强化金融市场与产品风险模型lzy

1、【】专业提供CFA FRM全程高清+讲义FRM一级培训讲义强化与估值与风险模型Henry LiangSenior FRM instructor, Golden Future【Framework】专业提供CFAFRM全程高清+讲义Ø Fixed-Income Productsl Bond Basicsl Bond Products Treasury Bondsl Bond Products Corporate Bondl Bond Products MBSl Valuation of Bondsl Risk Metricsl Rating Agencies2-279【Framework

2、】专业提供CFAFRM全程高清+讲义Ø DerivativesForward Market and Futures Market Forward and Futures Prices Interest Rate FuturesHedging Strategies using Futures Swap MarketProperties of Stock OptionsTrading Strategies involving Options Exotic OptionsOption ValuationRisk Metrics The Greek Lettersllllllllll3-27

3、9【Framework】专业提供CFAFRM全程高清+讲义Ø Central Counterpartiesl Introductionl Exchanges, OTC Derivatives, DPCs and SPVsl Basic Principles of Central Clearingl Risks Caused bys: Risks Faced bys4-279【Framework】专业提供CFAFRM全程高清+讲义Ø Risk Measurement and Managementl Measures of Final Riskl Putting VaR to

4、Workl Qufying Volatility in VaR Msl Expected and Unexpected Lossl Country Riskl Operational Riskl Stress Test5-279【Framework】专业提供CFAFRM全程高清+讲义Ø Fixed-Income Productsl Bond Products Treasury Bondsl Bond Products Corporate Bondl Bond Products MBSl Valuation of Bondsl Risk Metricsl Rating Agencies

5、6-279l Bond Basics【Bond Basics】专业提供CFA FRM全程高清+讲义ØRatel Treasury Ratesü The rates an investor earns on Treasury bills and Treasury bonds.ü Treasury rates are risk- rates in the sense that an investor whobuys a Treasury bill or Treasury bond is certain that interest andprincipal paymen

6、ts will bel LIBORas promised.ü A LIBOR quote by a particular bank is the rate of interest at which the bank is prepared to make a large wholesale deposit with other banks.l Repo Ratesü In a repurchase agreement, the difference between selling price (today) and the repurchased price (tomorr

7、ow or later) is called the repo rate.7-279【Bond Basics】专业提供CFA FRM全程高清+讲义Ø Compounding Frequenciesl Simple Interestl Compounding Interestü Suppose we have an where the simple interest is added ineach year and then that money also earns interest.ü AssuRc is the rate of interest with co

8、ntinuous compounding.Rmis the rate of interest with discrete compounding (m per annum)n is the number of years.8-279æRömnæRömnFV = PV ç1+ m ÷FV = PV ´ eRC ´nPV ´ eRcn = PV ç1+ m ÷èm øèm ø【Bond Basics】专业提供CFAFRM全程高清+讲义Ø B

9、ondsl Characteristics of Bondsü Coupon Rateü Face Valueü Maturityü Yield to Maturity (YTM)Ø Bond Pricing9-279åCtT+t=1 (1+ y)t【Exercises】专业提供CFA FRM全程高清+讲义Ø A bank uses a continuously-compounded annual interest rate of 5% inone of its risk ms. What is the equivalent

10、 interest rate the bank shoulduse if it converts to semi-annual compounding in the m?A.4.94%B.5%C.5.06%D.5.12%10-279【Framework】专业提供CFAFRM全程高清+讲义Ø Fixed-Income Productsl Bond Basicsl Bond Products Corporate Bondl Bond Products MBSl Valuation of Bondsl Risk Metricsl Rating Agencies11-279l Bond Pr

11、oducts Treasury Bonds【Treasury Bonds】专业提供CFA FRM全程高清+讲义Ø Treasury Marketl TreasuryBills:A short-termdebtobligationbackedbytheU.S.government with a maturity of less than one year.Example: Suppose you have a 180-day T-bill with a discount rate, or quoted price, of five (i.e., the annualized rate

12、of interest earned is 5%of face value). If face value is $100, the cash price is 97.5.l TreasurymaturityBonds:Fixed-interestU.S.governmentbondswithaofmorethan10years.Treasurybondsmakeinterestpayments semi-annually. Quoted Price: Dollars and thirty-seconds of adollar for a bond with a face value of $

