Module Manual Quantitative Finance

Total Page:16

File Type:pdf, Size:1020Kb

Module Manual Quantitative Finance module manual of the M. Sc. degree programme Quantitative Finance Date: Apr-13 A. Overview of the Degree Programme ............................................................................................................2 1. Structure of Curriculum: M.Sc. Quantitative Finance ............................................................................. 2 2. Programme Schedule: M.Sc. Quantitative Finance ................................................................................. 3 B. Modules provided by the Faculty of Business, Economics and Social Sciences ...........................................4 1. Modules in the Compulsory Section Financial Economics ...................................................................... 4 Theory of Financial Economics .....................................................................................................................4 Capital Markets and Corporate Finance .......................................................................................................9 2. Modules in the Compulsory Section Econometrics for Finance ............................................................ 11 Advanced Statistics I .................................................................................................................................. 11 Econometrics I ........................................................................................................................................... 12 Empirical Methods for Finance .................................................................................................................. 13 C. Modules provided by the Faculty of Mathematics and Natural Sciences ................................................. 15 1. Modules in the Compulsory Section Mathematical Finance ................................................................. 15 Computational Finance.............................................................................................................................. 15 Mathematical Finance ............................................................................................................................... 16 3. Modules of the Specialization in Mathematical Finance ...................................................................... 17 Risk Management ...................................................................................................................................... 17 Current Issues in Mathematical Finance ................................................................................................... 18 Current Issues in Computational Finance .................................................................................................. 19 Partial Differential Equations and Mathematical Finance ......................................................................... 20 Actuarial Mathematics and Risk Theory .................................................................................................... 21 Optimization in Mathematical Finance ..................................................................................................... 22 Models with jumps in Mathematical Finance ........................................................................................... 23 Interest Rate Theory .................................................................................................................................. 24 D. Seminars .................................................................................................................................................... 25 Seminar on Computational Finance and Mathematical Finance .............................................................. 25 Seminar on Stochastics and Mathematical Finance .................................................................................. 26 Seminar on Financial Economics ............................................................................................................... 27 E. Overview of the Minor Subjects ................................................................................................................ 28 1. Economics .............................................................................................................................................. 28 2. Business ................................................................................................................................................. 28 4. Comparative Economic Sociology ......................................................................................................... 28 5. Political Sciences .................................................................................................................................... 29 6. Agricultural Economics .......................................................................................................................... 29 7. Business Information Systems ............................................................................................................... 29 8. Computer Sciences ................................................................................................................................ 29 9. Empirical Economics .............................................................................................................................. 29 F. Alphabetical Directories ............................................................................................................................ 