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Professor Erik Schlogl

Director, Quantitative Finance Research Centre
Core Member, Quantitative Finance Research Centre

DipVw (Bonn), PhD (Bonn)

Member, Bachelier Finance Society

Email: Erik.Schlogl@uts.edu.au
Phone: +61 2 9514 7785
Fax:
Room: CB05D.03.27A (map)
Mailing address:

Links: http://www.schlogl.com

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Biography

Erik Schlögl currently is Professor and Director of the Quantitative Finance Research Centre at the University of Technology, Sydney (UTS), Australia. Erik received his doctorate in Economics from the University of Bonn, Germany, for work on term structure models and the pricing of fixed income derivatives and has gained broad-based experience in computational financial engineering. He has consulted for financial institutions and software developers in Europe, Australia and in the US, and served as an expert witness in cases before the Federal Court of Australia. His research interests cover a broad area of quantitative finance, in particular model calibration, interest rate term structure modelling, credit risk and the integration of multiple sources of risk. His research articles have been published in a number of international journals, including Finance & Stochastics, Quantitative Finance, Risk and the Journal of Economic Dynamics and Control. He is also the chairman of the organising committee of the Sydney Financial Mathematics Workshop (SFMW) and one of the co-organisers of the annual conference Quantitative Methods in Finance (QMF). In addition to UTS, he held positions at the University of New South Wales, Australia, and the University of Bonn, Germany.

Research

Research interests

Derivative securities pricing, term structure of interest rates, quantitative finance techniques, credit risk modelling, computational finance.

Research supervision: Yes


Postgraduate research degree students supervised:

Samson Assefa

King Ming Chan

In Hwan (David) Chung

Du Ke

Troy Morgan

Tao Peng

Liang Zhao

Projects

Publications

Research books

Schlogl, E. 2014, Quantitative finance: An object-oriented approach in C++, 1st, Taylor and Francis, Florida, USA.
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Quantitative Finance: An Object-Oriented Approach in C++ provides readers with a foundation in the key methods and models of quantitative finance. Keeping the material as self-contained as possible, the author introduces computational finance with a focus on practical implementation in C++. Through an approach based on C++ classes and templates, the text highlights the basic principles common to various methods and models while the algorithmic implementation guides readers to a more thorough, hands-on understanding. By moving beyond a purely theoretical treatment to the actual implementation of the models using C++, readers greatly enhance their career opportunities in the field.

Research books chapters

Chung, I., Dun, T. & Schlogl, E. 2010, 'Lognormal forward market model (LFM) volatility function approximation' in Chiarella, C; Novikov, A (eds), Contemporary Quantitative Finance: Essays in Honour of Eckhard Platen, Springer, Germany, pp. 369-405.
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In the lognormal forward Market model (LFM) framework, the specification for time-deterministic instantaneous volatility functions for state variable forward rates is required. In reality, only a discrete number of forward rates is observable in the market. For this reason, traders routinely construct time-deterministic volatility functions for these forward rates based on the tenor structure given by these rates. In any practical implementation, however, it is of considerable importance that volatility functions can also be evaluated for forward rates not matching the implied tenor structure. Following the deterministic arbitrage-free interpolation scheme introduced by Schl÷gl in (Advances in Finance and Stochastics: Essays in Honour of Dieter Sondermann. Springer, Berlin 2002) in the LFM, this paper, firstly, derives an approximate analytical formula for the volatility function of a forward rate not matching the original tenor structure. Secondly, the result is extended to a swap rate volatility function under the lognormal forward rate assumption.

Schlogl, E. & Schlogl, L. 2009, 'Factor Distributions Implied by Quoted CDO Spreads' in Cont, R (eds), Frontiers in Quantitative Finance, John Wiley and Sons, New Jersey, USA, pp. 217-234.
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Schlogl, E. 2008, 'Markov Models for CDOs' in Meissner, G (eds), The Definitive Guide to CDOs: Market, Application, Valuation and Hedging, Risk Books, Cambridge, UK, pp. 319-340.
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Schlogl, E. 2002, 'Arbitrage-free interpolation in models of market observable interest rates' in Sandmann K; Schonbucher PJ (eds), Advances in Finance and Stochastics: essays in honour of Dieter Sondermann, Springer-Verlag Berlin Heidelberg, Berlin, Germany, pp. 197-218.

Refereed journal articles

Pilz, K. & Schlogl, E. 2013, 'A hybrid commodity and interest rate market model', Quantitative Finance, vol. 13, no. 4, pp. 543-560.
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A joint model of commodity price and interest rate risk is constructed analogously to the multi-currency LIBOR Market Model (LMM). Going beyond a simple `re-interpretation´+¢ of the multi-currency LMM, issues arising in the application of the model to actual commodity market data are specifically addressed. Firstly, liquid market prices are only available for options on commodity futures, rather than forwards, thus the difference between forward and futures prices must be explicitly taken into account in the calibration. Secondly, we construct a procedure to achieve a consistent fit of the model to market data for interest options, commodity options and historically estimated correlations between interest rates and commodity prices. We illustrate the model by an application to real market data and derive pricing formulas for commodity spread options.

