...Valuing Energy Options in a One Factor Model Clewlow and Strickland Valuing Energy Options in a One Factor Model Fitted to Forward Prices Les Clewlow and Chris Strickland This Version: 15th April 1999 School of Finance and Economics University of Technology, Sydney, Australia The Financial Options Research Centre Warwick Business School, The University of Warwick, UK Centre for Financial Mathematics Australian National University, Canberra, Australia Instituto de Estudios Superiores de Administración Caracas, Venezuela The authors would like to acknowledge the financial support and hospitality of the School of Finance and Economics, University of Technology, Sydney. All comments welcome. chris_strickland@compuserve.com les_clewlow@compuserve.com The authors would also like the acknowledge discussions with Nadima El-Hassan (UTS) and the research assistance of Christina Nikitopoulos. All errors remain our own. energy_single_factor 1 Valuing Energy Options in a One Factor Model Clewlow and Strickland Valuing Energy Options in a One Factor Model Fitted to Forward Prices Les Clewlow and Chris Strickland Abstract In this paper we develop a single-factor modeling framework which is consistent with market observable forward prices and volatilities. The model is a special case of the multi-factor model developed in Clewlow and Strickland [1999b] and leads to analytical pricing formula for standard options, caps, floors, collars and swaptions. We also show how American style...
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...“correct” variables in the model as the effects of model misspecification can be detrimental. A misspecified model is one that does not include the best predictor variables: • underspecified model • overspecified model 2 Underspecified Model An underspecified model is one that fails to include important predictor variables and the effects of omitting important predictor variables are: • produce inaccurate estimates of the regression coefficients • produce inaccurate predictions of new response values • overestimate σ ε2 with MSE 3 Underspecified Model = • overestimate sb j 1 MSE 1 − R2 j ∑( X n i =1 ij −X) 2 since MSE is too large. predse • overestimate= MSE 1 + x ( * X ′X ) x*′ ( −1 ) since MSE is too large. 4 Overspecified Model An overspecified model is one that includes extra predictor variables and the effects are: • Multicollinearity 1 n 2 = MSE X −X) • overestimate sb 2 ∑ ( ij j since R 2 is too large. j • overestimate= predse since 1 + x 1− Rj i =1 ( * ′X ) x*′ is too large. (X −1 5 ) ′X ) x*′ MSE 1 + x ( X * −1 ( ) Variable Selection Techniques Automatic variable selection techniques: • All-Possible-Regressions Procedure/Best Subsets Regression (with several criteria to choose which is the best regression) • Forward Stepwise Regression • Forward Selection • Backward Elimination 6 All-Possible-Regressions Procedure This procedure calls for considering...
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...Applied Regression Analysis 41100-81 Christian Hansen Winter 2015 “I pledge my honor that I have not violated the Honor Code during this assignment.” Kataras, Peter Foltyn, Tom Erzen, Robert Scholl, Katie In order to begin we first had to gain a high level understanding of the 6000 observations that we were given. We ran descriptive statistics on all of the original variables after transforming the variable Color into a dummy variable called White (White Wine=1, Red wine=0). Descriptive Statistics | | N | Minimum | Maximum | Mean | Std. Deviation | quality | 6000 | 2.5000 | 9.5000 | 5.825317 | .9206965 | fixed_acidity | 6000 | 3.8000 | 15.9000 | 7.221233 | 1.3094165 | volatile_acidity | 6000 | .0800 | 1.5800 | .340727 | .1653986 | citric_acid | 6000 | .0000 | 1.6600 | .318008 | .1455540 | residual_sugar | 6000 | .6000 | 65.8000 | 5.425650 | 4.7411670 | chlorides | 6000 | .0100 | .6100 | .056483 | .0344872 | free_sulfur_dioxide | 6000 | 1.0 | 289.0 | 30.482 | 17.7550 | total_sulfur_dioxide | 6000 | 6.0 | 440.0 | 115.576 | 56.5940 | density | 6000 | .99 | 1.04 | .9949 | .00504 | pH | 6000 | 2.74 | 4.01 | 3.2195 | .16022 | sulphates | 6000 | .2200 | 2.0000 | .532073 | .1487300 | alcohol | 6000 | 8.0000 | 14.9000 | 10.491008 | 1.1901957 | White | 6000 | 0 | 1 | .75 | .433 | Some of our variables in the dataset have very tight ranges, for example density has a min of .99 and a max of 1.04. On the other hand, total sulfur dioxide...
