20110215FRM一级估值与&eacut

20110215FRM一级估值与&eacut

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1 上海金程国际金融专修学院 金程教育2011年FRM Part I基础班讲义 Valuation and Risk Models 讲师:程黄维 FRM 日期:2011年02月19~20日 地点:■上海□北京□深圳 100% Contribution Breeds Professionalism 100% Contribution Breeds Professionalism 2-125 125 ¾ Fixed Income Valuation 9 Bond Prices, Discount Factors, and Arbitrage 9 Bond Prices, Spot Rates, and Forward Rates 9 Yield to Maturity 9 One Factor Measures of Price Sensitivity ¾ Option Valuation 9 Binomial Trees 9 The Black-Scholes-Merton Model 9 The Greek Letters ¾ Value at Risk 9 Introduction to Value at Risk 9 VAR Methods 9 Forecasting Risk 9 Extending the VAR Approach to Operational Risk 9 Stress Testing ¾ Measuring Credit Risk 9 The Rating Agencies 9 External and Internal Ratings 9 Country Risk Models 9 Loan Portfolios and Expected Loss 9 Unexpected Loss Valuation and Risk Models-(30%) 100% Contribution Breeds Professionalism 3-125 125 Fixed Income Valuation 100% Contribution Breeds Professionalism 100% Contribution Breeds Professionalism 4-125 125 Bond Prices, Discount Factors, and Arbitrage ¾ Fundamentals of Bond Valuation Price Discount Rate Cash flow Principal () t t t1 cash flow 1 discount rate n P = = + coupon Spot Rates YTM
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100% Contribution Breeds Professionalism 5-125 125 Bond Prices, Discount Factors, and Arbitrage ¾ Price Quotations ¾ Bonds are quoted on a percentage basis relative to a par value (100). ¾ Treasury notes and bonds use a 32nds convention. A bond quoted as 97-6 (or 97:06 or 97.6) is interpreted as 97 6/32% of par value. ¾ Corporate and municipal bonds are quoted in eighths, e.g., 102 1/8 indicates the price of the bond is 102.125% of par. ¾ A + in the quote indicates a half tick. For example, if the price is quoted as 101-12+, then the bond would sell at 101+12.5/32. 100% Contribution Breeds Professionalism 100% Contribution Breeds Professionalism 6-125 125 Bond Prices, Discount Factors, and Arbitrage ¾ Discount Factors ¾ Discount factors are used to determine the present value. The discount function is expressed as d(t), where t denotes time in years. 0t y e a r s $1 d(t) Example: Calculating bond value using discount factors Suppose that the discount factor for the first 180-day coupon period is d(0.5)=0.92432, calculate the price of a bond that pays $108 six months from today. 100% Contribution Breeds Professionalism 7-125 125 Bond Prices, Discount Factors, and Arbitrage ¾ How to calculate discount factors for given bond prices Example: Calculating discount factors given bond prices Figure 1 shows selected T-bond prices for semiannual coupon $100 face value bonds. Figure 1: Selected Treasury Bond Prices 110-13+ 11/15/08 5.75% 5 120-30 5/15/08 12.00% 4 101-07 11/15/07 2.00% 3 105-31+ 5/15/07 7.25% 2 101-16 11/15/06 4.25% 1 price Maturity Coupon Bond Prices are from 5/14/06, with t+1 settlement 100% Contribution Breeds Professionalism 100% Contribution Breeds Professionalism 8-125 125 Bond Prices, Discount Factors, and Arbitrage ¾ How to identify arbitrage opportunities Example: Identifying arbitrage opportunities suppose you observe the annual coupon bonds shown in figure 2.
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20110215FRM一级估值与&eacut

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