Christian P. Fries

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics

Professor

Theresienstrasse 39

Munich

Germany

DZ Bank AG

60265 Frankfurt am Main

Germany

  • Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics

  • DZ Bank AG

SCHOLARLY PAPERS

50

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134

Scholarly Papers (50)

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1.

Lognormal vs Normal Volatilities and Sensitivities in Practice

Number of pages: 20 Posted: 08 Nov 2015 Last Revised: 20 Mar 2016
Georgi Dimitroff, Christian P. Fries, Mark Lichtner and Niklas Rodi
Independent, Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics, Independent and Independent
Downloads 3,131 (3,533)
Citation 3

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negative rates, low rates, lognormal volatility, normal volatility, displaced, displacement, normal delta, lognormal delta

2.

Discounting Revisited: Valuation Under Funding, Counterparty Risk and Collateralization

Number of pages: 34 Posted: 17 May 2010 Last Revised: 14 Mar 2011
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 2,997 (3,811)
Citation 30

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Discounting, Valuation, Counterparty Risk, Collateral, Netting, CVA, DVA, Bond, Swap, Credit Risk, Own Credit Risk, Wrong Way Risk

3.

Curves and Term Structure Models: Definition, Calibration and Application of Rate Curves and Term Structure Models

Number of pages: 22 Posted: 01 Jan 2013 Last Revised: 11 Apr 2013
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 2,844 (4,181)
Citation 2

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Curves, Discount Curve, Forward Curve, Calibration, Bootstrapping, Multi-Curve, Tenor-Basis, Cross-Currency-Basis, Collateralization, Funding, OIS Discounting, Funding Curve, Spread Curve

4.

Conditional Analytic Monte-Carlo Pricing Scheme of Auto-Callable Products

Number of pages: 28 Posted: 05 May 2008 Last Revised: 07 Apr 2010
Christian P. Fries and Mark S. Joshi
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and University of Melbourne - Centre for Actuarial Studies (deceased)
Downloads 1,913 (8,125)
Citation 8

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Monte Carlo Simulation, Pricing, Greeks, Variance Reduction, Auto-Callable, Trigger Product, Target Redemption Note

5.

Partial Proxy Simulation Schemes for Generic and Robust Monte-Carlo Greeks

Number of pages: 26 Posted: 03 Oct 2006
Christian P. Fries and Mark S. Joshi
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and University of Melbourne - Centre for Actuarial Studies (deceased)
Downloads 1,473 (12,397)
Citation 11

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Monte-Carlo Sensitivities, Likelihood Ratio, Importance Sampling, Greeks, Proxy Simulation Scheme, Digital Option, Binary Option, Trigger Product, Target Redemption Note

6.

Cross-Currency and Hybrid Markov-Functional Models

Number of pages: 23 Posted: 27 Apr 2004
Christian P. Fries and Marius G. Rott
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and Independent
Downloads 1,439 (12,868)
Citation 8

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Interest Rate Model, Markov Functional Model, Cross Currency Model, Spot Measure in Time Discrete Lattice Model

7.

Comments on Handling Objects in Spreadsheets

Number of pages: 18 Posted: 16 Oct 2008
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 855 (28,048)
Citation 1

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Spreadsheet, Object Oriented, Concurrency, Parallel Computing, Multithreadding, Excel, Java

8.

Arbitrage-free Asset Class Independent Volatility Surface Interpolation on Probability Space using Normed Call Prices

Number of pages: 27 Posted: 25 Nov 2011 Last Revised: 18 Oct 2013
Pijush Gope and Christian P. Fries
Independent and Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 832 (29,186)
Citation 2

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NCP, Volatility Surface, Volatility Smile, Probability Space, Arbitrage Free Interpolation

9.

Funded Replication: Valuing with Stochastic Funding

Number of pages: 26 Posted: 06 Mar 2011 Last Revised: 14 Apr 2011
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 817 (29,905)
Citation 6

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Discounting, Valuation, Funding, Collateral, Mark to Market, Held to Maturity

10.

