Economic Scenario Generator: Applications in Enterprise Risk Management. Ping Sun Executive Director, Financial Engineering Numerix LLC
|
|
- Geoffrey Simpson
- 6 years ago
- Views:
Transcription
1 Economic Scenario Generator: Applications in Enterprise Risk Management Ping Sun Executive Director, Financial Engineering Numerix LLC
2 Numerix makes no representation or warranties in relation to information contained in this proposal and shall have no liability or responsibility for any actions taken by the client in reliance on such information. The proposal (including, without limitation, its contents and any related information and documentation) is Numerix proprietary and confidential information and may not be disclosed outside or duplicated, used, or disclosed without consent for any purpose other than to Numerix. This document is protected under the copyright laws of the United States and other countries.
3 Outline Economic Capital and Solvency II: The Role of Economic Scenario Generator (ESG) Risk-Neutral (RN) vs Real World (RW): Bridging the Gap Algorithmic Exposures for Advanced Risk Measures
4 Outline Economic Capital and Solvency II: The Role of Economic Scenario Generator (ESG) Risk-Neutral (RN) vs Real World (RW): Bridging the Gap Algorithmic Exposures for Advanced Risk Measures
5 Economic Capital and Solvency II Basel II motivated, solvency capital requirement of EU insurance companies Pillar 1 Quantitative Measures Technical Provisions Minimal Capital Requirement (MCR) Solvency Capital Requirement (SCR) Pillar 2 Qualitative Processes Corporate Governance Risk Management Supervisory Interaction Capital Add-ons Pillar 3 Reporting & Disclosure Annual Solvency Reports Public Disclosure
6 Economic Capital and Solvency II ESG Requirements Model Choice Capturing the Entire Volatility Surface Describing Volatility Stochasticity and Clustering Handling Tail Distribution Specific Models to Different Asset Classes (interest rate, equity, credit, foreign exchange, inflation, etc.) Model Calibration Risk Neutral Calibrating to implied volatility surface Calibrating to variance swap, etc. Real World Time Series Analysis Based Methods (MLE, etc.) Calibrating to user specified projection Hybrid Model Joint Calibration of Models Across Different Asset Classes Correlation Input and Calibrating to User Projection Martingale Property Fast Model Calibration
7 ESG Example Cliquet Option : PV & Future Greeks
8 Outline Economic Capital and Solvency II: The Role of Economic Scenario Generator (ESG) Risk-Neutral (RN) vs Real World (RW): Bridging the Gap Algorithmic Exposures for Advanced Risk Measures
9 Real World Modeling Risk Neutral vs. Real Word Arbitrage Free Assumption under Risk Neutral (RN) Theory The values of all assets grow at the same instantaneous rate equal the risk-free rate of interest Deviation of the Real World (RW) Asset Dynamics Due to asset exposure to systematic risks and fundamental economic parameters such as risk preferences of investors 30 years of S&P500 accumulation (with dividend reinvestment) versus 30 years of rolling over at the risk-free (Fed Funds) rate (initialised at 1).
10 Real World Modeling Risk Neutral vs. Real Word RN pricing models often follows normal or log-normal distribution In RW historically realized distribution has fatter tail, different from those projected by the RN models. SPX returns distribution compared to Gaussian Source: J. Gatheral, The Volatility Surface: A Practitioner s Guide, Wiley, NJ.
11 Real World Modeling Risk Neutral vs. Real Word The presence of Variance Premium Consider the VIX and 22-day ahead S&P500 return variance. If there is no volatility premium, the VIX should be an unbiased redictor of future S&P500 return variance. Mean VIX=21.9% Mean RV=18.1% CBOE VIX index against 22-day ahead variance of S&P500 returns over the period Jan 1990-Jun Figures are reported as annualised volatilities.
12 Real World Modeling RW Heston Model with Risk Premium ds S = r + φv dt + VdW 1 dv = κ θ V dt + ξ V dw 2 with < dw 1, dw 2 >= ρ Equity premium φv Volatility premium θ and κ RN vs. RW Heston Simulated Real-World and Risk-Neutral Scenarios Risk-Neutral Path Real-World Path 0
13 Real World Modeling RW Heston Model with Risk Premium ds S = r + φv dt + VdW 1 dv = κ θ V dt + ξ V dw 2 with < dw 1, dw 2 >= ρ Equity premium φv Volatility premium θ and κ RN vs. RW Heston 40.00% 35.00% 30.00% 25.00% 20.00% 15.00% 10.00% 5.00% 0.00% Real-World and Risk-Neutral Volatility Paths Real-World Vol Risk-Neutral Vol
14 Hybrid Model Framework Fixed Income Hybrid Model Framework Select any Numerix model, with deterministic or stochastic components Inflation Define IR correlations IR HW1F Joint calibration (S)BK1F IR HW2F IR CIR 2F IR SV-LMM Credit INF JY (HW) INF JY (BK) Equity CR CTM HYBRID MODEL Foreign Exchange EQ BS EQ Dupire EQ Heston EQ Bates EQ LSV Commodities FX BS FX Heston Hybrids CMDTY Black CDMTY S1F CMDTY GS2F CMDTY Heston
15 Hybrid Model Framework Extended to Real World Nuemrix RW Hybrid Model Framework Joint Calibration Martingale Test RW Models in Individual Asset Classes Models with Variance Premium Equity & Foreign Exchange Black Model Heston Model Bates Model (Heston with Jumps) * Interest and Fixed Income Calibrated to IR projection CIR 2F HW 2F * Inflation Jarrow-Yildirim (JY) Model * Commodity Gabillon Model * Credit Transition Model (CTM) Transition probability implies the survival probability * Next Release
