Suppose the dollar-denominated interest rate is 5%, the yen-denominated interest rate is 1% (both rates are continuously compounded), the spot exchange rate is 0.009 $/¥, and the price of a dollar-denominated European call to buy one yen with 1 year to expiration and a strike price of $0.009 is $0.0006. a. What is the dollar-denominated European yen put price such that there is no arbitrage opportunity? b. Suppose that a dollar-denominated European yen put with a strike of $0.009 has a premium of $0.0004. Demonstrate the arbitrage. c. Now suppose that you are in Tokyo, trading options that are denominated in yen rather than dollars. If the price of a dollar-denominated at-the-money yen call in the United States is $0.0006, what is the price of a yen-denominated at-the-money dollar call—an option giving the right to buy one dollar, denominated in yen—in Tokyo? What is the relationship of this answer to your answer to (a)? What is the price of the at-the-money dollar put?
> Can 3PLs be effective supply chain partners? Why?
> What are 3PLs and why are they used? Why is their use growing so rapidly? What are 4PLs and why are they used?
> Why is logistics so important for successful supply chain management?
> How is lean production associated with JIT?
> What does the bullwhip effect refer to and what causes it? How then, would you try to reduce the bullwhip effect?
> Explain why lean production and Six Sigma are so important to successful supply chain management.
> What are the two types of process variation, and which one does statistical process control seek to eliminate? What can be done with the other one?
> What are the two most widely used ISO standards, and why are they so popular?
> Describe Deming’s Theory of Management and how it can be used to improve quality?
> Describe Six Sigma’s origins and the main parties involved. Why do you think the concept is called “Six Sigma”?
> Discuss the linkage between lean systems and environmental sustainability.
> What is kaizen, and why is it so important for successful lean production?
> What are kanbans and why are they used in lean production systems?
> What are manufacturing cells, and why are they important in lean production?
> What are the four foundation elements of supply chain management? Describe some activities within each element.
> How can reverse logistics have a positive impact on the environment? On profits? On customer service? On repeat purchases?
> Why should lean layouts be visual?
> What are the advantages and disadvantages of making small, frequent purchases from just a few suppliers? How do we overcome the disadvantages?
> Given the following inventory information, construct an (a) ABC analysis by annual dollar usage, (b) ABC analysis by current inventory value, and (c) an ABC inventory matrix. Is the firm stocking the correct inventories? ITEM NUMBER UNIT COST ($) AN
> Given the following information for an important purchased part, compute the (a) EOQ, (b) total purchase cost, (c) annual holding cost, (d) annual order cost, (e) annual total cost, (f) reorder point, (g) number of orders placed per year and (h) time bet
> Given the following information for an important purchased part, compute the (a) economic order quantity, (b) total purchase cost, (c) annual holding cost, (d) annual ordering cost, (e) annual total cost, (f) reorder point, (g) number of orders placed pe
> The weekly requirement of a part is 950 units. The order cost is $85 per order, the holding cost is $5 per unit per year and the part cost is $250 per unit. The firm operates fifty-two weeks per year. Compute the (a) EOQ, (b) annual holding cost, (c) ann
> Describe and provide examples of dependent and independent demand.
> Explain whether the continuous review or periodic review inventory system is likely to result in higher safety stock. Which is likely to require more time and effort to administer? Why?
> What is the purpose of the EOQ and the ROP? How can they be used together?
> What is the ABC inventory matrix, and how is it used to manage inventory?
> What is reverse logistics? How does it impact supply chain management?
> What is the profit-leverage effect of purchasing? What is the return on assets effect of purchasing?
> Describe the four basic types of inventory.
> Is a level production strategy suitable for a pure service industry, such as professional accounting and tax services or law firms? Can these firms inventory their outputs?
> Compare and contrast chase versus level production strategies. Which is more appropriate for an industry where highly skilled laborers are needed? Why?
> Describe the relationships among MRP, closed-loop MRP, MRP-II, and ERP.
> Describe aggregate production planning, master production planning, material requirements planning, and distribution requirements planning. How are these plans related?
> Describe long range, medium range, and short range planning in the context of the materials plan and capacity plan. How are they related?
> Explain best-of-breed and single integrator ERP implementations. What are the advantages and disadvantages of the best-of-breed implementation?
> Describe the limitations of a legacy MRP system.
> Why have so many firms rushed to implement ERP over the past ten years?
> How has NAFTA impacted trade between the U.S., Canada and Mexico? Is NAFTA good for domestic U.S. and Mexican producers?
> Ms. Winnie Lin’s company sells computers. Monthly sales for a six-month period are as follows: Jan ................................................................ 18,000 Feb ................................................................. 22,000 Mar ..