13、10012-279cash price = 100 æ1- discount - rate ´nöç360 ÷èø【Treasury Bonds】专业提供CFA FRM全程高清+讲义Ø Quotation of Treasury Bondsl Accrued Interest and Day Count Conventionsü Treasury bonds: actual/ actualü Corporate and municipal bonds: 30/360ü Money ma

14、rket instruments (Treasury bills): actual/360l Clean Priceü The price of a coupon bond not including any accrued interest. Immediately following each coupon payment, the clean price will equal the dirty price.l Dirty Priceü A bond pricing quote referring to the price of a coupon bond that

15、includes the present value of all future cash flows, including interest accruing on the next coupon payment.13-279dirty price = clean price + accrued interest【Treasury Bonds】专业提供CFA FRM全程高清+讲义l ExampleSuppose a 1000 par value US corporate bond pays a semi-annual 10 percent coupon on January 1 and Ju

16、ly 1. Assume that it is now April 1,2005, and the bond matures on July 1, 2015. Computethe invoice(full) price of this bond if the required annualCompute the flat (clean) price of the above bond.yieldis8percent.14-279TimeFeb 1stMar 1stApr 1stMay 1stJune 1stJuly 1stdirty price1147.771155.301162.87117

17、0.501178.181185.90clean price1139.441138.631137.871137.171136.511135.90【Treasury Bonds】专业提供CFA FRM全程高清+讲义Ø Treasury Stripsl Separate Trading Registered Interest and Principal Securities$5+$100$5$53-year bond$5C-STRIPS 1$5C-STRIPS 2$5C-STRIPS 2$100P-STRIPS15-279【Framework】专业提供CFAFRM全程高清+讲义Ø

18、 Fixed-Income Productsl Bond Basicsl Bond Products Treasury Bondsl Bond Products MBSl Valuation of Bondsl Risk Metricsl Rating Agencies16-279l Bond Products Corporate Bond【Corporate Bond】专业提供CFA FRM全程高清+讲义Ø Role of Corporate Trusteel The corporate trustee is a third party to the contract. The t

19、rustee acts in a fiduciary (legal) capacity on behalf of the investors. Acting on behalf of the bondholders, the trustee must ensure that the bond issuer is in compliance with the covenants of the indenture at all times.Ø Different Coupon Paymentl Straight-coupon; Zero-coupon bonds; Floating-ra

20、te bondsØ Different Types of Corporate Bondsl Mortgage Bondsl Collateral Trust Bondsl Equipment Trustl Debenture Bondsl Guaranteed Bondss17-279【Corporate Bond】专业提供CFA FRM全程高清+讲义Ø Zero-Coupon Corporate Bondsl A zero-coupon bond eliminates reinvestment risk (shifting all of the risk to inter

21、est rate risk;) because there is no coupon to reinvest.l In bankruptcy, zero-coupon bond creditor claim original offering price plus accrued and unpaid interest, but not the principal amount of$1,000.l A zero-coupon bonds interest rate is determined by the original issue discount (OID). The differen

22、ce between the face amount and the offering price when first issued is called the original-issue discount.l Example:N = 20; I/Y = 5;PMT = 0; FV = 1,000, CPT PV = -377 OID = 1,000 377 = 623ü Face value $1,000ü 20-year zero-coupon bondü Yield 5%ü Compounded annually18-279【Corporate

23、 Bond】专业提供CFA FRM全程高清+讲义Ø Corporate Bond Retirementsl Frequently, bonds are retired early, before maturity. There are several mechanisms by which a corporation may go about retiring their debt.Included below are some of the most important retirement mechanismsü Call provisionü Sinking

24、-fund provisionsü Maintenance and replacement fundsü Tender offersØ Corporate Bond Credit Riskl Credit Default Riskandcommonlyusedl Credit-SpRiskl Issuer Default Rate vs. Dollar Default Ratel Recovery Rate19-279【Corporate Bond】专业提供CFA FRM全程高清+讲义Ø High-Yield Bondl High-yieldbondsa

25、rethoserated below investment gradebytheratings agencies, these issues are also known as junk bonds.Ø Types of High-Yield Bond Issuersl Original Issuersl Fallen Angelsl Restructurings and Leverage BuyoutsØ Payment Featuresl Deferred-Interest Bondsl Step-Up Bondsl Payment-in-Kind (PIK) Bond