30 1 A. Overview of the Degree Programme 1. Structure of Curriculum: M.Sc. Quantitative Finance Module Courses SWS* ECTS credits ECTS credits per per module section Econometrics for Finance 24 Econometrics I 3 lect + 2 tut 5 8 Advanced Statistics I 3 lect + 2 tut 5 8 Empirical Methods for Finance 2 x 2 lect 4 8 Financial Economics 20-26 Theory of Financial Economics 3 x 2 lect 6 12 Capital Markets and Corporate Finance 2 x 2 lect 4 8 Seminar on Financial Economics** sem 2 6 Mathematical Finance 26-32 Mathematical Finance 4 lect + 2 tut 6 10 Computational Finance 4 lect + 2 tut 6 10 Specialization in Mathematical Finance 2 lect + 1 tut 3 6 Seminar on Mathematical Finance* S 2 6 Minor subject 14 - Economics*** Varies for the different minor subjects. - Business - Comparative Economic Sociology *** Currently, Empirical Economics and - Political Sciences Economics are the only minor subjects where - Agricultural Economics English as the language of instruction can be - Business Information Systems guaranteed. - Computer Sciences - Empirical Economics*** Master´s thesis 30 *"Semesterwochenstunden" = weekly 45-minute teaching for the duration of one semester of about 12 teaching weeks. ** The seminar can be completed either in the area of Financial Economics or Mathematical Finance. 2 2. Programme Schedule: M.Sc. Quantitative Finance ECTS credits Type of Module Courses P/WP PL SWS per course Sem. year VWL-PEcon-Eco1 Econometrics I V+Ü P K 5 8 r VWL-PQuEc-AdvStat1 Advanced Statistics I V+Ü P K 5 8 semes te MNF-math-finmath1-QF Mathematical Finance V+Ü P K 6 10 1st 1 VWL-QF-FinEc Theory of Financial Economics I V(+Ü) WP K 2 4 18 30 4 VWL-QF-EmpMeth Econometrics for Financial Markets V P MP 2 4 VWL-QF-FinEc Theory of Financial Economics II1 V(+Ü) WP K 2 4 MNF-math-compfin-QF Computational Finance V+Ü P K 6 10 1 semester VWL-QF-FinEc Theory of Financial Economics III V(+Ü) WP K 2 4 BWL-QF-FIWI Capital Markets & Corporate Finance I2 V WP K 2 4 2nd Minor subject: course 1* WP 2 4 16 30 60 VWL-QF-EmpMeth Statistics for Financial Markets4 V P MP 2 4 3 Specialization in Mathematical Finance V+Ü WP K 3 6 BWL-QF-FIWI Capital Markets & Corporate Finance II2 V WP K 2 4 semester Minor subject: course 2* WP 2 4 3rd VWL-QF-Sem Seminar S WP HS 2 6 Minor subject: course 3* WP 2 6 13 30 Master´s thesis 30 4th semester 30 60 120 Explanations: P / WP: status of the module: P = Compulsory / WP = Optional PL: type of examination: K = written examination, HA = essay and presentation, MP = oral examination SWS: Semesterwochenstunden = weekly 45-minute teaching for the duration of one semester of about 12 teaching weeks. types: V = lecture, Ü = tutorial, S = seminar WEcon: Optional modules in Economics AEM: Optional module Applied Empirical Economics * imported modules from other faculties (English as language of instruction cannot be guaranteed) 1: The courses "Theory of Financial Economics I-III" can be elected from the courses of the module Theory of Financial Economics: 1. International Financial Markets, 2. Theory of Financial Markets, 3. Pricing in Derivative Markets, 4. Economics of Risk and Uncertainty, 5. Foreign Exchange Markets–Theory and Empirics, 6. Applied Econometrics of Foreign Exchange Markets, 7. Advanced Topics in Financial Economics. 2: The courses "Capital Markets and Corporate Finance I and II" can be elected from the courses of the module Capital Markets and Corporate Finance: 1. Investments and Capital Markets, 2. Theory of Corporate Finance, 3. Behavioral Finance. 3: The specialization in Mathematical Finance can be elected from the following modules of the Faculty of Mathematics and Natural Sciences: 1. Current Issues in Mathematical Finance (Aktuelle Probleme der Finanzmathematik), 2. Current Issues in Computational Finance (Aktuelle Probleme aus Numerik und Finanzmathematik), 3. Partial Differential Equations and Mathematical Finance (Partielle Differentialgleichungen und Finanzmathematik), 4. Risk Management (English language guaranteed), 5. Actuarial Mathematics
Recommended publications
  • Mathematical Finance
    Mathematical Finance 6.1I nterest and Effective Rates In this section, you will learn about various ways to solve simple and compound interest problems related to bank accounts and calculate the effective rate of interest. Upon completion you will be able to: • Apply the simple interest formula to various financial scenarios. • Apply the continuously compounded interest formula to various financial scenarios. • State the difference between simple interest and compound interest. • Use technology to solve compound interest problems, not involving continuously compound interest. • Compute the effective rate of interest, using technology when possible. • Compare multiple accounts using the effective rates of interest/effective annual yields. Working with Simple Interest It costs money to borrow money. The rent one pays for the use of money is called interest. The amount of money that is being borrowed or loaned is called the principal or present value. Interest, in its simplest form, is called simple interest and is paid only on the original amount borrowed. When the money is loaned out, the person who borrows the money generally pays a fixed rate of interest on the principal for the time period the money is kept. Although the interest rate is often specified for a year, annual percentage rate, it may be specified for a week, a month, or a quarter, etc. When a person pays back the money owed, they pay back the original amount borrowed plus the interest earned on the loan, which is called the accumulated amount or future value. Definition Simple interest is the interest that is paid only on the principal, and is given by I = Prt where, I = Interest earned or paid P = Present value or Principal r = Annual percentage rate (APR) changed to a decimal* t = Number of years* *The units of time for r and t must be the same.