16 Outline Economic Capital and Solvency II: The Role of Economic Scenario Generator (ESG) Risk-Neutral (RN) vs Real World (RW): Bridging the Gap Algorithmic Exposures for Advanced Risk Measures
17 Risk Measure Based on Monte Carlo Simulation Risk Measures Market Risk Monte Carlo VaR Expected Shortfall Counter Party Risk Counterparty Credit Exposure (CCE) Potential Future Exposure (PFE) Expected Positive Exposure (EPE) Credit Valuation Adjustment (CVA) Exposure Distribution of Prices, Rates, Indexes on Future Dates Model Probability Measure Pricing Present Value (PV) of any instrument does not depends on the measure, guarantees by the arbitrage free theory CVA is measure independent Distribution Measure Dependent All exposure quantities are measure dependent
18 Option Value in the Future S t S 0 0 t 1 t 2 t 3 t 4 t n = T t
19 Option Value in the Future S t S t2 S 0 0 t 1 t 2 t 3 t 4 t n = T t
20 Option Value in the Future S t S t2 S 0 0 t 1 t 2 t 3 t 4 t n = T t
21 World of Black Scholes S t S t2 S 0 t S 0 e 2 r d 2 t Wt 0 t 1 t 2 t 3 t 4 t n = T t
22 Potential Future Exposure (PFE) PFE for European Call Option with Confidence Level S t S t2 S 0 0 t 1 t 2 t 3 t 4 t n = T t
23 Potential Future Exposure (PFE) PFE q inf x : P V, t, t t x PFE for European Call Option with Confidence Level x 0 - dx 2 e x 2 / % x t PFE d t, S ln t,0 S 0 e 2 2 r d / t x0 2 S / K r d / 2 T t t,0 T t T t r T t S N d e KN d, t e t,0 t, dt,
24 Exposure of Generic Instruments What if the pricing of a generic instrument requires MC? S t S t2 S 0 0 t 1 t 2 t 3 t 4 t n = T t
25 Challenges of Scenario Based Approach Scenario Based Approach (Brute Force) Methodology Generate scenarios Calibrate / Build a model associated to each scenario Price portfolio along each scenario If the portfolio contains plain vanilla instruments we can evaluate the price directly from the generated market Drawbacks Scenario generation There is a large variety of theoretical and phenomenological approaches to the scenario generation which becomes rather ambiguous for large cross-asset systems. Future Market Generation Scenarios of Underlying, Volatility, etc. Model Calibration Performance Nested Monte Carlo
26 Algorithmic Exposure Backward Pricing Backward Pricing with American (Least Square) Monte Carlo F. A. Longstaff and E. S. Schwartz, Valuing American Options by Simulation: A Simple Least-Square Approach Backward MC Pricing Procedure of American Option Generate MC paths, S T i Roll backward in time, determine the optimal exercise time 1. At time T i compute the option value along each MC paths O T i 2. At time T i 1 and along each MC path compute the conditional expectation of the option price via regression Assume the option price is a continuous function of the current state variables, defined through an expansion via certain basis functions Conduct least square fit of the option price along each MC path and determine the expansion coefficients Compute the option prices at time T i 1 as the continuation value from those at the previous time slide T i, V T i 1 3. Determine if it is optimal to exercise the option at T i 1, rather than later, V T i Update the option price if the answer is yes V T i 1 = max V T i 1, O T i 1 4. Roll back to time T i 2, T i 3,, T 0, repeat step 2 and 3 Option Price As a Continuous Function of the Current State Variables Stochastic process is Markovian Certain path-dependency requires extra state variable E.g. Asian or Lookback option
27 Algorithmic Exposure Price vs. Exposure A. Antonov, S. Issakov, and S. Mechkov, Risk January 2015 Backward induction for future values Algorithmic Exposure Procedure On Observation Date t obs, set Exposure the same as price distribution, v t obs = V t obs When roll back in time, apply the exercise update, but skip the conditional expectation. Examples American Option Update Pricing V T i 1 = max V T i 1, O T i 1 Exposure v T i 1 = V T i 1 1 Um T >U n T + O T i 1 1 Um T U n T Roll Procedure Between Dates Pricing V t = E N t Exposure v t = N t v T j N T j The Final Exposure is v = v 0 N t obs Other Examples Includes Bermudan Swaption, Autocap, etc. V T N T F t
28 Algorithmic Exposure Example Algorithmic Exposure Example FX European Option PFE as a Function of Time Horizon : Backward MC Simulation vs. Analytic Formula Numerix Simulation Analytic PFE 6 4 2
29 Algorithmic Exposure Example Algorithmic Exposure Example FX European Option ETL as a Function of Time Horizon : Backward MC Simulation vs. Analytic Formula Numerix Simulation Analytic ETL 6 4 2
30 Algorithmic Exposure Example Algorithmic Exposure Example IR Swap with One Way Collateral Call CCE as a Function of Time Horizon :
31 Algorithmic Exposure Under Real World Measure Algorithmic Exposure under Real World Measure Generate both the RN and RW scenarios from Now Date RW provides the economical scenarios RN provides the pricing scenarios On Observation Date t obs, set Exposure the same as price distribution, v t obs = V t obs When roll back in time, apply the exercise update, but skip the conditional expectation.
