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Questions and Answers of Personal Financial Planning

5. (Nongeometric Brownian motion) Write a MATLAB program to observe the implied volatility smile for the option based on the stock price following the dynamics of nongeometric Brownian motion. Use
4. (Stochastic volatility) Write a MATLAB program to observe the implied volatility smile for the option based on the stock price having stochastic volatility. Use the following data for the
3. Write a MATLAB program to observe the volatility payoff of stop loss hedged long call position and measure the performance of this strategy of replicating long call position when the frequency of
2. (Stop-loss hedge). Write a VBA program to show the stop-loss hedged portfolio adjustments and cash flows for 100 long calls from the dealers’ perspective with the following data:Sð0Þ 5 100;K 5
1. Consider the following table displaying the bidask 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
4. (Volatility swap price). Write a MATLAB program to show the invariance of the volatility payoff of a delta hedged long call for the various frequency of delta adjustment until the time of expiry
3. (Variance swap price). Write a MATLAB program to illustrate the variation of the price of an (equity) variance swap with respect to the change in the mean return of the underlying stock and also
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
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
3. Going back to the data given in Exercise 2, calculate the following:a. The bidask on a forward swap that starts in 2 years with maturity in 3 years. The swap is against 12-month LIBOR.b. The
2. You are given the following quotes for liquid swap rates. Assume that all time intervals are measured in 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 3 6 4.54.6 6 3 9 4.74.8 9 3 12 5.05.1 12 3 15
11. (BDT Model Calibration.) Write a MATLAB program to calibrate the BDT model based on the following data on bond prices and implied volatilities• B(t0, t1) 5 0.95; B(t0, t2) 5 0.93; B(t0, t3) 5
9. (Barrier Option.) Write a MATLAB program to document the efficiency of a Monte Carlo approach to the estimation of the price of Down-and-Out and Down-and-In Call options based on the following
8. (European Options.) Write a MATLAB program to document the efficiency of a Monte Carlo approach to the estimation of European Call and Put option prices based on the following data:• S(0) 5 100;
7. (Barrier Option.) Write a VBA program to simulate M 5 100 stock prices using a Monte Carlo technique to calculate the price of Barrier down-and-out and down-and-in call options based on the
6. (Digital Currency Options.) Write a VBA program to simulate M 5 100 stock prices using a Monte Carlo technique to calculate the prices of digital call and put options FX options as discussed in
5. (European Option.)Write a VBA program to simulate M 5 100 stock prices using a Monte Carlo technique to calculate the prices of European Call and Put options based on the following data:
4. (European FX option.) Suppose you know that the current value of the pesodollar exchange rate is 3.75 pesos per dollar. The yearly volatility of the Mexican peso is 20%.The Mexican interest rate
3. (European option.) Consider again the data given in the previous question.a. Use Δ 5 1 year to discretize the system.b. Generate five sets of standard normal random numbers with five random
2. (Exchange rates and LIBOR rates.) You know that the euro/dollar exchange rate et follows the real-world dynamics:det 5 μdt 1 0:15etdWt (13.152)The current value of the exchange rate is eo 5
1. (BlackDermanToy model.) You observe the following default-free discount bond prices B(t, Ti), where time is measured in years:Bð0; 1Þ 5 95; Bð0; 2Þ 5 93; Bð0; 3Þ 5 91; Bð0; 4Þ 5 89
14. FX European Option (Nonrecombining B-Tree)Write a VBA program to determine the initial price of European-style options on the British pound in a nonrecombining binomial tree model based on the
13. FX European Option Write a VBA program to determine the initial price of European-style options on the British pound in the binomial model based on the following data:S(0) 5 $1.54; K 5 $1.54; T 5
12. (FX American Option)Write a VBA program to determine the initial price of an American-style options on the British pound in a binomial model based on the following data:S(0) 5 $1.54; K 5 $1.54; T
11. European option on dividend paying index (nonrecombining binomial tree)Write a VBA program to determine the initial price of a European Call and European Put option in nonrecombining binomial
10. European option on dividend paying index Write a VBA program to determine the initial price of a European Call and European Put option in a binomial model based on the following data:S(0) 5 100;
9. (American Option)Write a VBA program to determine the initial price of an American Call and American Put option in a binomial model based on the following data:• S(0) 5 100; K 5 105; T 5 1; r 5
8. (European Option Nonrecombining Binomial Tree)Write a VBA program to determine the initial price of a European Call and European Put option in a nonrecombining binomial tree model based on the
7. (European Option)Write a VBA program to determine the initial price of a European Call and European Put option in a binomial model based on the following data:• S(0) 5 100; K 5 105; T 5 1; r 5
6. Barrier options belong to one of four main categories. They can be up-and-out, down-andout, up-and-in, or down-and-in. In each case, there is a specified “barrier,” and when the underlying
5. 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
4. 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
3. Suppose you are given the following data. The risk-free interest rate is 4%. The stock price follows:dSt 5 μSt 1 σStdWt (12.124)The percentage annual volatility is 18% a year. The stock pays no
2. The current time is t 5 1 and our framework is the LIBOR model. We consider a situation with four states of the world ωi at time t 5 3.
