates are expected to rise or to fall? c. What would be the effect, if any, of an increase in the volatility of interest rates on the prices of each bond?
• Conversely, if the coupon rate exceeds the market interest rate, the interest income by itself is greater than that available elsewhere in the market. • Investors will bid up the price of these bonds above their par values.
• 如果贴现率=息票率，债券是平价债券 • 如果贴现率>息票率，债券是折价债券 • 如果贴现率<息票率，债券是溢价债券
• a bond will sell at par value when its coupon rate equals the market interest rate. • No further capital gain is necessary to provide fair compensation.
a fixed-rate security ＝a floater ＋ an inverse floater
• 5.1 floater 的定价
• 5.2 inverse floater的构造 • 5.3 inverse floater的定价
6.收益率利差
• 6.1
n.spread y yT
1.3 贴现率的确定
2.债券价格和收益率的关系
• 债券价格和收益率(要求收益率)之间是反向变 动的关系 • 当收益率很高时,债券价格会非常低
• 如果收益率趋近0,债券价格等于未来现金流的 总和
Figure 14.3 The Inverse Relationship Between Bond Prices and Yields
Prices over Time of 30-Year Maturity, 6.5% Coupon Bonds
Figure 14.7 The Price of a 30-Year Zero-Coupon Bond over Time at a Yield to Maturity of 10%
4.无套利定价法
Table 14.2 Bond Prices at Different Interest Rates (8% Coupon Bond, Coupons Paid Semiannually)
Figure 14.4 Bond Prices: Callable and Straight Debt
3.债券的时间价值
Ct P t 1 yt t 1
• 债券的价格等于其未来每个现金流用其对应的即期利 率贴现的现值和。否则，市场存在套利机会。
T
Βιβλιοθήκη Baidu
•
5.浮动利率债券和反向浮动利率债券 的定价
• While firms do not commonly issue inverse floaters, they may be created synthetically by allocating the cash flows from a fixed-rate security into two derivative securities.
Ct P t 1 y Spread t 1 T
T
对应国债收益率曲线上某一点的spread 包含对信用风险、期权风险、流动性风险的补偿 缺点：
没有考虑对含权债券，其未来现金流会因利率波动而改变
• 6.2
• 如果债券持有到期，投资者在整个国债即期利率曲 线上实现的spread. • 债券价格等于其未来现金流使用国债即期利率 +spread贴现的现值 • 包含对信用风险、流动性风险和期权风险的补偿
T
Price: 10-yr, 8% Coupon, Face = $1,000
P 40
t 1 20
1
1.03
t

1000 (1.03)
20
P $1,148.77
C F T y = 40 (SA) = 1000 = 20 periods = 3% (SA)
1.2 预测债券现金流存在困难：
• 6.3
• 适用于含权债券
• 含赎回权的债券有更高的 • 含回售权的债权有更低的 • OAS是债券如果不含权时的 风险补偿。
和 和 ，不包含期权
1. On May 30, 2006, Janice Kerr is considering one of the newly issued 10-year AAA corporate bonds shown in the following exhibit. Description Coupon Price Callable Call Price Sentinal, due May 30, 2016 6.00% 100 Noncallable NA Colina, due May 30, 2016 6.20% 100 Currently callable 102
第4讲 债券的定价
• • • • • • 1 .到期收益率定价法 2 .债券价格和收益率的关系 3 .债券的时间价值 4.无套利定价方法 5.浮动利率债券和反向浮动利率债券的定价 6.收益率利差
1.到期收益率贴现定价法
1.1债券定价的步骤
债券价格＝利息现金流的现值＋本金现金流的现值
Ct P t 1 y t 1
• When the coupon rate is lower than the market interest rate, the coupon payments alone will not provide investors as high a return as they could earn elsewhere in the market. • The bonds, therefore, would have to sell below par value to provide a “built-in” capital gain on the investment.
Ct P t 1 yTt z.spread t 1
T
z.spread yt yTt
两种利差的比较：
• • • • • 当基准收益率曲线水平时，二者相等。 当基准收益率曲线上斜时， > 当基准收益率曲线下斜时， < 基准收益率曲线越陡峭，二者差异越大 债券的本金支付越早，二者的差异越大