32 Algorithmic Exposure Under Real World Measure The nested stochastic pattern: Outer-Loop: real-world dynamics Inner-Loop: risk-neutral dynamics
33 Algorithmic Exposure Under Real World Measure S t RW RN S tobs S 0 0 t 1 t obs t 3 t 4 t n = T t
34 Algorithmic Exposure Under Real World Measure S t RW RN S tobs S 0 0 t 1 t obs t 3 t 4 t n = T t
35 Algorithmic Exposure Under Real World Measure Algorithmic Exposure under Real World Measure Generate both the RN and RW scenarios from Now Date RW provides the economical scenarios RN provides the pricing scenarios On Observation Date t obs, set Exposure the same as price distribution, v t obs = V t obs Resampling of the RN price Distribution Option price v t obs is a continuous function of the current state variables Current state variable distribution is from real world simulation When roll back in time, apply the exercise update, but skip the conditional expectation.
36 Algorithmic Exposure Under Real World Measure Algorithmic Exposure under Real World Measure Generate both the RN and RW scenarios from Now Date RW provides the economical scenarios RN provides the pricing scenarios On Observation Date t obs, set Exposure the same as price distribution, v t obs = V t obs Resampling of the RN price Distribution Option price v t obs is a continuous function of the current state variables Current state variable distribution is from real world simulation When roll back in time, apply the exercise update, but skip the conditional expectation. Remains the same, except for the fixings being based on the RW scenarios
37 Algorithmic Exposure Under Real World Measure Algorithmic Exposure under Real World Measure Real World as Measure Change of Risk Neutral Apply the cross-currency analogy set our initial model as foreign one w.r.t. some FX rate process Set a domestic currency model. The initial model states will get a drift adjustment depending on FX vol and correlation (Quanto Drift) 6 Month LIBOR Averages for Different FX Volatilities (Different Measures)
38 Algorithmic Exposure Under Real World Measure Algorithmic Exposure under Real World Measure Real World as Measure Change of Risk Neutral Apply the cross-currency analogy set our initial model as foreign one w.r.t. some FX rate process Set a domestic currency model. The initial model states will get a drift adjustment depending on FX vol and correlation (Quanto Drift) PEF at 97.5% Confidence for Different FX Volatilities (Different Measures) 10Y cancelable swap on 1 EUR notional : Receiving semi-annually A 6M Libor Paying annually a fixed rate (= 2.57%) Owner has a right to cancel the swap annually from Year 4.
39 Conclusion ESG is One Key Tool in Determining SCR Required By Solvency II Role of Risk Premium : Risk Neutral and Real World Models are Different Not Only in Their Calibration Methods Algorithmic Exposure Provides a Powerful Tool for Computing Risk Factors in Both Risk Neutral and Real World Measures
40 Thank You Copyright 2014 Numerix LLC. All rights reserved. Numerix, the Numerix logo, and CrossAsset are either registered trademarks, or trademarks, of Numerix LLC in the United States and/or other countries.
Counterparty Credit Risk Simulation
Counterparty Credit Risk Simulation Alex Yang FinPricing http://www.finpricing.com Summary Counterparty Credit Risk Definition Counterparty Credit Risk Measures Monte Carlo Simulation Interest Rate Curve
More informationCollateral Management & CSA Discounting. Anna Barbashova Product Specialist CrossAsset Client Solutions Group, Numerix December 11, 2013
Collateral Management & CSA Discounting Anna Barbashova Product Specialist CrossAsset Client Solutions Group, Numerix December 11, 2013 About Our Presenters Contact Our Presenters: Follow Us: Anna Barbashova
More informationWHITE PAPER THINKING FORWARD ABOUT PRICING AND HEDGING VARIABLE ANNUITIES
WHITE PAPER THINKING FORWARD ABOUT PRICING AND HEDGING VARIABLE ANNUITIES We can t solve problems by using the same kind of thinking we used when we created them. Albert Einstein As difficult as the recent
More informationRisk and CVA for exotic derivatives: the universal modeling
Risk and CVA for exotic derivatives: the universal modeling Alexandre Antonov, Serguei Issakov and Serguei Mechkov Numerix Quant Congress USA, New-York July 2011 A. Antonov, S. Issakov and S. Mechkov;
More informationInstitute of Actuaries of India. Subject. ST6 Finance and Investment B. For 2018 Examinationspecialist Technical B. Syllabus
Institute of Actuaries of India Subject ST6 Finance and Investment B For 2018 Examinationspecialist Technical B Syllabus Aim The aim of the second finance and investment technical subject is to instil
More informationMartingale Methods in Financial Modelling
Marek Musiela Marek Rutkowski Martingale Methods in Financial Modelling Second Edition \ 42 Springer - . Preface to the First Edition... V Preface to the Second Edition... VII I Part I. Spot and Futures