1. The following prices of the four different stocks are reported from an arbitrage-free market at time t0 S1 t0 5 12:66; S2 t0 5 12:24; S3 t0 5 20:66; S4 t0 5 18:25 Find out the price of the 5th
10. Write a MATLAB program to plot the following spreads including the time value of the spread as well as its payoff at the expiration.a. Bull spread
9. Write a VBA program to show the fabrication of the butterfly spread composed of a strangle and straddle. Assume the following parameters:S(0) 5 100; T 5 1; r 5 8%; σ 5 30%; Spread 5 5%Plot the
8. Write a VBA program to show the construction of a bull and bear spread, first using calls only and then using puts only. Also plot both the call spread and put spread in both bull and bear phases.
7. 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
6. Double no-touch options is 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
5. 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
4. 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
3. 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
2. Assume that a trader believes that during the vacation periods actual realized volatility is lower than the implied volatility. To exploit this opportunity a trader takes a short position in a
1. Construct a payoff and profit diagram for the purchase of a 105-strike call and sale of a 95-strike call. Verify that you obtain exactly the same profit diagram for the purchase of a 105-strike
7. Consider the “CIR (Cox-Ingersoll-Ross)” model dr 5 αðμ 2 rÞdt 1 σOrdW t Plot the term structure (i.e., plot yield versus time) for the following parameter sets [α,μ,σ,r(0)]:½0:02;
6. Consider the Vasicek model dr 5 αðμ 2 rÞdt 1 σ dW t Plot the term structure (i.e., plot yield versus time) for the following parameter sets [α,μ,σ,r(0)]:½5:9; 0:3; 0:2; 0:1½3:9; 0:1;
5. Answer the following questions related to the case study “Convexity of long bonds, convexity and arbitrage.”a. First the preliminaries. Explain what is meant by convexity of long-dated
4. Assuming that the yield curve is flat and has only parallel shifts, determine the spread between the paid-in-arrear FRAs and market-traded linear FRAs if the FRA rates are expected to oscillate as
3. Consider the data given in the previous question.a. Suppose an anticipated movement as in the previous question. Market participants suddenly move to an anticipated trajectory such as f0:08; 0:02;
2. You are given a 30-year bond with yield y. The yield curve is flat and will have only parallel shifts. You have a liquid 3-month Eurodollar contract at your disposition. You can also borrow and
1. You are given the following default-free long bond:Face value: 100 Issuing price: 100 Currency: USD Maturity: 30 years Coupon: 6%No implicit calls or puts.Further, in this market there are no
11. MATLAB exercise on a Delta-Hedged Portfolio Write a MATLAB program to delta hedge the portfolio consisting only of the stock and the risk-free asset to cover the long call option. Observe the
10. (MATLAB exercise on Barrier Option)Write a MATLAB program to determine the initial price of Barrier Down and In Call option and Barrier Down and Out Call option using the BSM formula with the
9. (MATLAB exercise on Chooser Option)Write a MATLAB program to determine the initial price of chooser option using the BSM formula with the following data:S(0) 5 100; K 5 105; T0 5 0.5; T 5 1; r 5
8. (MATLAB exercise on European Option)Write a MATLAB program to determine the initial price of European Call and European Put option using the BSM formula with the following data:S(0) 5 100; K 5
7. Answer the questions related to the case study Swiss Central Bank, 2012:a. What is the rationale for the proposed futures strategyb. What options strategy could you consider that would also
6. 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?