    [Show full text]
  • Math 581/Econ 673: Mathematical Finance
    Math 581/Econ 673: Mathematical Finance This course is ideal for students who want a rigorous introduction to finance. The course covers the following fundamental topics in finance: the time value of money, portfolio theory, capital market theory, security price modeling, and financial derivatives. We shall dissect financial models by isolating their central assumptions and conceptual building blocks, showing rigorously how their gov- erning equations and relations are derived, and weighing critically their strengths and weaknesses. Prerequisites: The mathematical prerequisites are Math 212 (or 222), Math 221, and Math 230 (or 340) or consent of instructor. The course assumes no prior back- ground in finance. Assignments: assignments are team based. Grading: homework is 70% and the individual in-class project is 30%. The date, time, and location of the individual project will be given during the first week of classes. The project is mandatory; missing it is analogous to missing a final exam. Text: A. O. Petters and X. Dong, An Introduction to Mathematical Finance with Appli- cations (Springer, New York, 2016) The text will be allowed as a reference during the individual project. The following books are not required and may serve as supplements: - M. Capi´nski and T. Zastawniak, Mathematics for Finance (Springer, London, 2003) - J. Hull, Options, Futures, and Other Derivatives (Pearson Prentice Hall, Upper Saddle River, 2015) - R. McDonald, Derivative Markets, Second Edition (Addison-Wesley, Boston, 2006) - S. Roman, Introduction to the Mathematics of Finance (Springer, New York, 2004) - S. Ross, An Elementary Introduction to Mathematical Finance, Third Edition (Cambrige U. Press, Cambridge, 2011) - P. Wilmott, S.
    [Show full text]
  • Researchers in Computational Finance / Quant Portfolio Analysts Limassol, Cyprus
    Researchers in Computational Finance / Quant Portfolio Analysts Limassol, Cyprus Award winning Hedge Fund is seeking to build their team with top researchers to join their offices in Limassol, Cyprus. IKOS is an investment advisor that deploys quantitative hedge fund strategies to trade the global financial markets, with a long and successful track record. This is an exciting opportunity to join a fast growing company that is focused on the development of the best research and trading infrastructure. THE ROLE We are looking for top class mathematicians to work with us in modern quantitative finance. Our researchers participate in novel financial analysis and development efforts that require significant application of mathematical modelling techniques. The position involves working within the Global Research team; there is also significant interaction with the trading and fund management teams. The objective is the development of innovative products and computational methods in the equities, futures, currency and fixed income markets. In addition, the role involves statistical analysis of portfolio risk and returns, involvement in the portfolio management process and monitoring and analysing transactions on an ongoing basis. THE INDIVIDUAL The successful candidates will have a first class degree and practical science or engineering problem solving skills through a PhD in mathematics or mathematical sciences, together with excellent all round analytical and programming abilities. The following skills are also prerequisites for the job:
    [Show full text]
  • Mathematics and Financial Economics Editor-In-Chief: Elyès Jouini, CEREMADE, Université Paris-Dauphine, Paris, France; [email protected]
    ABCD springer.com 2nd Announcement and Call for Papers Mathematics and Financial Economics Editor-in-Chief: Elyès Jouini, CEREMADE, Université Paris-Dauphine, Paris, France; [email protected] New from Springer 1st issue in July 2007 NEW JOURNAL Submit your manuscript online springer.com Mathematics and Financial Economics In the last twenty years mathematical finance approach. When quantitative methods useful to has developed independently from economic economists are developed by mathematicians theory, and largely as a branch of probability and published in mathematical journals, they theory and stochastic analysis. This has led to often remain unknown and confined to a very important developments e.g. in asset pricing specific readership. More generally, there is a theory, and interest-rate modeling. need for bridges between these disciplines. This direction of research however can be The aim of this new journal is to reconcile these viewed as somewhat removed from real- two approaches and to provide the bridging world considerations and increasingly many links between mathematics, economics and academics in the field agree over the necessity finance. Typical areas of interest include of returning to foundational economic issues. foundational issues in asset pricing, financial Mainstream finance on the other hand has markets equilibrium, insurance models, port- often considered interesting economic folio management, quantitative risk manage- problems, but finance journals typically pay ment, intertemporal economics, uncertainty less
    [Show full text]
  • Master of Science in Finance (MSF) 1