More informationMartingale Methods in Financial Modelling
Marek Musiela Marek Rutkowski Martingale Methods in Financial Modelling Second Edition Springer Table of Contents Preface to the First Edition Preface to the Second Edition V VII Part I. Spot and Futures
More informationCalibration Lecture 4: LSV and Model Uncertainty
Calibration Lecture 4: LSV and Model Uncertainty March 2017 Recap: Heston model Recall the Heston stochastic volatility model ds t = rs t dt + Y t S t dw 1 t, dy t = κ(θ Y t ) dt + ξ Y t dw 2 t, where
More informationMonte Carlo Simulations
Monte Carlo Simulations Lecture 1 December 7, 2014 Outline Monte Carlo Methods Monte Carlo methods simulate the random behavior underlying the financial models Remember: When pricing you must simulate
More informationInterest Rate Cancelable Swap Valuation and Risk
Interest Rate Cancelable Swap Valuation and Risk Dmitry Popov FinPricing http://www.finpricing.com Summary Cancelable Swap Definition Bermudan Swaption Payoffs Valuation Model Selection Criteria LGM Model
More informationModelling Counterparty Exposure and CVA An Integrated Approach
Swissquote Conference Lausanne Modelling Counterparty Exposure and CVA An Integrated Approach Giovanni Cesari October 2010 1 Basic Concepts CVA Computation Underlying Models Modelling Framework: AMC CVA:
More informationPricing of a European Call Option Under a Local Volatility Interbank Offered Rate Model
American Journal of Theoretical and Applied Statistics 2018; 7(2): 80-84 http://www.sciencepublishinggroup.com/j/ajtas doi: 10.11648/j.ajtas.20180702.14 ISSN: 2326-8999 (Print); ISSN: 2326-9006 (Online)
More informationInterest Rate Bermudan Swaption Valuation and Risk
Interest Rate Bermudan Swaption Valuation and Risk Dmitry Popov FinPricing http://www.finpricing.com Summary Bermudan Swaption Definition Bermudan Swaption Payoffs Valuation Model Selection Criteria LGM
More informationManaging the Newest Derivatives Risks
Managing the Newest Derivatives Risks Michel Crouhy IXIS Corporate and Investment Bank / A subsidiary of NATIXIS Derivatives 2007: New Ideas, New Instruments, New markets NYU Stern School of Business,
More informationDevelopments in Volatility Derivatives Pricing
Developments in Volatility Derivatives Pricing Jim Gatheral Global Derivatives 2007 Paris, May 23, 2007 Motivation We would like to be able to price consistently at least 1 options on SPX 2 options on
More informationPricing Variance Swaps under Stochastic Volatility Model with Regime Switching - Discrete Observations Case
Pricing Variance Swaps under Stochastic Volatility Model with Regime Switching - Discrete Observations Case Guang-Hua Lian Collaboration with Robert Elliott University of Adelaide Feb. 2, 2011 Robert Elliott,
More informationNumerix Economic Scenario Generator
Numerix Economic Scenario Generator Transparency and Flexibility in an Easy-to-Use Application Risk neutral and real world scenarios Built on the world s largest capital market model library Easy to use
More informationHandbook of Financial Risk Management
Handbook of Financial Risk Management Simulations and Case Studies N.H. Chan H.Y. Wong The Chinese University of Hong Kong WILEY Contents Preface xi 1 An Introduction to Excel VBA 1 1.1 How to Start Excel
More informationAdvanced Topics in Derivative Pricing Models. Topic 4 - Variance products and volatility derivatives
Advanced Topics in Derivative Pricing Models Topic 4 - Variance products and volatility derivatives 4.1 Volatility trading and replication of variance swaps 4.2 Volatility swaps 4.3 Pricing of discrete
More informationSimple Robust Hedging with Nearby Contracts
Simple Robust Hedging with Nearby Contracts Liuren Wu and Jingyi Zhu Baruch College and University of Utah October 22, 2 at Worcester Polytechnic Institute Wu & Zhu (Baruch & Utah) Robust Hedging with
More informationRISKMETRICS. Dr Philip Symes
1 RISKMETRICS Dr Philip Symes 1. Introduction 2 RiskMetrics is JP Morgan's risk management methodology. It was released in 1994 This was to standardise risk analysis in the industry. Scenarios are generated
More informationINTRODUCTION TO THE ECONOMICS AND MATHEMATICS OF FINANCIAL MARKETS. Jakša Cvitanić and Fernando Zapatero
INTRODUCTION TO THE ECONOMICS AND MATHEMATICS OF FINANCIAL MARKETS Jakša Cvitanić and Fernando Zapatero INTRODUCTION TO THE ECONOMICS AND MATHEMATICS OF FINANCIAL MARKETS Table of Contents PREFACE...1
More informationComputer Exercise 2 Simulation
Lund University with Lund Institute of Technology Valuation of Derivative Assets Centre for Mathematical Sciences, Mathematical Statistics Fall 2017 Computer Exercise 2 Simulation This lab deals with pricing
More informationThe Use of Importance Sampling to Speed Up Stochastic Volatility Simulations
The Use of Importance Sampling to Speed Up Stochastic Volatility Simulations Stan Stilger June 6, 1 Fouque and Tullie use importance sampling for variance reduction in stochastic volatility simulations.
