Principles Of Financial Engineering 2nd Edition Salih N. Neftci - Solutions

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What is the present value of a perpetuity that pays $100 per year? Use an annual discount rate of 4%, and assume the first payment will be made in exactly one year.
You have a portfolio of 10 bonds. How many different ways can exactly two bonds default? Assume the order in which the bonds default is unimportant.
Over the course of a year, the log return on a stock market index is 11.2%. The starting value of the index is 100. What is the value at the end of the year?
Solve for y, where:a. y = ln(e5).b. y = ln(1/e)c. y = ln(10e)
7. What is the other solution mentioned in the text? What are the possible risks behind this solution?
6. What is a synthetic convertible?
5. How are the market professionals using reverse-convertibles? Why is there a “flood”?
4. What is a reverse-convertible bond? How would you decompose this instrument? How would a corporate treasurer use reverse-convertible bonds?
3. Give an example of a convertible bond issued, recently, in Europe. Discuss the main parameters. What is a conversion premium? What is the dilution effect?
2. What is a convertible bond? How would you decompose this instrument? How would a corporate treasurer use convertible bonds?
1. Let’s consider briefly some models of volatility. For example, what is the mean-reverting model for volatility? Are there any other models? Discuss briefly.
1. Read the article below carefully and answer the questions that follow.
4. Explain the purpose of the dislocation trades.
3. What are “balance-protected swaps”?
2. What does the reading mean by “dislocations”?
1. What is a corridor structure?
4. Explain carefully if this is true arbitrage. Are there any risks?
3. Show how you can do this using Bermudan options.
2. Show how you can hedge your Danish mortgage bond (DMB) positions in the swap and swaption markets and then earn a generous arbitrage. Why would this add liquidity to the Danish markets?
1. Define the following concepts: mortgage-backed security, prepayment risk, implicit option, and negative convexity.
1. The reading below deals with some typical swaption strategies and the factors that originate them. First, read it carefully.
10. Explain the following position using appropriate graphs. In particular, make sure that you define a barbell in credit sector. Finally, in what sense is this a convexity position? 1008 GMT [Dow Jones] LONDON—SG recommends selling 7-year 0–3% tranche protection versus 5-year and 10-year
9. Consider the following news from Reuters: HVB Suggests Covered Bond Switches 0843 GMT [Dow Jones] LONDON—Sell DG Hyp 4.25% 2008s at 6.5 bp under swaps and buy Landesbank Baden-Wuerttemberg(LBBW) 3.5% 2009s at swaps-4.2 bp, HVB says. The LBBW deal is grandfathered and will continue to enjoy
8. We consider a reference portfolio of four investment grade names with the following one-year CDS rates: c(1) = 56 c(2) = 80 c(3) = 137 c(3) = 12 The recovery rate is the same for all names at R = 25.The notional amount invested in every CDO tranche is $100. Consider the questions: (a) What are
7. Consider the following news from Reuters: 1008 GMT [Dow Jones] LONDON—SG recommends selling 7-year 0–3% tranche protection versus buying 5-year and 10-year 0–3% protection. 7-year equity correlation tightened versus 5-year and 10-year last year. SG’s barbell plays a steepening of the
6. We consider a reference portfolio of three investment grade names with the following one-year CDS rates: c(1) = 56 c(2) = 80 c(3) = 137 The recovery rate is the same for all names at R = 25. The notional amount invested in every CDO tranche is $1.00. Consider the questions: (a) What are the
5. Consider the following quote: Until last year, this correlation pricing of single-tranche CDOs and first-todefault baskets was dependent on each bank or hedge fund’s assessment of correlation. However, in 2003 the banks behind iBoxx and Trac-x started trading tranched versions of the indexes.