> Using the information in Table 8.9, verify that it is possible to derive the 8-quarter dollar interest swap rate from the 8-quarter euro interest swap rate by using equation (8.13). Equation (8.13). TABLE 8.9 Quarter 2 3 4 5 7 8 20.5 Oil forward pr
> Suppose you observe the following month-end stock prices for stocks A and B: For each stock: a. Compute the mean monthly continuously compounded return. What is the annual return? b. Compute the mean monthly standard deviation. What is the annual standar
> The firm is considering an investment project costing $1. What is the amount by which the project’s value must exceed its cost in order for shareholders to be willing to pay for it? Repeat for project values of $10 and $25.
> Explain how to synthetically create the equity-linked CD in Section 15.3 by using a forward contract on the S&P index and a put option instead of a call option. (Hint: Use put-call parity. Remember that the S&P index pays dividends.) B(0, T,
> Let S = $40, K = $45, σ = 0.30, r = 0.08, δ = 0, and T = {0.25, 0.5, 1, 2, 3, 4, 5, 100}. a. Compute the prices of knock-out calls with a barrier of $38. b. Compute the ratio of the knock-out call prices to the prices of standard calls. Explain the patte
> Suppose you buy a 950-strike S&R call, sell a 1000-strike S&R call, sell a 950-strike S&R put, and buy a 1000-strike S&R put. a. Verify that there is no S&R price risk in this transaction. b. What is the initial cost of the position? c. What is the value
> Suppose S = $100, K = $95, σ = 30%, r = 0.08, δ = 0.03, and T = 0.75. a. Compute the Black-Scholes price of a call. b. Compute the Black-Scholes price of a call for which S = $100 × e−0.03×0.75, K = $95 × e−0.08×0.75, σ = 0.3, T = 0.75, δ = 0, r = 0. How
> Use Itˆo’s Lemma to evaluate dS−1. For the following four problems, use Itˆo’s Lemma to determine the process followed by the specified equation, assuming that S(t) follows (a) a
> Let S = $100, K = $100, σ = 30%, r = 0.08, t = 1, and δ = 0. Let n = 10. Suppose the stock has an expected return of 15%. a. What is the expected return on a European call option? A European put option? b. What happens to the expected return if you incre
> Repeat the option price calculation in the previous question for stock prices of $80, $90, $110, $120, and $130, keeping everything else fixed. What happens to the initial option ∆ as the stock price increases?
> Using the information about zero-coupon bond prices and oil forward prices in Table 8.9, construct the set of swap prices for oil for 1 through 8 quarters. TABLE 8.9 Quarter 2 3 4 5 7 8 Pil forward price 21 21.1 20.8 20.5 20.2 20 19.9 19.8 Gas swap
> Consider the same facts as the previous problem, only now consider hedging with the 3-month Eurodollar futures. Suppose the Eurodollar futures contract that matures 60 days from today has a price on day 0 of 94. a. What issues arise in using the 3-month
> Suppose you are selecting a futures contract with which to hedge a portfolio. You have a choice of six contracts, each of which has the same variability, but with correlations of −0.95, −0.75, −0.50, 0, 0.25, and 0.85. Rank the futures contracts with res
> Using the information in Table 7.1, a. Compute the implied forward rate from time 1 to time 3. b. Compute the implied forward price of a par 2-year coupon bond that will be issued at time 1. TABLE 7.1 Five ways to present equivalent information abou
> The S&R index spot price is 1100, the risk-free rate is 5%, and the dividend yield on the index is 0. a. Suppose you observe a 6-month forward price of 1135. What arbitrage would you undertake? b. Suppose you observe a 6-month forward price of 1115. What
> Draw profit diagrams for the following positions: a. 1050-strike S&R straddle. b. Written 950-strike S&R straddle. c. Simultaneous purchase of a 1050-strike straddle and sale of a 950-strike S&R straddle.