More informationOptimal Hedging of Variance Derivatives. John Crosby. Centre for Economic and Financial Studies, Department of Economics, Glasgow University
Optimal Hedging of Variance Derivatives John Crosby Centre for Economic and Financial Studies, Department of Economics, Glasgow University Presentation at Baruch College, in New York, 16th November 2010
More informationInterest Rate Models: An ALM Perspective Ser-Huang Poon Manchester Business School
Interest Rate Models: An ALM Perspective Ser-Huang Poon Manchester Business School 1 Interest Rate Models: An ALM Perspective (with NAG implementation) Ser-Huang Poon Manchester Business School Full paper:
More informationChallenges In Modelling Inflation For Counterparty Risk
Challenges In Modelling Inflation For Counterparty Risk Vinay Kotecha, Head of Rates/Commodities, Market and Counterparty Risk Analytics Vladimir Chorniy, Head of Market & Counterparty Risk Analytics Quant
More informationOptimal Search for Parameters in Monte Carlo Simulation for Derivative Pricing
Optimal Search for Parameters in Monte Carlo Simulation for Derivative Pricing Prof. Chuan-Ju Wang Department of Computer Science University of Taipei Joint work with Prof. Ming-Yang Kao March 28, 2014
More informationLatest Developments: Interest Rate Modelling & Interest Rate Exotic & Hybrid Products
Latest Developments: Interest Rate Modelling & Interest Rate Exotic & Hybrid Products London: 30th March 1st April 2009 This workshop provides THREE booking options Register to ANY ONE day TWO days or
More informationA Consistent Pricing Model for Index Options and Volatility Derivatives
A Consistent Pricing Model for Index Options and Volatility Derivatives 6th World Congress of the Bachelier Society Thomas Kokholm Finance Research Group Department of Business Studies Aarhus School of
More informationEconomic Scenario Generators
Economic Scenario Generators A regulator s perspective Falk Tschirschnitz, FINMA Bahnhofskolloquium Motivation FINMA has observed: Calibrating the interest rate model of choice has become increasingly
More informationMarket Risk Analysis Volume IV. Value-at-Risk Models
Market Risk Analysis Volume IV Value-at-Risk Models Carol Alexander John Wiley & Sons, Ltd List of Figures List of Tables List of Examples Foreword Preface to Volume IV xiii xvi xxi xxv xxix IV.l Value
More informationAnalytical formulas for local volatility model with stochastic. Mohammed Miri
Analytical formulas for local volatility model with stochastic rates Mohammed Miri Joint work with Eric Benhamou (Pricing Partners) and Emmanuel Gobet (Ecole Polytechnique Modeling and Managing Financial
More informationPuttable Bond and Vaulation
and Vaulation Dmitry Popov FinPricing http://www.finpricing.com Summary Puttable Bond Definition The Advantages of Puttable Bonds Puttable Bond Payoffs Valuation Model Selection Criteria LGM Model LGM
More informationCredit Valuation Adjustment and Funding Valuation Adjustment
Credit Valuation Adjustment and Funding Valuation Adjustment Alex Yang FinPricing http://www.finpricing.com Summary Credit Valuation Adjustment (CVA) Definition Funding Valuation Adjustment (FVA) Definition
More informationMarket interest-rate models
Market interest-rate models Marco Marchioro www.marchioro.org November 24 th, 2012 Market interest-rate models 1 Lecture Summary No-arbitrage models Detailed example: Hull-White Monte Carlo simulations
More informationExploring Volatility Derivatives: New Advances in Modelling. Bruno Dupire Bloomberg L.P. NY
Exploring Volatility Derivatives: New Advances in Modelling Bruno Dupire Bloomberg L.P. NY bdupire@bloomberg.net Global Derivatives 2005, Paris May 25, 2005 1. Volatility Products Historical Volatility
More informationOn VIX Futures in the rough Bergomi model
On VIX Futures in the rough Bergomi model Oberwolfach Research Institute for Mathematics, February 28, 2017 joint work with Antoine Jacquier and Claude Martini Contents VIX future dynamics under rbergomi
More informationCONTINUOUS TIME PRICING AND TRADING: A REVIEW, WITH SOME EXTRA PIECES
CONTINUOUS TIME PRICING AND TRADING: A REVIEW, WITH SOME EXTRA PIECES THE SOURCE OF A PRICE IS ALWAYS A TRADING STRATEGY SPECIAL CASES WHERE TRADING STRATEGY IS INDEPENDENT OF PROBABILITY MEASURE COMPLETENESS,
More information- 1 - **** d(lns) = (µ (1/2)σ 2 )dt + σdw t
- 1 - **** These answers indicate the solutions to the 2014 exam questions. Obviously you should plot graphs where I have simply described the key features. It is important when plotting graphs to label
More informationSimple Robust Hedging with Nearby Contracts
Simple Robust Hedging with Nearby Contracts Liuren Wu and Jingyi Zhu Baruch College and University of Utah April 29, 211 Fourth Annual Triple Crown Conference Liuren Wu (Baruch) Robust Hedging with Nearby
More informationRough volatility models: When population processes become a new tool for trading and risk management
Rough volatility models: When population processes become a new tool for trading and risk management Omar El Euch and Mathieu Rosenbaum École Polytechnique 4 October 2017 Omar El Euch and Mathieu Rosenbaum
More information2 f. f t S 2. Delta measures the sensitivityof the portfolio value to changes in the price of the underlying
Sensitivity analysis Simulating the Greeks Meet the Greeks he value of a derivative on a single underlying asset depends upon the current asset price S and its volatility Σ, the risk-free interest rate
More informationCounterparty Credit Risk
Counterparty Credit Risk The New Challenge for Global Financial Markets Jon Gregory ) WILEY A John Wiley and Sons, Ltd, Publication Acknowledgements List of Spreadsheets List of Abbreviations Introduction
More informationPrinciples of Scenario Planning Under Solvency II. George Tyrakis Solutions Specialist
Principles of Scenario Planning Under Solvency II George Tyrakis Solutions Specialist George.Tyrakis@Moodys.com Agenda» Overview of Scenarios» Parallels between Insurance and Banking» Deterministic vs.