    Master of Science in Finance (MSF) 1 MASTER OF SCIENCE IN FINANCE (MSF) MSF 501 MSF 505 Mathematics with Financial Applications Futures, Options, and OTC Derivatives This course provides a systematic exposition of the primary This course provides the foundation for understanding the price mathematical methods used in financial economics. Mathematical and risk management of derivative securities. The course starts concepts and methods include logarithmic and exponential with simple derivatives, e.g., forwards and futures, and develops functions, algebra, mean-variance analysis, summations, matrix the concept of arbitrage-free pricing and hedging. Based upon algebra, differential and integral calculus, and optimization. The the work of Black, Scholes, and Merton, the course extends their course will include a variety of financial applications including pricing model through the use of lattices, Monte Carlo simulation compound interest, present and future value, term structure of methods, and more advanced strategies. Mathematical tools in interest rates, asset pricing, expected return, risk and measures stochastic processes are gradually introduced throughout the of risk aversion, capital asset pricing model (CAPM), portfolio course. Particular emphasis is given to the pricing of interest rate optimization, expected utility, and consumption capital asset pricing derivatives, e.g., FRAs, swaps, bond options, caps, collars, and (CCAPM). floors. Lecture: 3 Lab: 0 Credits: 3 Prerequisite(s): MSF 501 with min. grade of C and MSF 503 with min. grade of C and MSF 502 with min. grade of C MSF 502 Lecture: 3 Lab: 0 Credits: 3 Statistical Analysis in Financial Markets This course presents and applies statistical and econometric MSF 506 techniques useful for the analysis of financial markets.
    [Show full text]
  • From Arbitrage to Arbitrage-Free Implied Volatilities
    Journal of Computational Finance 20(3), 31–49 DOI: 10.21314/JCF.2016.316 Research Paper From arbitrage to arbitrage-free implied volatilities Lech A. Grzelak1,2 and Cornelis W. Oosterlee1,3 1Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands; email: [email protected] 2ING, Quantiative Analytics, Bijlmerplein 79, 1102 BH, Amsterdam, The Netherlands 3CWI: National Research Institute for Mathematics and Computer Science, Science Park 123, 1098 XG, Amsterdam, The Netherlands; email: [email protected] (Received October 14, 2015; revised March 6, 2016; accepted March 7, 2016) ABSTRACT We propose a method for determining an arbitrage-free density implied by the Hagan formula. (We use the wording “Hagan formula” as an abbreviation of the Hagan– Kumar–Le´sniewski–Woodward model.) Our method is based on the stochastic collo- cation method. The principle is to determine a few collocation points on the implied survival distribution function and project them onto the polynomial of an arbitrage- free variable for which we choose the Gaussian variable. In this way, we have equality in probability at the collocation points while the generated density is arbitrage free. Analytic European option prices are available, and the implied volatilities stay very close to those initially obtained by the Hagan formula. The proposed method is very fast and straightforward to implement, as it only involves one-dimensional Lagrange interpolation and the inversion of a linear system of equations. The method is generic and may be applied to other variants or other models that generate arbitrage. Keywords: arbitrage-free density; collocation method; orthogonal projection; arbitrage-free volatility; SCMC sampler; implied volatility parameterization.
    [Show full text]
  • Careers in Quantitative Finance by Steven E
    Careers in Quantitative Finance by Steven E. Shreve1 August 2018 1 What is Quantitative Finance? Quantitative finance as a discipline emerged in the 1980s. It is also called financial engineering, financial mathematics, mathematical finance, or, as we call it at Carnegie Mellon, computational finance. It uses the tools of mathematics, statistics, and computer science to solve problems in finance. Computational methods have become an indispensable part of the finance in- dustry. Originally, mathematical modeling played the dominant role in com- putational finance. Although this continues to be important, in recent years data science and machine learning have become more prominent. Persons working in the finance industry using mathematics, statistics and computer science have come to be known as quants. Initially relegated to peripheral roles in finance firms, quants have now taken center stage. No longer do traders make decisions based solely on instinct. Top traders rely on sophisticated mathematical models, together with analysis of the current economic and financial landscape, to guide their actions. Instead of sitting in front of monitors \following the market" and making split-second decisions, traders write algorithms that make these split- second decisions for them. Banks are eager to hire \quantitative traders" who know or are prepared to learn this craft. While trading may be the highest profile activity within financial firms, it is not the only critical function of these firms, nor is it the only place where quants can find intellectually stimulating and rewarding careers. I present below an overview of the finance industry, emphasizing areas in which quantitative skills play a role.