Displaced Relative Changes in Historical Simulation: Application to Risk Measures of Interest Rates with Phases of Negative Rates

Number of pages: 39 Posted: 01 Jan 2013 Last Revised: 19 Sep 2016
Christian P. Fries, Tobias Nigbur and Norman Seeger
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics, University of St. Gallen and VU University Amsterdam
Downloads 811 (30,217)

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Historical simulation, generalizations, negative risk factors, Value at Risk

11.

Localized Proxy Simulation Schemes for Generic and Robust Monte-Carlo Greeks

Number of pages: 15 Posted: 08 May 2007
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 669 (39,274)
Citation 8

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Monte-Carlo Sensitivities, Likelihood Ratio, Importance Sampling, Greeks, Proxy Simulation Scheme, Digital Option, Binary Option, Trigger Product, Target Redemption Note

12.

A Hybrid Markov-Functional Model with Simultaneous Calibration to Interest Rate and FX Smile

Number of pages: 23 Posted: 20 Aug 2006
Christian P. Fries and Fabian Eckstaedt
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and affiliation not provided to SSRN
Downloads 607 (44,735)

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Markov Functional Model, Hybrid Model, FX Model, Implied Modeling, Smile

13.

Monte-Carlo Simulation with Boundary Conditions (with Applications to Stress Testing, CEV and Variance-Gamma Simulation)

Number of pages: 40 Posted: 05 Apr 2010 Last Revised: 27 Apr 2010
Christian P. Fries and Joerg Kienitz
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and University of Cape Town
Downloads 588 (46,673)

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Monte Carlo Simulation, Valuation, Stress Test, Variance Reduction, Boundary Conditions, Numerical Schemes, CEV, Variance Gamma

14.

Collateralization and Funding Valuation Adjustments (FVA) for Total Return Swaps and Forward Contracts

Number of pages: 34 Posted: 02 Jun 2014 Last Revised: 08 Aug 2016
Christian P. Fries and Mark Lichtner
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and Independent
Downloads 580 (47,504)
Citation 3

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Funding Valuation Adjustments, FVA, Collateralization, Repo

15.

Smart Derivative Contracts (Detaching Transactions from Counterparty Credit Risk: Specification, Parametrisation, Valuation)

Number of pages: 22 Posted: 24 Apr 2018 Last Revised: 09 Jan 2019
Christian P. Fries and Peter Kohl-Landgraf
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and DZ Bank AG
Downloads 575 (48,075)
Citation 2

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Collateralization, CCP, Initial Margin, Smart Contract, Settlement Risk, Gap Risk

16.

Markov Functional Modeling of Equity, Commodity and Other Assets

Number of pages: 15 Posted: 05 Apr 2006
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 542 (51,718)
Citation 2

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Markov Functional Model, Equity, Implied Modeling

17.

Stochastic Automatic Differentiation: Automatic Differentiation for Monte-Carlo Simulations

Number of pages: 45 Posted: 01 Jul 2017 Last Revised: 03 Nov 2018
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 537 (52,350)
Citation 12

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Automatic Differentiation, Adjoint Automatic Differentiation Monte Carlo Simulation, American Monte Carlo, Conditional Expectation, Indicator Function, Bermudan Option, XVA

18.

Stable Monte-Carlo Sensitivities of Bermudan Callable Products

Number of pages: 20 Posted: 17 Apr 2009 Last Revised: 22 Apr 2009
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 516 (55,096)
Citation 2

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Monte Carlo Simulation, Pricing, Greeks, Variance Reduction, Bermudan Product, Cancelable Product, Early Exercise, Backward Algorithm

19.

Proxy Simulation Schemes for Generic Robust Monte-Carlo Sensitivities, Process Oriented Importance Sampling and High Accuracy Drift Approximation (with Applications to the Libor Market Model)

Number of pages: 32 Posted: 21 Apr 2005
Christian P. Fries and Joerg Kampen
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and Weierstrass Institute for Applied Analysis and Stochastics
Downloads 482 (60,050)
Citation 6

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Monte-Carlo, Likelihood Ratio, Malliavin Calculus, Sensitivities, Greeks, Likelihood Ratio, Importance Sampling, Proxy Simulation Scheme, Weak Scheme, Digital Option, Binary Option, Trigger Product

20.