> If Telco does nothing to manage copper price risk, what is its profit 1 year from now, per pound of copper that it buys? If it hedges the price of wire by buying copper forward, what is its estimated profit 1 year from now? Construct graphs illustrating
> Suppose XYZ stock pays no dividends and has a current price of $50. The forward price for delivery in 1 year is $55. Suppose the 1-year effective annual interest rate is 10%. a. Graph the payoff and profit diagrams for a forward contract on XYZ stock wit
> Suppose you short-sell 300 shares of XYZ stock at $30.19 with a commission charge of 0.5%. Supposing you pay commission charges for purchasing the security to cover the short-sale, how much profit have you made if you close the short-sale at a price of $
> Suppose that there is a 3%per year chance that the firm’s asset value can jump to zero. Assume that the firm issues 5-year zero-coupon debt with a promised payment of $110. Using the Merton jump model, compute the debt price and yield, and compare to the
> There are four debt issues with different priorities, each promising $30 at maturity. a. Compute the yield on each debt issue assuming that all four mature in 1 year, 2 years, 5 years, or 10 years. b. Assuming that each debt issue matures in 5 years, wha
> Using the delta-approximation method and assuming a $10m investment in stock A, compute the 95% and 99% 1-, 10-, and 20-day VaRs for a position consisting of stock A plus one 105-strike put option for each share. Use the same assumptions as in Example 26
> Consider two zero-coupon bonds with 2 years and 10 years to maturity. Let a =0.2, b = 0.1, r = 0.05, σVasicek = 10%, and σCIR = 44.721%. The interest rate risk premium is zero in each case. We will consider a position consisting of one $100 par value 2-y
> Use the following inputs to compute the price of a European call option: S = $100, K = $50, r = 0.06, σ = 0.30, T = 0.01, δ = 0. a. Verify that the Black-Scholes price is $50.0299. b. Verify that the vega for this option is almost zero. Why is this so? c
> Suppose the current exchange rate between Germany and Japan is 0.02 =C/¥. The euro-denominated annual continuously compounded risk-free rate is 4% and the yen-denominated annual continuously compounded risk-free rate is 1%. What are the 6-month euro/yen
> In this problem we will use Monte Carlo to simulate the behavior of the martingale St/Pt, with Pt as numeraire. Let x0 = S0/P0(0, T ). Simulate the process Let h be approximately 1 day. a. Evaluate b. Compute the mean and standard deviation of the di
> Suppose you know nothing about widgets. You are going to approach a widget merchant to borrow one in order to short-sell it. (That is, you will take physical possession of the widget, sell it, and return a widget at time T.) Before you ring the doorbell,
> Suppose that firms face a 40% income tax rate on all profits. In particular, losses receive full credit. Firm A has a 50% probability of a $1000 profit and a 50% probability of a $600 loss each year. Firm B has a 50% probability of a $300 profit and a 50
> Suppose that the yield curve is given by y(t) = 0.10 − 0.07e−0.12t, and that the short-term interest rate process is dr(t) = (θ(t) − 0.15r(t)) + 0.01dZ. Compute the calibrated Hull-White tree for 5 years, with time steps of h = 1. a. What is the probabil
> Using the Merton jump formula, generate an implied volatility plot for K = 50, 55, . . . 150. a. How is the implied volatility plot affected by changing αJ to−0.40 or−0.10? b. How is the implied volatility plot affected by changing λ to 0.01 or 0.05? c.
> Consider the Level 3 outperformance option with a multiplier, discussed in Section 16.2. This can be valued binomially using the single state variable SLevel 3/SS&P, and multiplying the resulting value by SS&P. a. Compute the value of this option if it w
> Refer to Figure 19.2. a. Verify that the price of a European put option is $0.0564. b. Verify that the price of an American put option is $0.1144. Be sure to allow for the possibility of exercise at time 0. FIGURE 19.2 12,000 10,000 Histograms for ri
> Consider the last row of Table 17.1. What is the solution for S∗ and S∗ when ks = kr = 0? (This answer does not require calculation.) In the following five problems, assume that the spot price of gold is $300/oz, the effective annual lease rate is 3%, an
> As discussed in the text, compensation options are prematurely exercised or canceled for a variety of reasons. Suppose that compensation options both vest and expire in 3 years and that the probability is 10% that the executive will die in year 1 and 10%
> Using the information in Table 15.5, assume that the volatility of oil is 15%. a. Show that a bond that pays one barrel of oil in 1 year sells today for $19.2454. b. Consider a bond that in 1 year has the payoff S1 + max (0, K1 − S1) &a
> Suppose x1∼ N (2, 0.5) and x2 ∼ N (8, 14). The correlation between x1 and x2 is −0.3. What is the distribution of x1+ x2? What is the distribution of x1+ x2?
> Let S = $40, σ = 0.30, r = 0.08, T = 1, and δ = 0. Also let Q = $60, σQ= 0.50, δQ= 0.04, and ρ = 0.5. What is the price of a standard 40-strike call with S as the underlying asset? What is the price of an exchange option with S as the underlying asset an
> You have sold one 45-strike put with 180 days to expiration. Compute and graph the 1-day holding period profit if you delta- and gamma-hedge this position using the stock and a 40-strike call with 180 days to expiration.
> Assume r = 8%, σ = 30%, δ = 0. In doing the following calculations, use a stock price range of $60–$140, stock price increments of $5, and two different times to expiration: 1 year and 1 day. Consider purchasing a 100-strike straddle, i.e., buying one 10
> Suppose S = $100, K = $95, r = 8% (continuously compounded), t = 1, σ = 30%, and δ = 5%. Explicitly construct an eight-period binomial tree using the Cox-Ross- Rubinstein expressions for u and d:
> Suppose that the exchange rate is $0.92/=C. Let r$ = 4%, and r=C = 3%, u = 1.2, d = 0.9, T = 0.75, n = 3, and K = $0.85. a. What is the price of a 9-month European call? b. What is the price of a 9-month American call?