4. Consider the following news from Reuters: 1407GMT [Dow Jones] LONDON—According to a large investment bank investors can boost yields using the following strategies: (1) In the strategy, sell 5-yr CDS on basket of Greece (9 bp), Italy (8.5 bp), Japan (4 bp), Poland (12 bp) and Hungary (16 bp),
3. We consider a reference portfolio of four investment grade names with the following one-year CDS rates: c(1) = 14 c(2) = 7 c(3) = 895 c(4) = 33 The recovery rate is the same for all names at R = 30%.
2. The iTraxx crossover index followed the path given below during three successive time periods: {330, 360, 320} Assume that there are 30 reference names in this portfolio. (a) You decide to select a leverage ratio of 2 and structure a five-year CPPI note on iTraxx crossover index. Libor rates are
1. We consider a reference portfolio of three investment grade names with the following one-year CDS rates: c(1) = 116 c(2) = 193 c(3) = 140 The recovery rate is the same for all names at R = 40. The notional amount invested in every CDO tranche is $1.50. Consider the questions: (a) What are the
2. The iTraxx equity tranche spread followed the path given below during three successive time periods: {14, 15, 5, 16} Assume that there are 30 reference names in this portfolio. (a) You decide to select a leverage ratio of 2 and structure a five-year CPPI note on iTraxx crossover index. Libor
1. We consider a reference portfolio of three investment grade names with the following one-year CDS rates: c(1) = 15 c(2) = 11 c(3) = 330 The recovery rate is the same for all names at R = 40. The notional amount invested in every CDO tranche is $1.50. Consider the questions: (a) What are the
3. Consider the following quote: Until last year, this correlation pricing of single-tranche CDOs and first-todefault baskets was dependent on each bank or hedge fund’s assessment of correlation. However, in 2003 the banks behind iBoxx and Trac-x started trading tranched versions of the
2. Consider the following quote: It is only when portfolios are tranched that the relative value of default correlation becomes meaningful. So, for subordinate tranches, the risk and spreads decrease as correlation between defaults increases, while for senior tranches the risk and spreads increase
1. Consider the following news from Reuters: 1008 GMT [Dow Jones] LONDON—SG recommends selling 7-year 0–3% tranche protection versus buying 5-year and 10-year 0–3% protection. 7-year equity correlation tightened versus 5-year and 10-year last year. SG’s barbell plays a steepening of the
4. Show how you would engineer the following CMS spread note. Issuer: ABC Notional: $10mio Tenor: 10 years Principal: Guaranteed at maturity Coupon: Yr 1: 11.50% Yr 2-10: 16 × (CMS30 − CMS10), max of 30%, min 0% Call: Callable on each coupon date by the issuer (a) What is the view of the
3. Show how you would engineer the following Snowball Note. Issuer: ABC bank Notional: $10 mio Tenor: 10 years; Principal: Guaranteed at maturity Coupon: Yr 1; Q1: 9.00% Q2: Previous Coupon + CMS10 4.65% Q3: Previous Coupon + CMS10 4.85% Q4: Previous Coupon + CMS10 5.25% Yr 2 Q1: Previous Coupon +
2. What follows is the description of a rather complex swap structured by a bank. The structure is sold for the purpose of liability management and involves an exotic option (digital cap) and a CMS component. At time 0 the bank and the client agree to exchange cash flows semiannually for 5 years
1. Consider the swap and Libor curves available in Reuters or Bloomberg. (a) Obtain the 3-month discount and forward curves (b) Obtain the 2-year forward curve (c) Find the components for the following note: maturity: 3 years callable : each coupon payment date payments: annual coupons: Year 1: R1
2. Consider the following statement: One prop trader noted that cap/floor volatility should be slightly higher than swaptions. Corporates buy caps and investors sell swaptions through callable bonds, said one London-based prop trader. The market is structurally short caps and long swaptions.(a)
1. Consider the following table displaying the bid-ask prices for all options on the OEX index passed on January 10, 2002, at 9:46. These options have February 22, 2002, expiry and at the time of data collection, the underlying was at 589.14. Calls Bid Ask Vol Puts Bid Ask Vol Feb 400 188.9 191.9 0
2. The following reading deals with another example of how spread positions on volatility can be taken. Yet, of interest here are further aspects of volatility positions. In fact, the episode is an example of the use of knock-in and knock-out options in volatility positions. (a) Suppose the
1. Read the quote carefully and describe how you would take this position using volatility swaps. Be precise about the parameters of these swaps. (a) How would you price this position? What does pricing mean in this context anyway? Which price are we trying to determine and write in the contract?
