Premium-Discount Formula and Other Bond Pricing Formulas
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1 Premium-Discount Formula and Other Bond Pricing Formulas 1 Premium-Discount Formula 2 Other Pricing Formulas for Bonds
2 Premium-Discount Formula and Other Bond Pricing Formulas 1 Premium-Discount Formula 2 Other Pricing Formulas for Bonds
3 The formula and selling at a premium Assignment: All the examples in section 6.2! The premium-discount pricing formula for bonds reads as P = C(g j)a n j + C where C is the redemption amount, g is the modified coupon rate, j is the effective yied rate per coupon period, and n is the number of coupons. If P > C, we say that the bond sells at a premium The value P C is called the premium or amount of premium for the bond, i.e., P C = C(g j)a n j So, the bond sells at a premium iff g > j
4 The formula and selling at a premium Assignment: All the examples in section 6.2! The premium-discount pricing formula for bonds reads as P = C(g j)a n j + C where C is the redemption amount, g is the modified coupon rate, j is the effective yied rate per coupon period, and n is the number of coupons. If P > C, we say that the bond sells at a premium The value P C is called the premium or amount of premium for the bond, i.e., P C = C(g j)a n j So, the bond sells at a premium iff g > j
5 The formula and selling at a premium Assignment: All the examples in section 6.2! The premium-discount pricing formula for bonds reads as P = C(g j)a n j + C where C is the redemption amount, g is the modified coupon rate, j is the effective yied rate per coupon period, and n is the number of coupons. If P > C, we say that the bond sells at a premium The value P C is called the premium or amount of premium for the bond, i.e., P C = C(g j)a n j So, the bond sells at a premium iff g > j
6 The formula and selling at a premium Assignment: All the examples in section 6.2! The premium-discount pricing formula for bonds reads as P = C(g j)a n j + C where C is the redemption amount, g is the modified coupon rate, j is the effective yied rate per coupon period, and n is the number of coupons. If P > C, we say that the bond sells at a premium The value P C is called the premium or amount of premium for the bond, i.e., P C = C(g j)a n j So, the bond sells at a premium iff g > j
7 Selling at a discount If P < C, we say that the bond sells at a discount Then, the value C P is called the discount or amount of discount on the bond and it equals C P = C(j g)a n j So, the bond sells at a discount iff g < j
8 Selling at a discount If P < C, we say that the bond sells at a discount Then, the value C P is called the discount or amount of discount on the bond and it equals C P = C(j g)a n j So, the bond sells at a discount iff g < j
9 Selling at a discount If P < C, we say that the bond sells at a discount Then, the value C P is called the discount or amount of discount on the bond and it equals C P = C(j g)a n j So, the bond sells at a discount iff g < j
10 Selling at a discount If P < C, we say that the bond sells at a discount Then, the value C P is called the discount or amount of discount on the bond and it equals C P = C(j g)a n j So, the bond sells at a discount iff g < j
11 An Example Find the price of a $1,000 par value 10-year bond with coupons at 8.4% convertible semiannually, which will be redeemed at $1,050. The bond is bought to yield 10% convertible semiannually. In this example, the parameters are: F = 1000 C = 1050 r = = g = = j = = 0.05 n = 20 K = = G = =
12 An Example Find the price of a $1,000 par value 10-year bond with coupons at 8.4% convertible semiannually, which will be redeemed at $1,050. The bond is bought to yield 10% convertible semiannually. In this example, the parameters are: F = 1000 C = 1050 r = = g = = j = = 0.05 n = 20 K = = G = =
13 An Example (cont d) Using the basic pricing formula, we get P = Fra n + K = a = = Using the premium-discount formula, we get P = C + (Fr Ci)a n = ( )a = ( 9.50) = Of course, the two prices are the same Assignment: Examples and 6.3.6
14 An Example (cont d) Using the basic pricing formula, we get P = Fra n + K = a = = Using the premium-discount formula, we get P = C + (Fr Ci)a n = ( )a = ( 9.50) = Of course, the two prices are the same Assignment: Examples and 6.3.6
15 An Example (cont d) Using the basic pricing formula, we get P = Fra n + K = a = = Using the premium-discount formula, we get P = C + (Fr Ci)a n = ( )a = ( 9.50) = Of course, the two prices are the same Assignment: Examples and 6.3.6
16 An Example (cont d) Using the basic pricing formula, we get P = Fra n + K = a = = Using the premium-discount formula, we get P = C + (Fr Ci)a n = ( )a = ( 9.50) = Of course, the two prices are the same Assignment: Examples and 6.3.6
17 Premium-Discount Formula and Other Bond Pricing Formulas 1 Premium-Discount Formula 2 Other Pricing Formulas for Bonds
18 The Base Amount Formula If we substitute the expression for the value of the annuity in the basic formula, we get P = G Gv n j + Cv n j = (C G)v n j + G where G denotes the base amount, v j is the discount factor per coupon period and n is the number of coupons The above formula is referred to as the base amount formula
19 The Base Amount Formula If we substitute the expression for the value of the annuity in the basic formula, we get P = G Gv n j + Cv n j = (C G)v n j + G where G denotes the base amount, v j is the discount factor per coupon period and n is the number of coupons The above formula is referred to as the base amount formula
20 An Example (cont d): Base amount formula Reconsidering the earlier example, we can reevaluate the price of the bond using the base amount formula as P = G + (C G)v n j = ( ) = = ( 1 )
21 Makeham s Formula If we do not know the number of coupons n, but we know the present value K of the redemption amount, we use Makeham s formula: P = K + g j (C K) where g stands for the coupon rate, j is the effective yield rate per coupon period, C is the redemption amount and K is the present value of the redemption amount
22 An Example (cont d): Makeham s formula If we look at our example again, using Makeham s formula, we obtain: P = K + g (C K) j = ( ) 0.05 =
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