Fast and Robust Monte Carlo Cdo Sensitivities and Their Efficient Object Oriented Implementation

Number of pages: 32 Posted: 01 Jun 2005
Marius G. Rott and Christian P. Fries
Independent and Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 421 (70,806)
Citation 9

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Monte Carlo, CDO, Sensitivities, Greeks, Li Model, Likelihood Ratio, OO

21.

Foresight Bias and Suboptimality Correction in Monte-Carlo Pricing of Options with Early Exercise: Classification, Calculation and Removal

Number of pages: 27 Posted: 07 Nov 2005
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 355 (86,381)
Citation 8

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Early Exercise, Bermudan Options, Compound Options, Monte-Carlo, Foresight

22.

Melting Sensitivities - Exact and Approximate Margin Valuation Adjustments

Number of pages: 44 Posted: 05 Jan 2018 Last Revised: 06 Mar 2018
Christian P. Fries, Peter Kohl-Landgraf and Mario Viehmann
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics, DZ Bank AG and Ludwig Maximilian University of Munich (LMU)
Downloads 308 (101,159)
Citation 5

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MVA, Initial Margin Simulation, ISDA SIMM, Automatic Differentiation, Adjoint Automatic Differentiation, Forward Sensitivities

23.

Volatility Risk

Number of pages: 23 Posted: 26 Sep 2016
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 298 (104,916)

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Historical Simulation, VaR, FRTB, Market Risk, Implied Volatility, SABR, Volatility Smile

24.

A Short Note on the Exact Stochastic Simulation Scheme of the Hull-White Model and Its Implementation

Number of pages: 18 Posted: 25 Feb 2016 Last Revised: 23 May 2016
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 261 (120,676)
Citation 1

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Hull-White model, Monte-Carlo simulation, Euler scheme, Exact scheme

25.

Fast Stochastic Forward Sensitivities in Monte-Carlo Simulations Using Stochastic Automatic Differentiation (with Applications to Initial Margin Valuation Adjustments (MVA))

Number of pages: 27 Posted: 15 Aug 2017 Last Revised: 22 Jan 2018
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 250 (126,244)
Citation 10

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Automatic Differentiation, Adjoint Automatic Differentiation, Monte Carlo Simulation, American Monte Carlo, Conditional Expectation, Forward Sensitivities, Initial Margin Simulation, MVA, ISDA SINM

26.

Funded Replication: Fund Exchange Process and the Valuation with Different Funding-Accounts (Cross-Currency Analogy to Funding Revisited)

Number of pages: 12 Posted: 23 Jul 2012 Last Revised: 25 Jul 2012
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 238 (132,644)
Citation 3

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discounting, funding, FVA, CVA, DVA, derivative pricing, funded replication

27.

Volatility Model Calibration With Convolutional Neural Networks

Number of pages: 12 Posted: 14 Oct 2018
Georgi Dimitroff, Dirk Röder and Christian P. Fries
Independent, DZ Bank AG and Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 235 (134,369)
Citation 5

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Heston Model, Convolutional Neural Network, Deep Learning, Machine Learning, Volatility Model Calibration

28.

Bumping the Model: Generic Robust Monte-Carlo Sensitivities Using the Proxy Simulation Scheme Method

Number of pages: 14 Posted: 02 Jan 2006
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 214 (146,986)
Citation 1

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Monte-Carlo, Likelihood Ratio, Malliavin Calculus, Sensitivities, Greeks, Proxy Scheme Simulation

29.

Automatic Backward Differentiation for American Monte-Carlo Algorithms - ADD for Conditional Expectations and Indicator Functions

Number of pages: 22 Posted: 18 Jul 2017 Last Revised: 19 Dec 2017
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 210 (149,640)
Citation 9

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Monte-Carlo Simulation, Automatic Differentiation, Adjoint Automatic Differentiation, Algorithmic Differentiation, AAD American Monte-Carlo, Bermudan Callables, Conditional Expectation, Exercise Boundary

30.

Keep It Simple - Notes on the Transition to New Interest Rate Benchmarks from a Quant Perspective

Number of pages: 3 Posted: 12 Sep 2018
Claus Christian Beier, Christian P. Fries and Marius G. Rott
DZ Bank AG, Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and Independent
Downloads 182 (170,773)

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Interest Rate Modelling, Benchmark Rates, IBOR

31.

