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Derivatives10Lec5

# Derivatives10Lec5 - Duration and Convexity of Bonds and...

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Click to edit Master subtitle style 11.1 Duration and Convexity of Bonds and Options

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21.2 Where we are l Last Week: Swaps (Chapter 7, OFOD) l This Week: Duration and Convexity of Bonds and Options (Chapter 4, 8-9, OFOD) l Next Week: Black Sholes Formula and Option Valuation (Chapter 11, OFOD)
31.3 Duration l Bond Duration is the (value-weighted) average time to receipt of cash l Duration, D, of a bond that provides cash flow c i at time t i is with price and (continuously compounded ) yield y l Since a small change in yield, , leads to a change in price as and l So and l The percentage change in price is negatively related to a change in yield. = - = B e c t D i yt i n i i 1 y D B B - = y y dy dB B = = - - = n i yt i i i e t c dy dB 1 = - - = n i yt i i i e t c y B 1

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41.4 Duration Continued l When the yield y is expressed with compounding m times per year l The expression defines D* and it is referred to as Modified Duration l Duration measures are important for risk management l Which exhibits the well known characteristic for bonds that yield and price move in opposite direction l Note that for continuous compounding, duration doesn’t have to be “modified”. m y D D + = 1 * y m y D B m y y BD B + - = + - = / 1 1
51.5 Convexity l The convexity of a bond is defined as l A useful result to show the limitation of duration hedging as yield changes become larger – the effect of the non- linearity of the price-yield relationship 2 1 2 2 2 ) ( 2 1 that so 1 y C y D B B B e t c y B B C n i yt i i i + - = = = = -

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61.6 Swap contracts are agreements between two parties to exchange a series of assets or cash flows at specified future dates. In particular, an interest rate swap is a contract to exchange interest payments on a given amount of “notional” principal at specified future dates. The most common type of (plain vanilla) interest rate swap is where one party pays floating rate interest payments (usually equal to six-month LIBOR) in exchange for the other party paying fixed rate interest payments. These swaps are sold by dealers in large banks to FIs and other corporations that seek to hedge interest rate risk. Interest Rate Swaps
71.7 Example: A bank’s depositors usually prefer short maturities that can be readily liquidated. Its borrowing customers may prefer longer maturity loans at fixed-interest rates because the loans finance longer maturity projects and borrowers wish to know their exact fixed-interest borrowing costs. If a bank satisfies both its borrowing and depositor customers, its longer duration loans financed by shorter duration deposits exposes the bank to interest rate risk. Consider a bank that makes a \$1 million, five-year loan at a fixed 8 % interest rate, where the borrower is required to make semi-annual payments of ½(.08)(\$1 m) = \$40,000 and repay the \$1 m principal at maturity. The bank finances this loan by issuing \$1 m of six-month maturity CDs.

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81.8 These transactions expose the bank to interest rate risk. If
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Derivatives10Lec5 - Duration and Convexity of Bonds and...

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