The current price for a stock index is 1,000. The following premiums exist for various options to buy or sell the stock index six months from now: Strike Price Call Premium Put Premium 950 120.41 51.78 1,000 93.81 74.20 1,050 71.80 101.21 Strategy I is to buy the 1,050-strike call and to sell the 950-strike call. Strategy II is to buy the 1,050-strike put and to sell the 950-strike put. Strategy III is to buy the 950-strike call, sell the 1,000-strike call, sell the 950-strike put, and buy the 1,000-strike put. Assume that the price of the stock index in 6 months will be between 950 and 1,050. Determine which, if any, of the three strategies will have greater payoffs in six months for lower prices of the stock index than for relatively higher prices. A market maker in stock index forward contracts observes a 6-month forward price of 112 on the index. The index spot price is 110 and the continuously compounded dividend yield on the index is 2%. The continuously compounded risk-free interest rate is 5%. Describe actions the market maker could take to exploit an arbitrage opportunity and calculate the resulting profit (per index unit).

answer every question.

Continuation passing allows lambda calculus and functional languages to describe many forms of sequential control structure. If you write code in your answer to this question you may write it either in lambda-calculus or in an equivalent ML-like syntax, but in the latter case you must not rely on ML's order of evaluation. (a) Using the continuation passing style, show how to model the following impure code without use of ref or := but so that the exact sequence of values that k takes during a calculation still arise. val k = ref 0; fun c(n, r) = ( k := !k + r; if r=0 orelse r=n then 1 else c(n-1,r-1) + c(n-1,r)); You may suppose that conditions and basic arithmetic are available to you as existing primitives, so if, orelse and + can all appear in your answer, even though !, := and the use of ; that indicates sequential execution must not. [14 marks] (b) Discuss how exception-handling mechanisms such as ML's raise and handle can be mapped onto uses of continuations. Construct a small example to illustrate your explanation. [6 marks] All code you write will be expected to be annotated so that it is easy for a human reader to see what it sets out to achieve: clarity of exposition will be considered much more important than exact syntactic validity in any particular programming language's syntax.

) A transaction processing system is using a write-ahead log as a mechanism for providing persistent storage. What information must be written to the log (i) when a transaction starts; (ii) when a transaction performs an operation on a persistent object; (iii) when a transaction commits? [2 marks each] (b) Describe how the log can be used to roll-back a transaction that has aborted or become deadlocked. [6 marks] (c) The log can also be used to recover after some kinds of system failure. (i) Describe how the log can be used to recover after a fail-stop crash. [2 marks] (ii) What is meant by checkpointing? How will using it affect the structure of the log and the recovery procedure after a crash? [6 marks] 3 [TURN OVER CST.2004.6.4 SECTION B 5 Computer Graphics and Image Processing (a) Explain why display devices appear to be able to reproduce (almost) all the colours of the spectrum using only red, green and blue light. [4 marks] (b) Describe an algorithm (other than thresholding) which will convert a greyscale image (8 bits per pixel) to a bi-level black and white image (1 bit per pixel), with the same number of pixels, while retaining as much detail as possible. [8 marks] (c) Explain what specular and diffuse reflection are in the real world. State and explain equations for calculating approximations to both in a computer. [8 marks] 6 Databases (a) Define the operators of the core relational algebra. [5 marks] (b) Let R be a relation with schema (A1, . . . , An, B1, . . . , Bm) and S be a relation with schema (B1, . . . , Bm). The quotient of R and S, written R S, is the set of tuples t over attributes (A1, . . . , An) such that for every tuple s in S, the tuple ts (i.e. the concatenation of tuples t and s) is a member of R. Define the quotient operator using the operators of the core relational algebra. [8 marks] (c) The core relational algebra can be extended with a duplicate elimination operator, and a grouping operator. (i) Define carefully these two operators. [3 marks] (ii) Assuming the grouping operator, show how the duplicate elimination operator is, in fact, unnecessary. [2 marks] (iii) Can the grouping operator be used to define the projection operator? Justify your answer.

