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Lecture_02

Lecture_02 - 2 The Classical Approach A Motivation The...

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1 2 The Classical Approach A Motivation The chapter studies the classical approach to pricing fixed income securities– yields, duration, modified duration and convexity. For the classical approach, pricing fixed income securities means just the pricing of coupon bearing bonds. This is due to the limitation of the tools and techniques involved. We present the classical approach in this book for two reasons.

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2 One, these tools are still in use by many fixed income traders today (although these tools are slowly being replaced by the techniques presented in subsequent chapters). Two, understanding the limitations of these classical techniques motivates the approach used in the subsequent chapters.
3 B Coupon Bonds United States government notes and bonds are coupon bearing. A coupon-bearing bond is a loan for a fixed amount of dollars (e.g. \$10,000), called the principal or face value. The loan extends for a fixed time period, called the life or maturity of the bond (usually 5, 10, 20 or 30 years). Over its life, the issuer is required to make periodic interest payments (usually semi-annually) on the loan’s principal. These interest payments are called coupons.

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4 A callable coupon bond is a coupon bond that can be repurchased by the issuer, at predetermined times and prices, prior to its maturity. This repurchase provision is labeled a “call” provision. Unfortunately, the techniques of the classical approach cannot be used to price callable coupon bonds. This is the first limitation of the classical approach.
5 Consider a time horizon of length T , divided into unit subintervals with dates 0, 1, 2, …, T-1, T . We define a coupon bond with principal L , coupons C , and maturity T to be a financial security that is entitled to a receive a sequence of future coupon payments of C dollars at times 1, …, T with a principal repayment of L at time T . The coupon rate on the bond is c = 1+C/L.

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6 Figure 2.1: Cash Flows to a Coupon Bond with Price B (0), Principal L, Coupons C and Maturity T time ||| || 012… T - 1 T B ( 0 ) CC… CC + L coupon rate c =1+ C/L
7 Let B (t) denote the price of this coupon bond at time t ( it is the bond's price ex-coupon ). A zero-coupon bond paying a dollar at time T is a special case of this definition, (C = 0 ) and (L = 1 ) .

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8 C The Bond’s Yield, Duration, Modified Duration and Convexity The bond's yield , Y(t)>0 , is defined as one plus the percentage internal rate of return on the bond, i.e., t T t Y L i t Y C t T i t + = = ) ( ) ( 1 ) ( B . (2 .1 ) This expression assumes that time t is a coupon payment date. As a convention in this book, for simplicity of notation and exposition, all rates will be denoted as one plus a percentage (these are sometimes called dollar returns).
9 EXAMPLE: COMPUTING A BOND’S YIELD Consider a coupon bond with maturity T = 10 years, a coupon of C = 5 dollars per year on a face value of L = 100 dollars.

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Lecture_02 - 2 The Classical Approach A Motivation The...

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