3. Going back to the data given in Exercise 2, calculate the following: (a) The bid-ask on a forward swap that starts in two years with maturity in three years. The swap is against 12-month Libor. (b) The forward price of a coupon bond that will be delivered at time 2. The bond pays coupon 7% and
2. You are given the following quotes for liquid swap rates. Assume that all time intervals are measured in years. Term Bid/Ask 2 6.2–6.5 3 6.4–6.7 4 7.0–7.3 5 7.5–7.8 6 8.1–8.4 You know that the current 12-month Libor rate is 5%. (a) Calculate the FRA rates for the next five years,
1. You are given the following quotes for liquid FRAs paid in arrears. Assume that all time intervals are measured in months of 30 days. Term Bid/Ask 3 × 6 4.5–4.6 6 × 9 4.7–4.8 9 × 12 5.0–5.1 12 × 15 5.5–5.7 15 × 18 6.1–6.3 You also know that the current 3-month Libor rate is 4%.
4. Suppose you know that the current value of the peso-dollar exchange rate is 3.75 pesos per dollar. The yearly volatility of the Mexican peso is 20%. The Mexican interest rate is 8%, whereas the U.S. rate is 3%. You will price a dollar option written on the Mexican peso. The option is of European
3. Consider again the data given in the previous question. (a) Use Δ=1 year to discretize the system. (b) Generate five sets of standard normal random numbers with five random numbers in each set. How do you know that these five trajectories are arbitrage-free? (c) Calculate the value of the
2. You know that the euro/dollar exchange rate et follows the real-world dynamics: det = μdt + .15etdWt (152) The current value of the exchange rate is eo = 1.1015. You also know that the price of a 1-year USD discount bond is given by B(t, t + 1)US = 98.93 (153) while the corresponding
1. You observe the following default-free discount bond prices B(t, Ti), where time is measured in years: B(0, 1) = 95, B(0, 2) = 93, B(0, 3) = 91, B(0, 4) = 89 (150) These prices are assumed to be arbitrage-free. In addition, you are given the following cap-floor volatilities: σ(0, 1) = .20,
5. Barrier options belong to one of four main categories. They can be up-and-out, downand-out, up-and-in, or down-and-in. In each case, there is a specified “barrier,” and when the underlying asset price down or up-crosses this barrier, the option either expires automatically (the “out”
4. We use binomial trees to value American-style options on the British pound. Assume that the British pound is currently worth $1.40. Volatility is 20%. The current British risk-free rate is 6% and the U.S. risk-free rate is 3%. The put option has a strike price of $1.50. It expires in 200 days.