    [Show full text]
  • Financial Mathematics
    Financial Mathematics Alec Kercheval (Chair, Florida State University) Ronnie Sircar (Princeton University) Jim Sochacki (James Madison University) Tim Sullivan (Economics, Towson University) Introduction Financial Mathematics developed in the mid-1980s as research mathematicians became interested in problems, largely involving stochastic control, that had until then been studied primarily by economists. The subject grew slowly at first and then more rapidly from the mid- 1990s through to today as mathematicians with backgrounds first in probability and control, then partial differential equations and numerical analysis, got into it and discovered new issues and challenges. A society of mostly mathematicians and some economists, the Bachelier Finance Society, began in 1997 and holds biannual world congresses. The Society for Industrial and Applied Mathematics (SIAM) started an Activity Group in Financial Mathematics & Engineering in 2002; it now has about 800 members. The 4th SIAM conference in this area was held jointly with its annual meeting in Minneapolis in 2013, and attracted over 300 participants to the Financial Mathematics meeting. In 2009 the SIAM Journal on Financial Mathematics was launched and it has been very successful gauged by numbers of submissions. Student interest grew enormously over the same period, fueled partly by the growing financial services sector of modern economies. This growth created a demand first for quantitatively trained PhDs (typically physicists); it then fostered the creation of a large number of Master’s programs around the world, especially in Europe and in the U.S. At a number of institutions undergraduate programs have developed and become quite popular, either as majors or tracks within a mathematics major, or as joint degrees with Business or Economics.
    [Show full text]
  • Financial Engineering and Computational Finance with R Rmetrics Built 221.10065
    Rmetrics An Environment for Teaching Financial Engineering and Computational Finance with R Rmetrics Built 221.10065 Diethelm Würtz Institute for Theoretical Physics Swiss Federal Institute of Technology, ETH Zürich Rmetrics is a collection of several hundreds of functions designed and written for teaching "Financial Engineering" and "Computational Finance". Rmetrics was initiated in 1999 as an outcome of my lectures held on topics in econophysics at ETH Zürich. The family of the Rmetrics packages build on ttop of the statistical software environment R includes members dealing with the following subjects: fBasics - Markets and Basic Statistics, fCalendar - Date, Time and Calendar Management, fSeries - The Dynamical Process Behind Financial Markets, fMultivar - Multivariate Data Analysis, fExtremes - Beyond the Sample, Dealing with Extreme Values, fOptions – The Valuation of Options, and fPortfolio - Portfolio Selection and Optimization. Rmetrics has become the premier open source to download data sets from the Internet. The solution for financial market analysis and valu- major concern is given to financial return series ation of financial instruments. With hundreds of and their stylized facts. Distribution functions functions build on modern and powerful methods relevant in finance are added like the stable, the Rmetrics combines explorative data analysis and hyperbolic, or the normal inverse Gaussian statistical modeling with object oriented rapid distribution function to compute densities, pro- prototyping. Rmetrics is embedded in R, both babilities, quantiles and random deviates. Esti- building an environment which creates especially mators to fit the distributional parameters are for students and researchers in the third world a also available. Furthermore, hypothesis tests for first class system for applications in statistics and the investigation of distributional properties, of finance.