More informationDynamic Relative Valuation
Dynamic Relative Valuation Liuren Wu, Baruch College Joint work with Peter Carr from Morgan Stanley October 15, 2013 Liuren Wu (Baruch) Dynamic Relative Valuation 10/15/2013 1 / 20 The standard approach
More informationApproximation Methods in Derivatives Pricing
Approximation Methods in Derivatives Pricing Minqiang Li Bloomberg LP September 24, 2013 1 / 27 Outline of the talk A brief overview of approximation methods Timer option price approximation Perpetual
More informationby Kian Guan Lim Professor of Finance Head, Quantitative Finance Unit Singapore Management University
by Kian Guan Lim Professor of Finance Head, Quantitative Finance Unit Singapore Management University Presentation at Hitotsubashi University, August 8, 2009 There are 14 compulsory semester courses out
More informationCross Asset CVA Application
Cross Asset CVA Application Roland Lichters Quaternion Risk Management IKB QuantLib User Meeting IKB Deutsche Industriebank AG, 13-14 November 2013 1 About Quaternion Specialist risk consulting and solutions,
More informationModern Derivatives. Pricing and Credit. Exposure Anatysis. Theory and Practice of CSA and XVA Pricing, Exposure Simulation and Backtest!
Modern Derivatives Pricing and Credit Exposure Anatysis Theory and Practice of CSA and XVA Pricing, Exposure Simulation and Backtest!ng Roland Lichters, Roland Stamm, Donal Gallagher Contents List of Figures
More informationEuropean option pricing under parameter uncertainty
European option pricing under parameter uncertainty Martin Jönsson (joint work with Samuel Cohen) University of Oxford Workshop on BSDEs, SPDEs and their Applications July 4, 2017 Introduction 2/29 Introduction
More informationRiccardo Rebonato Global Head of Quantitative Research, FM, RBS Global Head of Market Risk, CBFM, RBS
Why Neither Time Homogeneity nor Time Dependence Will Do: Evidence from the US$ Swaption Market Cambridge, May 2005 Riccardo Rebonato Global Head of Quantitative Research, FM, RBS Global Head of Market
More information2.1 Mathematical Basis: Risk-Neutral Pricing
Chapter Monte-Carlo Simulation.1 Mathematical Basis: Risk-Neutral Pricing Suppose that F T is the payoff at T for a European-type derivative f. Then the price at times t before T is given by f t = e r(t
More informationCalculating VaR. There are several approaches for calculating the Value at Risk figure. The most popular are the
VaR Pro and Contra Pro: Easy to calculate and to understand. It is a common language of communication within the organizations as well as outside (e.g. regulators, auditors, shareholders). It is not really
More informationCrashcourse Interest Rate Models
Crashcourse Interest Rate Models Stefan Gerhold August 30, 2006 Interest Rate Models Model the evolution of the yield curve Can be used for forecasting the future yield curve or for pricing interest rate
More informationSample Path Large Deviations and Optimal Importance Sampling for Stochastic Volatility Models
Sample Path Large Deviations and Optimal Importance Sampling for Stochastic Volatility Models Scott Robertson Carnegie Mellon University scottrob@andrew.cmu.edu http://www.math.cmu.edu/users/scottrob June
More informationDerivative Securities Fall 2012 Final Exam Guidance Extended version includes full semester
Derivative Securities Fall 2012 Final Exam Guidance Extended version includes full semester Our exam is Wednesday, December 19, at the normal class place and time. You may bring two sheets of notes (8.5
More informationProxy Techniques for Estimating Variable Annuity Greeks. Presenter(s): Aubrey Clayton, Aaron Guimaraes
Sponsored by and Proxy Techniques for Estimating Variable Annuity Greeks Presenter(s): Aubrey Clayton, Aaron Guimaraes Proxy Techniques for Estimating Variable Annuity Greeks Aubrey Clayton, Moody s Analytics
More informationModelling Credit Spreads for Counterparty Risk: Mean-Reversion is not Needed
Modelling Credit Spreads for Counterparty Risk: Mean-Reversion is not Needed Ignacio Ruiz, Piero Del Boca May 2012 Version 1.0.5 A version of this paper was published in Intelligent Risk, October 2012
More informationComputer Exercise 2 Simulation
Lund University with Lund Institute of Technology Valuation of Derivative Assets Centre for Mathematical Sciences, Mathematical Statistics Spring 2010 Computer Exercise 2 Simulation This lab deals with
More informationCallable Bond and Vaulation
and Vaulation Dmitry Popov FinPricing http://www.finpricing.com Summary Callable Bond Definition The Advantages of Callable Bonds Callable Bond Payoffs Valuation Model Selection Criteria LGM Model LGM