3. Suppose the stock discussed in the previous exercise pays dividends. Assume all parameters are the same. Consider three forms of dividends paid by the firm: (a) The stock pays a continuous, known stream of dividends at a rate of 4% per time. (b) The stock pays 5% of the value of the stock at
2. Suppose you are given the following data. The risk-free interest rate is 4%. The stock price follows: dSt = μSt + σStdWt (124) The percentage annual volatility is 18% a year. The stock pays no dividends and the current stock price is 100. Using these data, you are asked to calculate the
1. The current time is t = 1 and our framework is the Libor model. We consider a situation with four states of the world ωi at time t = 3. Suppose Li is the Libor process with a particular tenor and B(1, 3), B(1, 4), and B(1, 4) are zero-coupon bond prices with indicated maturities. The possible
5. The next question deals with a different type range option, called a range accrual option. Range accrual options can be used to take a view on volatility directly. When a trader is short volatility, the trader expects the actual volatility to be less than the implied volatility. Yet, within the
4. Double no-touch optionsis another name for range binaries. Read the following carefully, and then answer the questions at the end. Fluctuating U.S. dollar/yen volatility is prompting option traders managing their books to capture high volatilities through range binary structures while hedging
3. The following questions deal with range binaries. These are another example of exotic options. Read the following carefully and then answer the questions at the end. Investors are looking to purchase range options. The product is like a straightforward range binary in that the holder pays an
2. Consider this reading carefully and then answer the questions that follow. A bank suggested risk reversals to investors that want to hedge their Danish krone assets, before Denmark’s Sept. 28 referendum on whether to join the Economic and Monetary Union. A currency options trader in New York
1. Consider a bear spread. An investor takes a short position in a futures denoted by xt. But he or she thinks that xt will not fall below a level xmin. (a) How would you create a position that trades off gains beyond a certain level against large losses if xt increases above what is expected? (b)
11. Is this a true arbitrage? Are there any risks?
10. Do they have to hedge using caps only? Can floors do as well? Explain your answer graphically.
9. In particular, is this a position on the direction of rates or something else? In fact, can you explain why the professionals had to hedge their position using caps or floors?
8. Now the real issue. Explain the position taken by “knowledgeable” professionals.
7. What is a cap? What volatility do you buy or sell using caps?
6. What is the convexity adjustment for FRAs?
5. Describe the cash flows of FRAs. When are FRAs settled in the market?
2. What is meant by the convexity of long-dated interest rate swaps? 3. Explain the notion of convexity using a graph. 4. If bonds are convex, which fixed income instrument is not convex?
1. First the preliminaries. Explain what is meant by convexity of long-dated bonds.
5. Search the Internet for the following questions. (a) Which sensitivities do the Greeks, volga and Vanna represent? (b) Why are they relevant for vega hedging?
4. You are given the following table concerning the price of a put option satisfying all Black-Scholes assumptions. The strike is 20 and the volatility is 30%. The risk-free rate is 2.5%. Option price Underlying asset price 10 10 5 15 1.3 20 .25 25 .14 30 The option expires in 100 days. Assume (for
3. Consider the following episode: EUR/USD one-month implied volatility sank by 2.7% to 10% Wednesday as traders hedged this euro exposure against the greenback, as the euro plunged to historic lows on the spot market. After the European Central Bank raised interest rates by 25 basis points, the
2. Consider the following quote: Implied U.S. dollar/New Zeland dollar volatility fell to 10.1%/11.1% on Tuesday. Traders bought at-the-money options at the beginning of the week, ahead of the Federal Reserve interest-rate cut. They anticipated a rate cut which would increase short-term volatility.
1. Consider the following comment dealing with options written on the euro-dollar exchange rate: Some traders, thinking that implied volatility was too high entered new trades. One example was to sell one-year in-the-money euro Puts with strikes around USD1.10 and buy one-year at-the-money euro
3. Would there be ways DB can still take such a position? What are they?
2. Suppose these rules had been in effect during March, would they have prevented DB’s arbitrage position?
1. Eurex has made some changes in the Bund futures trading rules. What are these?
8. Explain how cheapest-to-deliver (CTD) bonds are determined. For needed information go to Web sites of futures exchanges.
7. Could taking a carefully chosen position in the relevant maturity FRA, offset the losses that shorts have suffered? Explain carefully.
6. Would an asset swap (e.g., swapping Libor against the relevant bond mentioned in the paper) have helped the shorts? Explain.
5. Why are penalties for failure to deliver relevant?
4. What is the importance of the size of ’05 Bund issue? How do traders “rustle up” such bonds to be delivered?
3. What is DB’s position aiming for?
2. Put this together with DB’s position in the repo market.
1. What is a calendar spread? Show DB’s position using cash flow diagrams.
3. A treasurer in Europe would like to borrow USD for 3 months. But instead of an outright loan, the treasurer decides to use the repo market. The company has holdings of Euro 40 million bonds. The treasurer uses a cross-currency repo. The details of the transaction are as follows: • Clean price
2. A dealer repos $10 million T-bills. The haircut is 5%. The parameters of the deal are as follows: • T-bill yield: 2% • Maturity of T-bills: 90 days • Repo rate: 2.5% term: 1 week (a) How much cash does the dealer receive? (b) How much interest will be paid at the end of the repo deal?