XVA of a Derivative on an Underlying Modelled by a Default Jump Process with an Analysis of CVA Wrong Way Risk for Bond Forwards

Number of pages: 37 Posted: 22 Apr 2015
Mark Lichtner and Christian P. Fries
Independent and Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 172 (179,546)

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Black Scholes, defaultable underlying, bond derivatives, funding costs (FVA), counterparty credit value adjustment (CVA), underlying credit value adjustment, XVA, cash collateralization, bond forwards, total return swaps, wrong way Risk, default correlation

32.

Funded Inside: The Internal Transfer of Costs and Risks from Collateralized and Funded Derivatives

Number of pages: 25 Posted: 28 Aug 2012 Last Revised: 07 Jan 2013
Christian P. Fries and Joerg Zinnegger
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and z-frm
Downloads 172 (179,546)

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funding, derivative, collateral, valuation, FVA

33.

Smart Derivative Contracts (Presentation Slides of the 14th Quant Finance Conference)

Number of pages: 43 Posted: 19 Nov 2018
Christian P. Fries and Peter Kohl-Landgraf
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and DZ Bank AG
Downloads 170 (181,381)
Citation 1

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Collateralization, CCP, Initial Margin, Smart Contract, Settlement Risk, Gap Risk

34.

A Short Note on the Regularization of the Diffusion Matrix for the Euler Scheme of an Sde

Number of pages: 10 Posted: 21 Mar 2006
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 112 (252,695)
Citation 1

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Monte-Carlo simulation, Euler scheme, singular diffusion matrix

35.

Portfolio Risk with Selected Revaluation

Number of pages: 20 Posted: 19 Apr 2011
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 99 (275,238)

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Portfolio Risk, Value at Risk, Historic Simulation, Computational Performance

36.

A Local Linear Regression Method Using a Discrete Kernel Function with Applications to Bond Curve Construction

Number of pages: 41 Posted: 21 Nov 2017 Last Revised: 18 Dec 2017
Claus Christian Beier and Christian P. Fries
DZ Bank AG and Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 98 (277,033)
Citation 1

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37.

Stochastic Automatic Differentiation - AAD for Monte-Carlo Simulations - MVA Approximation Methods (Presentation Slides from the 14th Quant Finance Conference, Nice)

Number of pages: 187 Posted: 19 Nov 2018
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 86 (301,044)
Citation 2

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Automatic Differentiation, Adjoint Automatic Differentiation Monte Carlo Simulation, American Monte Carlo, Conditional Expectation, Indicator Function, Bermudan Option, XVA, MVA, MVA Approximations

38.

Dynamic Refinement of the Term Structure - Time Homogenous Term Structure Modeling

Number of pages: 28 Posted: 29 Dec 2016 Last Revised: 06 Mar 2017
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 85 (303,266)
Citation 1

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LIBOR Market Model, Heath-Jarrow-Morton Framework, Tenor Discretization, Term-Structure Models

39.

Stochastic Automatic Differentiation - AAD for Monte-Carlo Simulations (Presentation at the 13th Fixed Income Conference) (Presentation Slides)

Number of pages: 129 Posted: 29 Nov 2017
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 84 (305,433)

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Monte-Carlo Simulation, Automatic Differentiation, Adjoint Automatic Differentiation, American Monte-Carlo, Bermudan Callables, Conditional Expectation, Forward Sensitivities, Initial Margin, MVA

40.

Interest Rate Curve Interpolations and Their Assessment via Hedge Simulations

Number of pages: 34 Posted: 26 Jul 2015 Last Revised: 17 Nov 2015
Christian P. Fries and Christoph Plum
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 84 (305,433)

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41.