More informationLIBOR models, multi-curve extensions, and the pricing of callable structured derivatives
Weierstrass Institute for Applied Analysis and Stochastics LIBOR models, multi-curve extensions, and the pricing of callable structured derivatives John Schoenmakers 9th Summer School in Mathematical Finance
More informationInterest Rate Modeling
Chapman & Hall/CRC FINANCIAL MATHEMATICS SERIES Interest Rate Modeling Theory and Practice Lixin Wu CRC Press Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis
More informationValue at Risk Ch.12. PAK Study Manual
Value at Risk Ch.12 Related Learning Objectives 3a) Apply and construct risk metrics to quantify major types of risk exposure such as market risk, credit risk, liquidity risk, regulatory risk etc., and
More informationAdvances in Valuation Adjustments. Topquants Autumn 2015
Advances in Valuation Adjustments Topquants Autumn 2015 Quantitative Advisory Services EY QAS team Modelling methodology design and model build Methodology and model validation Methodology and model optimisation
More informationManaging the Newest Derivatives Risks
Managing the Newest Derivatives Risks Michel Crouhy NATIXIS Corporate and Investment Bank European Summer School in Financial Mathematics Tuesday, September 9, 2008 Natixis 2006 Agenda Some Practical Aspects
More informationHANDBOOK OF. Market Risk CHRISTIAN SZYLAR WILEY
HANDBOOK OF Market Risk CHRISTIAN SZYLAR WILEY Contents FOREWORD ACKNOWLEDGMENTS ABOUT THE AUTHOR INTRODUCTION XV XVII XIX XXI 1 INTRODUCTION TO FINANCIAL MARKETS t 1.1 The Money Market 4 1.2 The Capital
More informationRisk Neutral Valuation
copyright 2012 Christian Fries 1 / 51 Risk Neutral Valuation Christian Fries Version 2.2 http://www.christian-fries.de/finmath April 19-20, 2012 copyright 2012 Christian Fries 2 / 51 Outline Notation Differential
More informationFrom Financial Engineering to Risk Management. Radu Tunaru University of Kent, UK
Model Risk in Financial Markets From Financial Engineering to Risk Management Radu Tunaru University of Kent, UK \Yp World Scientific NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI CHENNAI
More informationHedging under Model Uncertainty
Hedging under Model Uncertainty Efficient Computation of the Hedging Error using the POD 6th World Congress of the Bachelier Finance Society June, 24th 2010 M. Monoyios, T. Schröter, Oxford University
More informationSession 61 L, Economic Scenario Generators: Risk-Neutral and Real-World Considerations from an Investment Perspective
Session 61 L, Economic Scenario Generators: Risk-Neutral and Real-World Considerations from an Investment Perspective Moderator: Ryan Joel Stowe, FSA, MAAA Presenter: Jinsung Yoo, FSA, Ph.D. Session 61:
More informationSYLLABUS. IEOR E4728 Topics in Quantitative Finance: Inflation Derivatives
SYLLABUS IEOR E4728 Topics in Quantitative Finance: Inflation Derivatives Term: Summer 2007 Department: Industrial Engineering and Operations Research (IEOR) Instructor: Iraj Kani TA: Wayne Lu References:
More informationParametric Inference and Dynamic State Recovery from Option Panels. Torben G. Andersen
Parametric Inference and Dynamic State Recovery from Option Panels Torben G. Andersen Joint work with Nicola Fusari and Viktor Todorov The Third International Conference High-Frequency Data Analysis in
More informationAccelerated Option Pricing Multiple Scenarios
Accelerated Option Pricing in Multiple Scenarios 04.07.2008 Stefan Dirnstorfer (stefan@thetaris.com) Andreas J. Grau (grau@thetaris.com) 1 Abstract This paper covers a massive acceleration of Monte-Carlo
More informationValuation of Equity Derivatives
Valuation of Equity Derivatives Dr. Mark W. Beinker XXV Heidelberg Physics Graduate Days, October 4, 010 1 What s a derivative? More complex financial products are derived from simpler products What s
More informationFinancial Risk Management
r r Financial Risk Management A Practitioner's Guide to Managing Market and Credit Risk Second Edition STEVEN ALLEN WILEY John Wiley & Sons, Inc. Contents Foreword Preface Acknowledgments About the Author
More informationReduce to the max. Efficient solutions for mid- size problems in interest rate derivative pricing and risk management at RLB OOE.
Reduce to the max Efficient solutions for mid- size problems in interest rate derivative pricing and risk management at RLB OOE Stefan Fink Raiffeisenlandesbank OÖ, Treasury fink@rlbooe.at www.rlbooe.at
More informationESGs: Spoilt for choice or no alternatives?