1. A dealer needs to borrow EUR 30 million. He uses a Bund as collateral. The Bund has the following characteristics: • Collateral 4.3% Bund, June 12, 2004 • Price: 100.50 • Start date: September 10 • Term: 7 days • Repo rate: 2.7% • Haircut: 0% (a) How much collateral does the dealer
7. Consider a 2-year currency swap between USD and EUR involving floating rates only. The EUR benchmark is selected as 6-month Euro Libor, the dollar benchmark is 6-month BBA Libor. You also have the following information:Notional amount = USD10,000,000 Exchange rate EUR/USD = 0.84 (a) Show the
6. Foreigners buying Australian dollar instruments issued in Australia have to pay withholding taxes on interest earnings. This withholding tax can be exploited in tax-arbitrage portfolios using swaps and bonds. First let us consider an episode from the markets related to this issue.Under
5. Going back to Question 4, suppose you are given, in addition, data on FRAs both for USD and for EUR. Also suppose you are looking for arbitrage opportunities. Would these additional data be relevant for you? Discuss briefly.
4. Suppose at time t = 0, we are given prices for four zero-coupon bonds (B1, B2, B3, B4) that mature at times t = 1, 2, 3, and 4. This forms the term structure of interest rates. We also have the one-period forward rates (f0, f1, f2, f3), where each fi is the rate contracted at time t = 0 on a
3. You are a swap dealer and you have the following deals on your book: Long • 2-year receiver vanilla interest rate swap, at 6.75% p.a. 30/360. USD N = 50 million. • 3-year receiver vanilla interest rate swap, at 7.00% p.a. 30/360. USD N = 10 million.• 5-year receiver vanilla interest rate
2. Read the following episode carefully. Italian Asset Swap Volumes Soar on Buyback Plans Volumes in the basis-swap spread market doubled last week as traders entered swaps in response to the Italian treasury’s announcement that it “does not rule out buybacks.” Traders said the increase in
1. You have a 4-year coupon bond that pays semiannual interest. The coupon rate is 8% and the par value is 100. (a) Can you construct a synthetic equivalent of this bond? Be explicit and show your cash flows. (b) Price this coupon bond assuming the following term structure: B1 = .90/.91, B2 =
6. You are given the following information: 3-m Libor 3.2% 92 days 3 × 6 FRA 3.3%–3.4% 90 days 6 × 9 FRA 3.6%–3.7% 90 days 9 × 12 FRA 3.8%–3.9% 90 days (a) Show how to construct a synthetic 9-month loan with fixed rate beginning with a 3-month loan. Plot the cash flow diagram. (b) What is
5. You are hired by a financial company in New Zealand and you have instant access to markets. You would like to lock in a 3-month borrowing cost in NZ$ for your client. You consider a NZ$ 1 × 4 FRA. But you find that it is overpriced as the market is thin. So you turn to Aussie. A$ FRAs are very
4. Suppose practitioners learn that the British Banker’s Association (BBA) will change the panel of banks used to calculate the yen Libor. One or more of the “weaker” banks will be replaced by “stronger” banks at a future date. The issue here is not whether yen Libor will go down, as a
3. A corporation will receive USD7 million in 3 months’ time for a period of 3 months. The current 3-month interest rate quotes are 5.67 to 5.61. The Eurodollar futures price is 94.90. Suppose in 3 months the interest rate becomes 5.25% for 3-month Eurodeposits and the Eurodollar futures price is

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Principles Of Financial Engineering 2nd Edition Salih N. Neftci - Solutions

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