26、s20-279【Corporate Bond】专业提供CFA FRM全程高清+讲义Ø The Spof a Bondl Themarket priceofanysecurity canbe thought ofasitsvaluecomputed using some term structure of interest rates plus a premiumor discount.c + F(1+ f (1) + s)(1+ f (2) + s)(1+ f (T) + s)c1+ f (1) + sc(1+ f (1) + s)(1+ f (2) + s)+ +P =+c + F

27、(1+ f (1) + s(1)(1+ f (2) + s(2)(1+ f (T) + s(T)c1+ f (1) + s(1)c(1+ f (1) + s(1)(1+ f (2) + s(2)+ +P =+21-279【Corporate Bond】专业提供CFA FRM全程高清+讲义Ø Callable and Puttable Bondl Withcallablebond,theupside price appreciation in response todecreasing yield is limited(sometimescalledpricecompression).

28、Consider the case of a bond that is currently callable at 102.PriceOption-Call Option ValueBond102Callable BondNegative ConvexityPositive ConvexityyYield22-279【Corporate Bond】专业提供CFA FRM全程高清+讲义l With puttable bond, the downside price appreciation in response to increasing yield is limited. It gives

29、the holder the right to sell the bondback to the issuer at a set price.Priced97yYield23-279Puttable BonOption ValueMore ConvexityOption-BondPut【Exercises】专业提供CFA FRM全程高清+讲义Ø A portfolio manager has recently purchased a 10-year investment-grade corporate bond. Which of the following tasks must t

30、ypically be performedby the corporate trustee listed in the bonds indenture?A.B.Act in a fiduciary capacity for the bond issuer. Ensure that the bond issuers reported fin requirements in the indenture.Change the terms of the indenture to providepurchaser.al ratios meet theC.for the bondD.Monitortheb

31、ondissuersbalancesheettoensurecovenantcompliance.24-279【Framework】专业提供CFAFRM全程高清+讲义Ø Fixed-Income Productsl Bond Basicsl Bond Products Treasury Bondsl Bond Products Corporate Bondl Valuation of Bondsl Risk Metricsl Rating Agencies25-279l Bond Products MBS【】专业提供CFA FRM全程高清+讲义MBSØ Mortgage L

32、oansl Almost exclusively on fixed rate residential mortgages.l Agency or conforloans are eligible to be securitized by such entities asFederalNationalMortgageAssociation(FNMA),FederalHomeLoanMortgageCorporation(FHLMS),orGovernmentNationalMortgageAssociation (GNMA). These Loans are relatively creditw

33、orthy.l Non-agency or non-conforsecuritizations.loans have to be part of private-labelThe relevant loan types include jumbos, which are larger in notional thanüconforloans but otherwise similar;üüAlt-A, which deviate from conforSubprime, which deviate from About 80% of subprime loans

34、aloans in one requirement.conforloans in several dimensions.justable-rate mortgages (ARMS)26-279【】专业提供CFA FRM全程高清+讲义MBSØ Fixed Rate Mortgage Paymentsl The mortgage loan is fair in the sense that the present value of the monthlymortgage payments, discounted at the monthly compounded mortgage rat

35、e,equals the original amount borrowed. In general, for a monthly payment X on aT-year mortgage withamortgagerateyandanoriginalprincipalamountorloan balance of B(0):27-279【】专业提供CFA FRM全程高清+讲义MBSl The fixed monthly payment is often divided into its interest and principal components, a division interes

36、ting in its own right as well as for tax purposes; mortgage interest payments are deductible from income tax while principal payments are not. Letting B(n) be the principal amount outstanding after the mortgage payment due on daten, the interest component on the payment on date n + 1 is:l In words,

37、the monthly interest payment over a particular period equals the mortgage rate times the principal outstanding at the beginning of that period. The principal component of the monthly payment is theremainder, that is:28-279【】专业提供CFA FRM全程高清+讲义MBSExample: A homeowner might borrow $100,000 from a bank

38、at 4% and agree to make payments of $477.42 every month for 30 years. The mortgage rate and themonthly payment are related by the following equation:1360$477.42ån=1= $100,000næö0.041+ç÷12èøIn the example, the original balance is $100,000. At theend of the first mon

39、th,interest at 4% is due on this balance, which comes to $100,000×0.04/12 or$333.33. The rest of the monthly payment, $477.42 - $333.33 or $144.08, is payment of principal. This $144.08 principal payment reduces the outstanding balance from the original $100,000 to $100,000 - $144.08 or $99,855