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...Payoff Diagrams (16p) Draw the gross payoff (not net-payoff/profit) diagram as a function of MLM stock for the following portfolios consisting of: (Strike values are given in parentheses) (a) one long position in the stock and two short positions in the same put option (K). (b) two long positions in the stock, two short call options (2K), and one long position ina put (K). (c) two short positions in the stock, two long call options (2K), and one short put option(3K). (d) one long position in the stock, two short call options (2K), two short call options (3K),and one short put option (2K). For this question, take into account the net profit only for the stock. You can assume that the stock is purchased at a price of K. Binomial Model (27p) Chevron Corporation has stakes in various oil development projects in Yemen and is considering to bid on a development of a new oil platform in Yemen in the future. However, due to ongoing civil war in Yemen and the instability of the Yemeni Currency (YER), Chevron wants to be hedged against two possible scenarios: * First scenario: The country becomes stable in the future and Chevron decides to go on with the bid and the bid is accepted, in that case Chevron would need Yemeni Rial (YER). * Second scenario: The country’s situation deteriorates and Chevron is forced to liquidate its current assets, in that case Chevron would want to exchange Yemeni Rial for USD and would want to be hedged against a possible depreciation...
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...Life Coach: Drug Issues Jared Hall Kaplan University CM107-01 Professor Gregg August 8, 2011 Life Coach: Drug Issues Dear Tom, As someone I have been friends for over ten years, it has not been easy for me to see you make some bad choices in your life. In the last few years, you have been arrested on multiple occasions for having possession of illegal drugs; you have lost your wife, and visitation rights for you to be able to see your kids until you straighten up your life. But you have been making improvements such as going to drug rehab and trying to find a job. Just to be clear, a life coach is not a therapist. It’s someone that is a friend who will help you improve your career and your life so you can get back on your feet into the direction that you should be going. (Hamilton,1996). If you choose to decide to hire a life coach you will be introduce to what is known as the Hero’s journey. It’s long-marathon journey that will help you get to your full potential. As a friend, I know you have a lot more in you than you really show. By taking this Hero’s journey marathon you will be able to be succeeding at your full potential. Life is a long marathon and it seems like things come up when you less expect it and everything comes down before you can even blink your eye. By choosing to take the hero’s journey you will be able to separate from your life struggles and be able to move on in the direction your family and friends want you to go in...
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...Addiction is one of the most common and devastating diseases in the United States. Drug abuse and addiction have negative consequences for individuals and for society. Assessments of the total overall costs of substance abuse in the United States, to include productivity, health, and crime related costs exceed $600 billion annually. Drug addiction is a brain-related disease that requires a treatment plan that addresses the problem of addiction effectively and sustainably. If left untreated, the destructive effects of drug addiction eventually damage every aspect of the addict's life. The goal of a treatment plan is to help the addict be able to live a life free of drug abuse and integrate with family and society in a healthy and productive...
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...$100/(1.10)6 = $56.45. $100/(1.05)12 = $55.68. $100/e.20×3 = $54.88. y= So yB = and yA = 2nLN nSN 1 + c/2 −1 . P/100 2 · 184 1 + .09125/2 − 1 = 2.991185% 105 103.6776495/100 2 · 184 1 + .09125/2 − 1 = 2.778233% . 105 103.7401495/100 2. Remember we are trying to find r such that the growth in our initial investment is the ˙ same as the growth from an alternative investment providing a rate of r(m). That is, find r ˙ Part a. Part b. Part c. Part d. ˙ ˙ such that er = (1 + r(m)/m)m so r = m ln(1 + r(m)/m). m = 1: ln(1.04) = 3.922%. m = 1: ln(1.20) = 18.232%. m = 4: 4 ln(1.05) = 19.516%. m = 1: ln(2) = 69.315%. In addition, we have Part b. Ignoring for the moment any restrictions on lot size, we note that a cash flow of $100 to be received on 12/31/92 and purchased on 9/17/92 is available either in the form of $100 par amount of the 12/31/92 bill or in the form of $100/(1+.09125/2) par amount of the 9 1/8’s of 12/31/92. (Indeed, since $100 par of the 9 1/8’s will pay off $(100 + 9.125/2) on 12/31/92, $100/(1 + .09125/2) par amount of the 9 1/8’s will pay off $100.) Can we buy this cash flow low through one instrument and sell it high through the other? We must see if the asked price of one of the instruments is lower than the bid price of the other. For the T -bill, we have computed from Example 14 the asked price: A PBILL ≈ 99.17 . B PBILL = 100 1 − d nSM 360 = 100 1 − .0288 105 360 ≈ 99.15 . 3. Part a. Settlement is 9/17/92, the next coupon date is 12/31 the last coupon date is 6/30/92...