9. Which of the following are public relations activities: A. Writing press releases, distributing company newsletters, and sponsoring events B. Holding press conferences, identifying trends, and hiring new staff members C. Sponsoring events, developing new products, and distributing company newsletters D. Identifying trends, writing press releases, and hiring new staff members 90. The cost of employing product inspectors is a(n) A. appraisal cost. B. prevention cost. C. internal failure cost. D. external failure cost. 91. Because __________ measures of risk can be too general, it is also useful to perform __________ assessment of risk. A. quantitative; qualitative B. qualitative; quantitative C. preventative; responsive D. responsive; preventative 92. Which of the following is a potential risk of implementing enterprise risk management (ERM) software: A. Standardization of reporting B. More emphasis on risk C. Loss of data during the transfer D. Less efficient use of resources 93. Salespersons should have good communication skills, but the sales presentation should not include too many __________ words. A. expressive B. picturesque C. personal D. technical 94. Which management function lays the groundwork for all of the other management functions? A. Directing B. Organizing C. Staffing D. Planning 95. One way that managers can promote ethical behavior on the part of everyone in the business is by encouraging employees to A. develop a code of ethics. B. report unethical actions. C. be thoughtful of others. D. avoid social situations. 96. The ski shop manager set an objective to increase sales by 10% over the previous year even though the forecast was for a mild and rainy winter. The manager's objective was A. reasonable. B. practical. C. unrealistic. D. scientific.

Chad is buying a new car. Although the first car is a great deal and a more practical choice, he just loves the look of the second car. As a result, he decides to purchase the second car. His decision is based on which of the following internal factors: A. Insight or intuition B. Experience C. Framing D. Emotion 74. Time management helps to reduce stress because it A. provides less time for rest and relaxation. B. increases feelings of pressure and tension. C. encourages procrastination in planning necessary activities. D. allows adequate time for personal and professional activities. 75. Who typically reviews and approves the guidelines for running a corporation, which are also known as corporate governance policies? A. The investors B. The shareholders C. The management team D. The board of directors 76. What is the relationship between shareholders and the board of directors? A. The shareholders pay dividends to the board of directors. B. The board of directors represents the shareholders. C. The shareholders make decisions for the board of directors. D. The board of directors holds the shareholders accountable. 77. An organization should include independent members on its board of directors because they A. provide an objective perspective. B. represent the interests of management. C. understand the company's inner workings. D. are less likely to act unethically. 78. When buyers and sellers have agreed on a value for a product, they have established the A. price policy. B. exchange price. C. equilibrium price. D. price line. 79. True or false: In determining the selling price of a good or service, most of the factors to be considered by the seller are internal to the business. A. True, most factors affecting price are internal to the business. B. False, most factors affecting price are not controlled by the firm. C. True, most factors affecting price are directly controlled by the business. D. False, most factors affecting price are directly controlled by the business

1 Data Structures and Algorithms (a) Describe an efficient algorithm to determine whether two finite line segments in a plane intersect. You may assume that the end points of each line are given as x-y coordinates. [8 marks] (b) Describe in detail an efficient algorithm to find the convex hull of a set of points lying on a plane. Show that the complexity of the Graham scan used in the algorithm is O(n) and that the algorithm as a whole has complexity O(n log n). [8 marks] (c) Discuss how it is possible to eliminate many of the points before the convex hull algorithm is entered. [4 marks] 2 Computer Design The ARM processor allows the second operand to be shifted by an arbitrary amount. In order to improve the performance, a six-stage pipeline is proposed with the following stages: instruction decode and shift execute memory register fetch register fetch operand 2 access write back (a) What are control hazards and how could they be resolved in the above pipeline? [4 marks] (b) What are data hazards and how could they be resolved in the above pipeline? [4 marks] (c) What are feed-forward paths and where could they be added to the above pipeline to improve performance? [6 marks] (d) Why might a branch instruction result in pipeline bubbles and how many bubbles will appear in the above pipeline as a result of taking a branch instruction?