> Suppose that to buy either a call or a put option you pay the quoted ask price, denoted Ca(K, T ) and Pa(K, T ), and to sell an option you receive the bid, Cb(K, T ) and Pb(K, T ). Similarly, the ask and bid prices for the stock are Sa and Sb. Finally, s
> Suppose the September Eurodollar futures contract has a price of 96.4. You plan to borrow $50m for 3 months in September at LIBOR, and you intend to use the Eurodollar contract to hedge your borrowing rate. a. What rate can you secure? b. Will you be lon
> Suppose the S&P 500 currently has a level of 875. The continuously compounded return on a 1-year T-bill is 4.75%. You wish to hedge an $800,000 portfolio that has a beta of 1.1 and a correlation of 1.0 with the S&P 500. a. What is the 1-year futures pric
> The profit calculation in the chapter assumes that you borrow at a fixed interest rate to finance investments. An alternative way to borrow is to short-sell stock. What complications would arise in calculating profit if you financed a $1000 S&R index inv
> Repeat the previous problem, assuming that default correlations are 0.25. Repeat the previous problem, Following Table 27.10, compute the prices of first, second, and Nth-to-default bonds assuming that defaults are uncorrelated and that there are 5, 10,
> Consider the widget investment problem outlined in Section 17.1. Show the following in a spreadsheet. a. Compute annual widget prices for the next 50 years. b. For each year, compute the net present value of investing in that year. c. Discount the net pr
> You are going to borrow $250m at a floating rate for 5 years. You wish to protect yourself against borrowing rates greater than 10.5%. Using each tree, what is the price of a 5-year interest rate cap? (Assume that the cap settles each year at the time yo
> Explain why the VIX formula in equation (24.29) overestimates implied volatility if options are American. The following three problems use the Merton jump formula. As a base case, assume S = $100, r = 8%, σ = 30%, T = 1, and δ = 0
> A European shout option is an option for which the payoff at expiration is max(0, S − K, G − K), where G is the price at which you shouted. (Suppose you have an XYZ shout call with a strike price of $100. Today XYZ is $130. If you shout at $130, you are
> Warren Buffett stated in the 2009 Letter to Shareholders: “Our derivatives dealings require our counterparties to make payments to us when contracts are initiated. Berkshire therefore always holds the money, which leaves us assuming no meaningful counte
> Refer to Table 19.1. a. Verify the regression coefficients in equation (19.12). b. Perform the analysis for t = 1, verifying that exercise is optimal on paths 4, 6, 7, and 8, and not on path 1. TABLE 19.1 Computation of option price using expected v
> Verify in Figure 17.2 that if volatility were 30% instead of 50%, immediate exercise would be optimal. FIGURE 17.2 YEAR O YEAR 1 YEAR 2 nt: $407.74 Binomial tree for project value, assuming 50% volatil- ity. The value at each node is the project val
> Consider Panels B and D in Figure 16.4. Using the information in each panel, compute the share price at each node for each bond issue. FIGURE 16.4 Binomial valuation of a callable nonconvertible and a callable convertible bond. The assumptions are t
> Using the information in Table 15.5, suppose we have a bond that after 2 years pays one barrel of oil plus λ × max(0, S2 − 20.90), where S2 is the year-2 spot price of oil. If the bond is to sell for $20.90 and
> Consider the gap put in Figure 14.4. Using the technique in Problem 12.11, compute vega for this option at stock prices of $90, $95, $99, $101, $105, and $110, and for times to expiration of 1 week, 3 months, and 1 year. Explain the values you compute.
> You own one 45-strike call with 180 days to expiration. Compute and graph the 1-day holding period profit if you delta- and gamma-hedge this position using a 40-strike call with 180 days to expiration.
> Suppose there is a single 5-year zero-coupon debt issue with a maturity value of $120. The expected return on assets is 12%. What is the expected return on equity? The volatility of equity? What happens to the expected return on equity as you vary A, σ,
> Consider a bull spread where you buy a 40-strike put and sell a 45-strike put. Suppose σ = 0.30, r = 0.08, δ = 0, and T = 0.5. a. Suppose S = $40. What are delta, gamma, vega, theta, and rho? b. Suppose S = $45. What are delta, gamma, vega, theta, and rh
> Compute the 1-year forward price using the 50-step binomial tree in Problem 11.13. Problem 11.13 Repeat the previous problem for n = 50. What is the risk-neutral probability that S1< $80? S1> $120? Previous Problem Let S = $100, σ = 0.30, r = 0.08, t = 1
> Use the same data as in the previous problem, only suppose that the call price is $5 instead of $4.110. Data from Previous Problem: Let S = $40, K = $40, r = 8% (continuously compounded), σ = 30%, δ = 0, T =0.5 year, and n = 2. The call price is $4.110