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...Applied Thermal Engineering 29 (2009) 75–90 www.elsevier.com/locate/apthermeng An axiomatic design approach in development of nanofluid coolants In Cheol Bang a,*, Gyunyoung Heo b b a Energy Sciences, Global Edge Institute, Tokyo Institute of Technology, 2-12-1-S6-13 O-okayama, Meguro-ku, Tokyo 152-8550, Japan Department of Nuclear Engineering, Kyung Hee University, 1 Seocheon-dong, Giheung-gu, Yongin-si, Gyunggi-do 446-701, Republic of Korea Received 4 September 2007; accepted 4 February 2008 Available online 12 February 2008 Abstract The experimental data for nanofluids in thermal-fluid systems have shown that the new fluids promise to become advanced heat transfer fluids in terms of thermal performance. While enhancing thermal characteristics, the solid–liquid mixtures present an unavoidable disadvantage in terms of pumping cost for economic operation of thermal-fluid systems. In addition, there is a lack of agreement between experimental data provided in the literature. The present work found that there would be no comprehensible design strategy in developing nanofluids. In this work, the Axiomatic Design (AD) theory is applied to systemize the design of nanofluids in order to bring its practical use forward. According to the Independence Axiom of the AD theory, the excessive couplings between the functional requirements and the parameters of a nanofluid system prevent from meeting the functional goals of the entire system. At a parametric level, the design of a nanofluid...
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...DISCUSSION PAPER ON THE ENHANCED K+12 BASIC EDUCATION PROGRAM DepEd discussion paper 05 October 2010 ! "! Discussion Paper As of 05 October 2010 ! DISCUSSION PAPER ON THE ENHANCED K+12 BASIC EDUCATION PROGRAM Table of Contents RATIONALE ............................................................................................................... 3 HISTORICAL BACKGROUND ................................................................................... 5 EDUCATION VISION.................................................................................................. 6 GOALS........................................................................................................................ 7 BENEFITS OF ENHANCED BASIC EDUCATION PROGRAM................................. 7 ENHANCED K+12 BASIC EDUCATION MODEL...................................................... 8 GUIDING PRINCIPLES ............................................................................................ 10 ACTION STEPS........................................................................................................ 11 List of Figures and Tables Table 1 Philippine Average TIMSS Scores ................................................................. 3 Table 2 Unemployment Statistics in the Philippines, 2010 ......................................... 4 Table 3 Comparative Data on the Basic Education Programs in Asia ........................ 4 Figure 1 K-6-4-2 Model ....................
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...byte can be stored To write to RAM: CPU sends signal to RAM over the bus g to write (store) value into byte of RAM Address in RAM Value to be written To read from RAM: CPU uses similar process (see example in Figure 1-3 on next slide) 5 CPU Reads Byte 4 from RAM The CPU uses the same bus to read the current value of a byte in RAM as it does to send a message to RAM. The read request lists the address of the particular byte, asking for its value. RAM returns the binary value stored at that address. CPU Reads Byte 4 from RAM 6 Figure 1-3 Writing Individual Bits in Byte 4 of RAM RAM circuitry sends a slightly different electrical input to the bits that need to store a 1 versus a 0 to control the capacitors . Essentially, RAM chooses one of two inputs to each bit, which results in either a full or partial charge in the capacitor, which in turn represents either a 1 or 0, respectively. Writing Individual Bits in Byte 4 of RAM 7 Figure 1-4 Converting Binary...
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... Output: – – – – – PERT/CPM is supposed to answer questions such as: ■ How long does the project take? ■ What are the bottle-neck tasks of the project? ■ What is the time for a task ready to start? ■ What is the probability that the project is finished by some date? ■ How additional resources are allocated among the tasks? PERT Network: • • • • • It is a directed network. Each activity is represented by a node. An arc from task X to task Y if task Y follows task X. A ‘start’ node and a ‘finish’ node are added to show project start and project finish. Every node must have at least one outgoing arc except the ‘finish’ node. Example of Foundry Inc., p.523 Activity A B C D E F G H Immediate Predecessors A B C C D, E F, G PERT Network for Foundry Inc. Example Example of a Hospital Project: Activity A B C D E F G H I J K Immediate Predecessor(s) — — A B B A C D A E, G, H F, I, G PERT Network for Hospital Project Performance Time t of an Activity § t is calculated as follows: a + 4m + b t = 6 where a=optimistic time, b=pessimistic time, m=most likely time. § Note: t is also called the expected performance time of an activity. Variance of Activity...
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...our algorithm performs favorably in comparison to several state-of-the-art algorithms. In particular, it runs orders of magnitude faster than the lagged diffusivity algorithm for TV-based deblurring. Some extensions of our algorithm are also discussed. Key words. half-quadratic, image deblurring, isotropic total variation, fast Fourier transform AMS subject classifications. 68U10, 65J22, 65K10, 65T50, 90C25 DOI. 10.1137/080724265 1. Introduction. In this paper, we propose a fast algorithm for reconstructing images from blurry and noisy observations. For simplicity, we assume that the underlying images have square domains, but all discussions can be equally applied to rectangle domains. Let 2 2 2 u0 ∈ Rn be an original n×n grayscale image, K ∈ Rn ×n represent a blurring (or convolution) 2 2 operator, ω ∈ Rn be additive noise, and f ∈ Rn be an observation which...