    [Show full text]
  • Mathematical Finance MS and Ph.D. Course Requirements
    Mathematical Finance M.S. and Ph.D. Course requirements Master of Science with a Specialization in Mathematical Finance The full-time program of study for the M.S. degree specializing in Mathematical Finance focuses on building a solid foundation in applied mathematics, uncovers models used in financial applications, and teaches computational tools for developing solutions. The M.S. degree consists of 36 hours of graduate work including 3 hours of credit for a departmental report or 6 hours of credit for the master’s thesis. Up to 3 hours of graduate work are permitted in other areas such as mathematics, statistics, business, economics, finance or fields as approved by the graduate advisor. M.S. students share core courses with beginning Ph.D. students. To enter the program of study leading to a Master of Science Degree specializing in Mathematical Finance, the applicant must meet the requirements of the Graduate School and of the Department of Mathematics and Statistics. The degree requirements are as follows. A. Completion of the following required courses. A.1 FIN 5328 - Options and Futures A.2 STAT 5328 - Mathematical Statistics I A.3 STAT 5329 - Mathematical Statistics II A.4 MATH 5399 (Special Topics) - Applied Time Series A.5 MATH 6351 - Quantitative Methods with Applications to Financial Data A.6 MATH 6353 - Stochastic Calculus with Applications to Financial Derivatives B. Completion of any two courses from the following elective list. B.1 STAT 5371 - Regression Analysis B.2 STAT 5386 - Statistical Computation and Simulation B.3
    [Show full text]
  • Econophysics: a Brief Review of Historical Development, Present Status and Future Trends
    1 Econophysics: A Brief Review of Historical Development, Present Status and Future Trends. B.G.Sharma Sadhana Agrawal Department of Physics and Computer Science, Department of Physics Govt. Science College Raipur. (India) NIT Raipur. (India) [email protected] [email protected] Malti Sharma WQ-1, Govt. Science College Raipur. (India) [email protected] D.P.Bisen SOS in Physics, Pt. Ravishankar Shukla University Raipur. (India) [email protected] Ravi Sharma Devendra Nagar Girls College Raipur. (India) [email protected] Abstract: The conventional economic 1. Introduction: approaches explore very little about the dynamics of the economic systems. Since such How is the stock market like the cosmos systems consist of a large number of agents or like the nucleus of an atom? To a interacting nonlinearly they exhibit the conservative physicist, or to an economist, properties of a complex system. Therefore the the question sounds like a joke. It is no tools of statistical physics and nonlinear laughing matter, however, for dynamics has been proved to be very useful Econophysicists seeking to plant their flag in the underlying dynamics of the system. In the field of economics. In the past few years, this paper we introduce the concept of the these trespassers have borrowed ideas from multidisciplinary field of econophysics, a quantum mechanics, string theory, and other neologism that denotes the activities of accomplishments of physics in an attempt to Physicists who are working on economic explore the divine undiscovered laws of problems to test a variety of new conceptual finance. They are already tallying what they approaches deriving from the physical science say are important gains.
    [Show full text]
  • Computational Finance
    Computational Finance Christian Bayer & Antonis Papapantoleon Lecture course @ TU Berlin, SS 2013 Important information The course takes place every Monday 12:00{14:00 @ MA 751 Friday 10:00{12:00 @ MA 848 The website of the course is: http://www.math.tu-berlin.de/~papapan/ ComputationalFinance.html contains: course description, recommended literature, and other material related to the course Lecture notes are available on the website E-mails: [email protected] [email protected] Office: MA 703 Office hours: Tuesday 11-12 1 / 22 Structure of the course Teaching (per week): 3h Theory 1h Computational practice (Scilab) Exam: 3 Computational exercises Oral examination Credit points: 10 2 / 22 Key points of the course 1 Review of stochastic analysis and mathematical finance 2 Monte Carlo simulation Random number generation Monte Carlo method Quasi Monte Carlo method 3 Discretization of SDEs Generating sample paths Euler scheme Advanced methods (Milstein) 4 PDE methods (finite differences, finite elements) 5 L´evyand affine processes 6 Fourier methods 7 Pricing American options with Monte Carlo 3 / 22 Books P. Glasserman Monte Carlo Methods in Financial Engineering Springer, 2003 R. Seydel Tools for Computational Finance Springer, 2009 S. Shreve Stochastic Calculus for Finance II Springer, 2004 M. Musiela, M. Rutkowski Martingale Methods in Financial Modeling Springer, 2nd ed., 2005 D. Filipovi´c Term-structure Models: A Graduate Course Springer, 2009 4 / 22 Options European options \plain vanilla" options + call (ST K) − digital 1 ST >B f g exotic options + barrier (ST K) 1 maxt≤T St >B − f g one-touch 1 maxt≤T St >B 1 Pnf g+ Asian ( ST K) n i=1 i − options on several assets Pd i + basket call ( i=1 ST K) best-of call (S 1 − S d K)+ T ^ · · · ^ T − American options + call (Sτ K) − τ: stopping time 5 / 22 Decomposition of options Payoff function: Underlying process: d map f : R R+ random variable X on the path ! d f (x) = (x K)+ space D([0; T ]; R ) − X = S f (x) = 1fx>Bg T + X = max S f (x) = (x1+ +xd K) t≤T t ··· − 1 d ..
    [Show full text]