ESGs: Spoilt for choice or no alternatives? FA L K T S C H I R S C H N I T Z ( F I N M A ) 1 0 3. M i t g l i e d e r v e r s a m m l u n g S AV A F I R, 3 1. A u g u s t 2 0 1 2 Agenda 1. Why do we need
More informationThree prices of three risks: A real world measure IR-FX hybrid model
Three prices of three risks: A real world measure IR-FX hybrid model Alexander Sokol* Head of Quant Research, CompatibL *Includes material from a recent paper by Hull, Sokol, and White http://ssrn.com/abstract=2403067
More informationAdvanced Equity Derivatives by Oliver Brockhaus
Advanced Equity Derivatives by Oliver Brockhaus Frankfurt: 10th & 11th September 2012 This workshop provides TWO booking options Register to ANY ONE day of the workshop Register to BOTH days of the workshop
More informationTraded Risk & Regulation
DRAFT Traded Risk & Regulation University of Essex Expert Lecture 14 March 2014 Dr Paula Haynes Managing Partner Traded Risk Associates 2014 www.tradedrisk.com Traded Risk Associates Ltd Contents Introduction
More informationOperational Risk. Robert Jarrow. September 2006
1 Operational Risk Robert Jarrow September 2006 2 Introduction Risk management considers four risks: market (equities, interest rates, fx, commodities) credit (default) liquidity (selling pressure) operational
More information1.1 Basic Financial Derivatives: Forward Contracts and Options
Chapter 1 Preliminaries 1.1 Basic Financial Derivatives: Forward Contracts and Options A derivative is a financial instrument whose value depends on the values of other, more basic underlying variables
More informationPricing with a Smile. Bruno Dupire. Bloomberg
CP-Bruno Dupire.qxd 10/08/04 6:38 PM Page 1 11 Pricing with a Smile Bruno Dupire Bloomberg The Black Scholes model (see Black and Scholes, 1973) gives options prices as a function of volatility. If an
More informationSimulating Stochastic Differential Equations
IEOR E4603: Monte-Carlo Simulation c 2017 by Martin Haugh Columbia University Simulating Stochastic Differential Equations In these lecture notes we discuss the simulation of stochastic differential equations
More informationNear Real-Time Risk Simulation of Complex Portfolios on Heterogeneous Computing Systems with OpenCL
Near Real-Time Risk Simulation of Complex Portfolios on Heterogeneous Computing Systems with OpenCL Javier Alejandro Varela, Norbert Wehn Microelectronic Systems Design Research Group University of Kaiserslautern,
More informationValuation of Volatility Derivatives. Jim Gatheral Global Derivatives & Risk Management 2005 Paris May 24, 2005
Valuation of Volatility Derivatives Jim Gatheral Global Derivatives & Risk Management 005 Paris May 4, 005 he opinions expressed in this presentation are those of the author alone, and do not necessarily
More informationA Two Factor Forward Curve Model with Stochastic Volatility for Commodity Prices arxiv: v2 [q-fin.pr] 8 Aug 2017
A Two Factor Forward Curve Model with Stochastic Volatility for Commodity Prices arxiv:1708.01665v2 [q-fin.pr] 8 Aug 2017 Mark Higgins, PhD - Beacon Platform Incorporated August 10, 2017 Abstract We describe
More informationSolvency II Risk Management Forecasting. Presenter(s): Peter M. Phillips
Sponsored by and Solvency II Risk Management Forecasting Presenter(s): Peter M. Phillips Solvency II Risk Management Forecasting Peter M Phillips Equity Based Insurance Guarantees 2015 Nov 17, 2015 8:30
More informationEconomic Scenario Generation: Some practicalities. David Grundy July 2011
Economic Scenario Generation: Some practicalities David Grundy July 2011 my perspective stochastic model owner and user practical rather than theoretical 8 economies, 100 sensitivity tests per economy
More informationOIS and Its Impact on Modeling, Calibration and Funding of OTC Derivatives. May 31, 2012 Satyam Kancharla SVP, Client Solutions Group Numerix LLC
OIS and Its Impact on Modeling, Calibration and Funding of OTC Derivatives May 31, 2012 Satyam Kancharla SVP, Client Solutions Group Numerix LLC Agenda Changes in Interest Rate market dynamics after the
More informationJohn Hull and Wulin Suo. This Version: July, 2001
A METHODOLOGY FOR ASSESSING MODEL RISK AND ITS APPLICATION TO THE IMPLIED VOLATILITY FUNCTION MODEL Forthcoming: Journal of Financial and Quantitative Analysis John Hull and Wulin Suo This Version: July,
More informationCounterparty Credit Risk under Basel III
Counterparty Credit Risk under Basel III Application on simple portfolios Mabelle SAYAH European Actuarial Journal Conference September 8 th, 2016 Recent crisis and Basel III After recent crisis, and the
More informationVariance Derivatives and the Effect of Jumps on Them
Eötvös Loránd University Corvinus University of Budapest Variance Derivatives and the Effect of Jumps on Them MSc Thesis Zsófia Tagscherer MSc in Actuarial and Financial Mathematics Faculty of Quantitative
More informationSTOCHASTIC VOLATILITY MODELS: CALIBRATION, PRICING AND HEDGING. Warrick Poklewski-Koziell
STOCHASTIC VOLATILITY MODELS: CALIBRATION, PRICING AND HEDGING by Warrick Poklewski-Koziell Programme in Advanced Mathematics of Finance School of Computational and Applied Mathematics University of the
More informationIntroduction to Financial Mathematics
Department of Mathematics University of Michigan November 7, 2008 My Information E-mail address: marymorj (at) umich.edu Financial work experience includes 2 years in public finance investment banking
More information2nd Order Sensis: PnL and Hedging
2nd Order Sensis: PnL and Hedging Chris Kenyon 19.10.2017 Acknowledgements & Disclaimers Joint work with Jacques du Toit. The views expressed in this presentation are the personal views of the speaker
More informationMonte Carlo Methods in Structuring and Derivatives Pricing
Monte Carlo Methods in Structuring and Derivatives Pricing Prof. Manuela Pedio (guest) 20263 Advanced Tools for Risk Management and Pricing Spring 2017 Outline and objectives The basic Monte Carlo algorithm
More informationCounterparty Risk - wrong way risk and liquidity issues. Antonio Castagna -
Counterparty Risk - wrong way risk and liquidity issues Antonio Castagna antonio.castagna@iasonltd.com - www.iasonltd.com 2011 Index Counterparty Wrong-Way Risk 1 Counterparty Wrong-Way Risk 2 Liquidity
More informationApplication of Stochastic Calculus to Price a Quanto Spread
Application of Stochastic Calculus to Price a Quanto Spread Christopher Ting http://www.mysmu.edu/faculty/christophert/ Algorithmic Quantitative Finance July 15, 2017 Christopher Ting July 15, 2017 1/33
More information