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...CHAPTER 14 CHEMICAL KINETICS PRACTICE EXAMPLES 1A (E) The rate of consumption for a reactant is expressed as the negative of the change in molarity divided by the time interval. The rate of reaction is expressed as the rate of consumption of a reactant or production of a product divided by its stoichiometric coefficient. A 0.3187 M 0.3629 M 1min rate of consumption of A = = = 8.93 105 M s 1 t 8.25 min 60 s rate of reaction = rate of consumption of A2 = 8.93 105 M s 1 4.46 105 M s 1 2 1B (E) We use the rate of reaction of A to determine the rate of formation of B, noting from the balanced equation that 3 moles of B form (+3 moles B) when 2 moles of A react (–2 moles A). (Recall that “M” means “moles per liter.”) 0.5522 M A 0.5684 M A 3moles B rate of B formation= 1.62 104 M s 1 60s 2 moles A 2.50 min 1min 2A (M) (a) The 2400-s tangent line intersects the 1200-s vertical line at 0.75 M and reaches 0 M at 3500 s. The slope of that tangent line is thus 0 M 0.75 M slope = = 3.3 104 M s 1 = instantaneous rate of reaction 3500 s 1200 s The instantaneous rate of reaction = 3.3 104 M s 1 . (b) At 2400 s, H 2 O 2 = 0.39 M. At 2450 s, H 2 O 2 = 0.39 M + rate t At 2450 s, H 2 O 2 = 0.39 M + 3.3 10 4 mol H 2 O 2 L1s 1 50s = 0.39 M 0.017 M = 0.37 M 2B (M) With only the data of Table 14.2 we can use only the reaction rate during the...
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...spot rates and forward rates PART II: MEASUREMENT OF INTEREST RATE RISK 7) Introduction to the measurement of interest rate risk 8) Term structure and volatility of interest rates PART III: EMBEDDED OPTIONS AND INTEREST RATE DERIVATIVES 9) Valuing bonds with embedded options 10) Interest rate derivative instruments 11) Valuation of interest rate derivative instruments 2 • • 1. Features of Debt Securities • Issuers: – Central government (e.g. US government) – Government agency (e.g. Fannie Mae, Freddie Mac) – Municipal government (e.g. city of Detroit) – Corporation (e.g. Coca-cola) – Supranational government (e.g. World Bank) Categories of Fixed income securities 1. Debt Obligations: • Borrower promises to pay amounts x1…x2 at times t1…tn to Lender (creditor) • Interest and Principal 2. Preferred stock: • Ownership interest in a corporation • Priority over common stockholders Bond’s indenture: – Contains promises of the issuer and bondholder rights – Identifies a trustee as representative of the interests of bondholders – Contains covenants • • • • • • • Affirmative covenants – What borrower should do, e.g.: • Pay interest and principal on timely basis • Pay all taxes when due • Maintain all properties in good condition Negative covenants – What borrower is not allowed to do, e.g.: • Not to issue additional debt Term to maturity (maturity, term): years remaining – 1 to 5 years=short term – 5 to 12 years=intermediate term – More than 12 years=long...
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...acaDemy Class 9 NCO, NSO, IMO, IEO Sample Paper 2014 careers 360 A Career is a Life NatioNal DefeNce acaDemy CLASS SAMPLE PAPER 2014-15 SYLLABUS 9 The actual test paper has 50 questions. Time allowed : 60 minutes. There are 4 sections: 10 questions in section I, 10 in section II, 25 in section III and 5 in section IV. Section – I (Mental Ability) : Number Systems, Polynomials, Coordinate Geometry, Linear Equations in Two Variables, Introduction to Euclid’s Geometry, Lines and Angles, Triangles, Quadrilaterals, Areas of Parallelograms and Triangles, Circles, Constructions, Heron’s Formula, Surface Areas and Volumes, Statistics, Probability. Section – II (Logical and Analytical Reasoning) : Problems Based on Figures, Odd One Out, Series Completion, Coding-Decoding, Mathematical Reasoning, Analytical Reasoning, Mirror Images, Embedded Figures, Direction Sense Test, Cubes and Dice. Section – III (Computers and IT) : Algorithms and Flowcharts in Programming, Visual Basic, Animations, HTML, Internet and Viruses, MS-Word, MS-Excel, MS-PowerPoint, Hardware, Software, Input & Output Devices, Memory & Storage Devices, Flash, Networking, Latest Developments in the field of IT. Section – IV (Achievers Section ) : Syllabus as per section III. Questions are based on Windows 7 and MS-Office 2010. The actual test paper has 50 questions. Time allowed : 60 minutes. There are 3 sections: 15 questions in section I, 30 in section II and 5 in section III. SYLLABUS Section – I (Mental...
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