5. You are given the following table concerning the price of a put option satisfying all BlackScholes assumptions. The strike is 20 and the volatility is 30%. The risk-free rate is 2.5%.Option Price
4. 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
3. Consider the following quote:Implied U.S. dollar/New Zealand 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
2. (Delta Hedge Portfolio)Write a VBA program to show the delta-hedged portfolio adjustments and cash flows for a long call from the dealers’ perspective with the following data:Total number of
1. Consider the following comment dealing with options written on the eurodollar exchange rate:Some traders, thinking that implied volatility was too high entered new trades. One example was to sell
7. Consider the replication of a European call option. Write a VBA program to show the dynamic hedging strategy using only stocks and a saving account to replicate a short European option.Calculate
6. How could you determine whether the trees in Figure 8.7 are arbitrage-free or not?
5. Consider the reading that follows which deals with the effects of straightforward delta hedging.Read the events described and then answer the questions that follow.
4. You are going to use binomial trees to value American-style options on the British pound.Assume that the British pound is currently worth $1.40. Volatility is 10%. The current British risk-free
3. Suppose the stock discussed in Exercise 1 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
2. Suppose you are given the following data:The risk-free interest rate is 6%.The stock price follows:dSt 5 μSt dt 1 σSt dWt (8.83)Volatility is 12% a year.The stock pays no dividends and the
1. Consider the immunization example given in Section 8.4. Assume that the zero-coupon yield curve is flat at y 5 5% and not 8% as in the example. The shifts in the yield curve are parallel.What
3. Consider the oil calendar swap example provided in the text. Table 7.5 provided the swap curve derived from the futures curve. To calculate the mark-to-market value of the swap and its “fair
2. Consider the JPMorgan heating oil example in the text of this chapter. We calculated the expected profit from the spot oil purchases and forward sale after making assumptions about borrowing and
1. In this question we consider a gold miner’s hedging activities.a. What is the natural position of a gold miner? Describe using payoff diagrams.b. How would a gold miner hedge her position if
8. Suppose the quoted swap rate is 5.06/5.10. Calculate the amount of fixed payments for a fixed payer swap for the currencies below in a 100 million swap.USD.EUR.Now calculate the amount of fixed
7. 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 EUR40 million bonds. The
6. 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
5. 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
4. Going back to the previous exercise, 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
3. Suppose at time t 5 0, we are given prices for four zero-coupon bonds (B1, B2, B3, B4) that mature at times t 5 1, 2, 3, and 4. This forms the term structure of interest rates.We also have the
2. 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 3 4 FRA.
1. Today is March 1, 2004. The day-count basis is actual/365. You have the following contracts on your FX book.CONTRACT A: On March 15, 2004, you will sell 1,000,000 EUR at a price F1 t dollars per
8. Explain how 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.
4. A dealer wants to borrow $10 million using a bond repo but due to certain market restriction he cannot repo out the bond for 2 months.a. Suggest a strategy so that he can borrow the cash for the
3. 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 weeka. How much cash does the
2. 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
1. Suppose you are a newly employed investment banker and you find that your bank got stuck in a deal where it has to deliver a bond to close a short future position. The bond has just gone
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 5 50 million.3-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
1. On March 3, 2000, the Financial Accounting Standards Board, a crucial player in financial engineering problems, published a series of important new proposals concerning the accounting of certain
11. Barbell example.On June 16, 2014, a fund manager is considering the purchase of $1 million face amount of US Treasury 1 1 2s with a maturity date of May 31, 2019 at a cost of 990,468.75. The
10. Using the following bond price data calculate the 3 3 6, 6 3 9, 3 3 9 and 6 3 12 FRA rates.Bðt0; t1Þ 5 98:79; Bðt0; t2Þ 5 97:21; Bðt0; t3Þ 5 95:84; Bðt0; t4Þ 5 93:82
9. Assume the Eurodollar futures price at time t0 is 93.83 and the contract expires in 3 months timea. Calculate the 3-month forward rate implied by this price.b. Calculate the repayment amount for

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