40、.92 at theend of the first month.29-279【】专业提供CFA FRM全程高清+讲义MBSl Discounting using the mortgage rate at origination, the present value of the remaining payments equals the principal outstanding. This is a fair pricing condition under the assumptions that the term structure is flat and that interest r

41、ates have not changed since the origination of the mortgage.Example: To illustrate this shortcut in this example, after 5 years or 60monthly payments there remain 300 payments.these payments at the mortgage rate of 4% isThepresentvalueof30-279【】专业提供CFA FRM全程高清+讲义MBSØ Prepayment Optionl Mortgage

42、 borrowers have a prepayment option, that is, the option topay the lender the outstanding principal at any time and be obligation to make further payments.d of thel The prepayment option is valuable when mortgage rates have fallen. In that case, the present value of the remaining monthly payments ex

43、ceeds the principal outstanding. Therefore, the borrower gains in present value from paying the principal outstanding in exchange for not having to make further payments.l Example: In the example of the previous subsection, the mortgage balance at the end of five years Is $ 90,448. At that time, the

44、refore, the borrower can pay the lender this balance and no longer have to makemonthly payments.31-279【】专业提供CFA FRM全程高清+讲义MBSl The single monthly mortality rate at month n, denoted SMMn, is the percentage of principal outstanding at the beginning of month n that is prepaid during month n. The SMM is

45、 often annualized to a constantprepayment rate or conditional prepayment rate (CPR). A pool that prepays at a constant rate equal to SMMn has 1 SMMn of theprincipal remaining at the end of one month, (1 SMMn)12 remaining atthe end of 12 months, and therefore 1 (1the SMMn)12annualizedprincipalprepayi

46、ngoverthose12months.Hence,CPRisrelated to SMM as follows:32-279【】专业提供CFA FRM全程高清+讲义MBSØ Mortgage-Backed Securities Marketl In the simplest structure, a mortgage pass-through, the cash flows from the underlying mortgages, that is, interest, scheduled principal, and prepayments, are passed from t

47、he borrowers to the investors with some short processing delay.l Mortgageservicersmanagetheflowofcashfromborrowerstoinvestors in exchange for a fee taken from those cash flows.l Mortgage guarantors guarantee investors the payment of interestand principalborrower defaults, also in exchange for a fee.

48、l The weighted-average coupon or WAC is the weighted average of the mortgage rates of the loans.l Weighted-average maturity (WAM)33-279【】专业提供CFA FRM全程高清+讲义MBSØ Agency mortgage pools trade in two forms: specified pools and TBAs (To Be Announced)l In the specified pools market, buyer and sellers

49、agree to trade a particular pool of loans. Consequently, the price of a trade reflects the characteristics of the particular pool.l Much more liquid, however, is the TBA market, which is a forwardmarket with a delivery option. The TBA seller will pick the cheapest-to-deliver pool, that is, the pool

50、that is worthissuer, maturity, and coupon requirements.theleastsubjecttothe34-279【】专业提供CFA FRM全程高清+讲义MBSØ Dollar Rollsl Consider an investor who has just purchased a mortgage pool but wants to finance that purchase over the next month. One alternative is an MBS repo. The investor could sell the

51、 repo, i.e., sell the pool todaywhile simultaneously agreeing to repurchase it after a month.l An alternative for finthe roll sells a TBA for ong mortgages is the dollar roll. The buyer ofttlement month and buys the same TBAfor the following settlement month. Two difference: 1) the buyer of the roll

52、 may not get back in the later month the same pool delivered in the earlier month. 2) the buyer of the roll does not receive any interest orprincipal payments from the pool over the roll.35-279【】专业提供CFA FRM全程高清+讲义MBSØ Prepayment Componentsl Borrowers may prepay a mortgage due to the sale of the

53、 property or a desire to refinance at lower prevailing rates. In addition, prepayments may occur when the borrower has defaulted on the mortgage or when the borrower has cash available to make partial prepayments (curtailment).Ø Valuing MBSl The Monte Carlo methodology is a simulation approach for valuing MBSs. Thebinomial m is not appropriate for valuing MBSs because MBSs haveembedded prepayment options and the historical evolution of interest rates over time impacts prepayments.l A mortgage security is valued using the Monte Carlo methodology by:üüüSimulating the interes