session 3b (new font).pptx - SMU Classification Restricted Spot Rates Curve FNCE 6043 Oct – Dec 2019 Joe Zhang SMU Classification Restricted Outline

# session 3b (new font).pptx - SMU Classification Restricted...

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FNCE 6043 Oct – Dec , 2019 Joe Zhang SMU Classification: Restricted Spot Rates Curve 1

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FNCE 6043 Oct – Dec , 2019 Joe Zhang SMU Classification: Restricted Outline Spot rates and spot rate curve Constructing theoretical spot rate curve Bond pricing using spot rate curve Forward rates and using forward rates as hedgable rates Relation between spot rates and forward rates Swap rate curve Yield spreads Theories of the term structure of interest rates 2
FNCE 6043 Oct – Dec , 2019 Joe Zhang SMU Classification: Restricted Pricing Bonds with Spot Rates Previously, we use the market discount rate to price bonds. The same discount rate is used for each cash flow. A more fundamental approach to calculate the bond price is to sue a sequence of market discount rates that correspond to the cash flow dates. These market discount rates are called spot rates. Spot rates are yields-to-maturities on zero-coupon bonds maturing at the date of each cash flow. A general formula for calculating a bond price given the spot rates: where Z X = spot rate, or the zero-coupon yield, or zero rate, for period X 3 ?? = ??? ( 1 + ? 1 ) + ??? ( 1 + ? 2 ) 2 + + ??? + ?? ( 1 + ? ? ) ?

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FNCE 6043 Oct – Dec , 2019 Joe Zhang SMU Classification: Restricted Pricing Bonds with Spot Rates An example: suppose that the one-year spot rate is 2%, the two-year sport rate is 3%, and the three-year spot rate is 4%. What is the price of a three-year bond that makes a 5% annual coupon payment? What is the yield to maturity? 4
FNCE 6043 Oct – Dec , 2019 Joe Zhang SMU Classification: Restricted The Yield Curve The yield curve gives the yield (rate of return) on fixed income securities as a function of their time to maturity It is also known as the "term structure of interest rates." We will study how the yield curve is used for: Pricing securities and fixed income derivatives (options, futures and forwards) Looking for arbitrage opportunities Predicting market expectations of future interest rates The slope of the yield curve changes over time as economic conditions and expectations of future economic conditions change 5

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FNCE 6043 Oct – Dec , 2019 Joe Zhang SMU Classification: Restricted 6 Shape of Price-Yield Relationship for an Option-Free Bond Yield Maturity (a) Positive Inverted Maturity Yield (b) Humped Maturity (d) Flat Maturity (c) Yield Yield
FNCE 6043 Oct – Dec , 2019 Joe Zhang SMU Classification: Restricted The Yield Curve (cont.) There are many types of yield curves... ...when people refer to " The yield curve", they mean the yield curve for government securities, which is constructed using Treasury bill and Treasury bond price data, for two reasons: First, Treasury securities are free of default risk, and differences in credit worthiness do not affect yields.

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