1/12 Your lecturer Introduction to Module Goals Module outline Module material Module assessment Contact details SMM313 Numerical Methods: Applications Module Outline Ioannis Kyriakou
[email protected] www.cass.city.ac.uk/experts/I.Kyriakou Cass Business School City, University of London Ioannis Kyriakou Module Outline 2/12 Your lecturer Introduction to Module Goals Module outline Module material Module assessment Contact details Your lecturer Work experience: 2011 Senior Lecturer in Actuarial Finance, Faculty of Actuarial Science & Insurance, Cass Business School, City, University of London 2016 Visiting Professor, Dipartimento di Studi per lEconomia e lImpresa, Università del Piemonte Orientale 2018 A¢ liated Faculty, Cyprus International Institute of Management 201011 Lloyds Investment Risk Model project analyst, Lloyds Treasury and Investment Management Quali
cations achieved: 2016 Diploma in Actuarial Techniques, Institute and Faculty of Actuaries, UK 200610 PhD Finance: E¢ cient valuation of exotic derivatives with path-dependence and early-exercise features, Cass Business School, City, University of London 200506 MSc Risk and Stochastics (with Distinction), London School of Economics and Political Science 200205 BSc (Hons) Actuarial Science (First Class), Cass Business School, City, University of London Ioannis Kyriakou Module Outline 3/12 Your lecturer Introduction to Module Goals Module outline Module material Module assessment Contact details Your lecturer Research interests: Stochastic Asset Modelling Exotic Derivatives Freight Market and Energy Commodity Markets Numerical Methods and Computational Finance: Transform Techniques and Monte Carlo Simulation Pension Product Design and Communication Investor Sentiment: Real Assets Ioannis Kyriakou Module Outline 4/12 Your lecturer Introduction to Module Goals Module outline Module material Module assessment Contact details Introduction to Module As the
nancial models and option contracts used in practice are becoming increasingly complex, e¢ cient methods have to be developed to cope with such models. In the absence of true closed-form solutions, standard numerical methods used in computational
nance include: Monte Carlo simulation Lattices Numerical integration (quadrature) / transform methods Partial-(integro) di¤erential equation (PIDE) methods (not considered in this module) Within any pricing and risk-management system, interesting questions can be raised: Product pricing requires robust numerical techniques. Model calibration additionally relies on e¢ ciency and speed of computation. Practitioners demand fast and accurate price sensitivities. In this module, we present state-of-the-art methodologies and their applications in
nance. Ioannis Kyriakou Module Outline 5/12 Your lecturer Introduction to Module Goals Module outline Module material Module assessment Contact details Goals Understand how to compute prices and price sensitivities of complex derivative instruments using numerical methods. Become aware of practical (numerical) issues in derivatives valuation and learn how to cope with these / reduce their e¤ect. Recognize the merits and limitations of di¤erent numerical techniques. Study univariate, multivariate modelling, and advanced stochastic asset price models. Perform model calibration. Construct and implement relevant codes in Matlab. Ioannis Kyriakou Module Outline 6/12 Your lecturer Introduction to Module Goals Module outline Module material Module assessment Contact details Module outline: Monte Carlo simulation Introduce and explore the inverse transform method for generating random samples. Generate univariate normal samples. Generate multivariate normal samples. Introduce principles of derivatives pricing by Monte Carlo simulation. Apply Monte Carlo simulation in pricing: Path-independent derivatives: European plain vanilla options, etc. Path-dependent, exotic (nonstandard) derivatives: Asian, barrier, lookback options, etc. Options depending on multiple assets. Explore the randomness of Monte Carlo price estimates. Introduce and implement variance reduction techniques. Perform estimation of price sensitivities. Ioannis Kyriakou Module Outline 7/12 Your lecturer Introduction to Module Goals Module outline Module material Module assessment Contact details Module outline: Multinomial lattices & Fourier transforms Extend the classical notion of a binomial lattice to a multinomial lattice. Demonstrate the accuracy gain of a multinomial lattice. Apply to pricing path-independent and path-dependent options, and options with possible early exercise (Bermudan / American type). Explain the notion of the discrete Fourier transform. Demonstrate its relevance to option pricing on a multinomial lattice. Discuss implementation using the fast Fourier transform. Ioannis Kyriakou Module Outline 8/12 Your lecturer Introduction to Module Goals Module outline Module material Module assessment Contact details Module outline: Advanced stochastic modelling & Model calibration I In the past couple of years a vast body of literature has considered the modelling of (log-)asset returns as Lévy processes, due to their ability to adequately describe their empirical features and provide a reasonable
t to the implied volatility surfaces observed in option markets. Nowadays, numerical integration methods, usually based on a transformation to the Fourier domain (so-called transform methods), are very popular being very e¢ cient for pricing products (path-independent / dependent, vanilla / exotic, European / American, multi-asset,...) under general underlying model assumptions. Thus, transform methods are very useful in calibration: Monte Carlo simulation does not generally serve to this end... Ioannis Kyriakou Module Outline 9/12 Your lecturer Introduction to Module Goals Module outline Module material Module assessment Contact details Module outline: Advanced stochastic modelling & Model calibration II Apply to path-independent structures: vanilla and digital / cash-or-nothing options (references for more complicated payo¤ structures provided). Extend beyond BlackScholes model to exponential Lévy models. Perform model calibration. Compute implied volatility pro
les. Introduce stochastic volatility. Ioannis Kyriakou Module Outline 10/12 Your lecturer Introduction to Module Goals Module outline Module material Module assessment Contact details Module material Slides will be made available electronically through Moodle. Matlab-based exercises we deal with in lectures and computer labs will also be made available through Moodle. Ioannis Kyriakou Module Outline 11/12 Your lecturer Introduction to Module Goals Module outline Module material Module assessment Contact details Module assessment Group coursework (25%): Pre-assigned groups by course o¢ ce Submission deadline: TBC by course o¢ ce Written exam (75%): 2 hours & 15 mins duration Closed-book Calculators permissible, NO PCs Exact date will be con
rmed by the course o¢ ce in due course Ioannis Kyriakou Module Outline 12/12 Your lecturer Introduction to Module Goals Module outline Module material Module assessment Contact details Contact details E:
[email protected] H: www.cass.city.ac.uk/experts/I.Kyriakou SSRN author page: http://ssrn.com/author=1123635 Room number: 5094 Appointment requests by e-mail Ioannis Kyriakou Module Outline
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