Implementing a Financial Derivative as Smart Contract

Number of pages: 51 Posted: 19 Mar 2019 Last Revised: 28 May 2019
Christian P. Fries, Peter Kohl-Landgraf, Björn Paffen, Stefanie Weddigen, Luca Del Re, Wilfried Schütte, David Bacher, Rebecca Declara, Daniel Eichsteller, Florian Weichand and Michael Streubel
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics, DZ Bank AG, DZ Bank AG, DZ Bank AG, DZ Bank AG, DZ Bank AG, Bayerische Landesbank, Bayerische Landesbank, Cofinpro AG, Cofinpro AG and Cofinpro AG
Downloads 81 (312,302)

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Smart Derivative Contracts, Derivative, Settlement, Distributed Ledger, Blockchain, Code is Law

42.

Standardization of Call Prices and No-Arbitrage Properties with Extension to Negative Forwards Post Financial Crisis

Number of pages: 5 Posted: 19 Oct 2013 Last Revised: 18 Jun 2018
Pijush Gope and Christian P. Fries
Independent and Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 78 (319,276)

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NCP, normed call prices, arbitrage free pricing, negative forwards, multi curve

43.

Back to the Future: Comparing Forward and Backward Differentiation for Forward Sensitivities in Monte-Carlo Simulations

Number of pages: 12 Posted: 26 Jan 2018 Last Revised: 31 Jan 2018
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 76 (324,096)
Citation 3

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Automatic Differentiation, Adjoint Automatic Differentiation, Forward Sensitivities

44.

Rethinking Financial Derivatives Inspired by Smart Contracts - A Request for Comments

Number of pages: 5 Posted: 09 Oct 2018
Christian P. Fries and Peter Kohl-Landgraf
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and DZ Bank AG
Downloads 73 (331,625)
Citation 1

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Settlement Risk, Financial Derivatives, Smart Contract, Distributed Ledger

45.

On a Class of Semi-Elliptic Diffusion Models - Part I: A Constructive Analytical Approach for Global Solutions, Densities and Numerical Schemes with Applications to the LIBOR Market Model

Number of pages: 28 Posted: 05 Apr 2010
Christian P. Fries and Joerg Kampen
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and Weierstrass Institute for Applied Analysis and Stochastics
Downloads 73 (331,625)

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Degenerate parabolic equations, financial derivatives, sensitivities, Monte-Carlo methods

46.

Stochastic Algorithmic Differentiation of (Expectations of) Discontinuous Functions (Indicator Functions)

Number of pages: 21 Posted: 19 Nov 2018 Last Revised: 12 Nov 2019
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 55 (383,554)

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Algorithmic Differentiation, Automatic Differentiation, Adjoint Automatic Differentiation, Monte Carlo Simulation, Indicator Function, Object Oriented Implementation, Variance Reduction

47.

Automatic Type Tracking: Operator Result Type Priority and Applications in Algorithmic Differentiation (with Examples from Mathematical Finance using Stochastic Automatic Differentiation)

Number of pages: 14 Posted: 12 Sep 2018 Last Revised: 21 Sep 2018
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 41 (433,408)

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Automatic Differentiation, Adjoint Automatic Differentiation, Monte Carlo Simulation, Object Oriented Implementation

48.

An Analytical Valuation Framework for Financial Assets with Trading Suspensions

Number of pages: 31 Posted: 27 Mar 2018 Last Revised: 02 Jul 2019
Christian P. Fries and Lorenzo Torricelli
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and University of Parma, Department of Economics and Management
Downloads 40 (437,528)
Citation 1

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Market Halts and Suspensions, Time Changes, Levy Subordinators, Derivative Pricing, Levy Processes

49.

Fast Stochastic Forward Sensitivities in Monte Carlo Simulations Using Stochastic Automatic Differentiation (with Applications to Initial Margin Valuation Adjustments)

Journal of Computational Finance, Vol. 22, No. 4, 2019
Number of pages: 24 Posted: 26 Feb 2019
Christian P. Fries
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics
Downloads 1 (670,653)
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automatic differentiation, algorithmic differentiation, Monte Carlo simulation, forward sensitivities, initial margin simulation, margin valuation adjustment (MVA)

50.

Stochastic Automatic Differentiation: Efficient Tapeless Implementation of Automatic Differentiation for Monte-Carlo Simulations

Posted: 01 Aug 2017
Christian P. Fries and Stefan Sedlmair
Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics and Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics

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Automatic Differentiation, Adjoint Automatic Differentiation Monte Carlo Simulation, Object Oriented Implementation