Schlogl, E. 2013, 'Option pricing where the underlying assets follow a Gram/Charlier density of arbitrary order', Journal of Economic Dynamics and Control, vol. 37, no. 3, pp. 611-632.
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If a probability distribution is sufficiently close to a normal distribution, its density can be approximated by a Gram/Charlier Series A expansion. In option pricing, this has been used to fit risk-neutral asset price distributions to the implied volatility smile, ensuring an arbitrage-free interpolation of implied volatilities across exercise prices. However, the existing literature is restricted to truncating the series expansion after the fourth moment. This paper presents an option pricing formula in terms of the full (untruncated) series and discusses a fitting algorithm, which ensures that a series truncated at a moment of arbitrary order represents a valid probability density. While it is well known that valid densities resulting from truncated Gram/Charlier Series A expansions do not always have sufficient flexibility to fit all market-observed option prices perfectly, this paper demonstrates that option pricing in a model based on these densities is as tractable as the (far less flexible) original model of Black and Scholes (1973), allowing non-trivial higher moments such as skewness, excess kurtosis and so on to be incorporated into the pricing of exotic options: Generalising the Gram/Charlier Series A approach to the multiperiod, multivariate case, a model calibrated to standard option prices is developed, in which a large class of exotic payoffs can be priced in closed form. Furthermore, this approach, when applied to a foreign exchange option market involving several currencies, can be used to ensure that the volatility smiles for options on the cross exchange rate are constructed in a consistent, arbitrage-free manner

Nielsen, J.A., Sandmann, K. & Schlogl, E. 2011, 'Equity-linked pension schemes with guarantees', Insurance: Mathematics and Economics, vol. 49, no. 3, pp. 547-564.
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This paper analyses the relationship between the level of a return guarantee in an equity-linked pension scheme and the proportion of an investor+s contribution needed to finance this guarantee. Three types of schemes are considered: investment guarantee, contribution guarantee and surplus participation. The evaluation of each scheme involves pricing an Asian option, for which relatively tight upper and lower bounds can be calculated in a numerically efficient manner. We find a negative (and for two contract specifications also concave) relationship between the participation in the surplus return of the investment strategy and the guarantee level in terms of a minimum rate of return. Furthermore, the introduction of the possibility of early termination of the contract (e.g. due to the death of the investor) has no qualitative and very little quantitative impact on this relationship.

Bruti Liberati, N., Nikitopoulos Sklibosios, C., Platen, E. & Schlogl, E. 2009, 'Alternative defaultable term structure models', Asia - Pacific Financial Markets, vol. 16, no. 1, pp. 1-31.
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The objective of this paper is to consider defaultable term structure models in a general setting beyond standard risk-neutral models. Using as numeraire the growth optimal portfolio, defaultable interest rate derivatives are priced under the real-world probability measure. Therefore, the existence of an equivalent risk-neutral probability measure is not required. In particular, the real-world dynamics of the instantaneous defaultable forward rates under a jump-diffusion extension of a HJM type framework are derived. Thus, by establishing a modelling framework fully under the real-world probability measure, the challenge of reconciling real-world and risk-neutral probabilities of default is deliberately avoided, which provides significant extra modelling freedom. In addition, for certain volatility specifications, finite dimensional Markovian defaultable term structure models are derived. The paper also demonstrates an alternative defaultable term structure model. It provides tractable expressions for the prices of defaultable derivatives under the assumption of independence between the discounted growth optimal portfolio and the default-adjusted short rate. These expressions are then used in a more general model as control variates for Monte Carlo simulations of credit derivatives.

Mahayni, A.B. & Schlogl, E. 2008, 'The Risk Management of Minimum Return Guarantees', BuR - Business Research, vol. 1, no. 1, pp. 55-76.
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Contracts paying a guaranteed minimum rate of return and a fraction of a positive excess rate, which is specified relative to a benchmark portfolio, are closely related to unit-linked life-insurance products and can be considered as alternatives to direct investment in the underlying benchmark. They contain an embedded power option, and the key issue is the tractable and realistic hedging of this option, in order to rigorously justify valuation by arbitrage arguments and prevent the guarantees from becoming uncontrollable liabilities to the issuer. We show how to determine the contract parameters conservatively and implement robust risk-management strategies.

Chiarella, C., Nikitopoulos Sklibosios, C. & Schlogl, E. 2007, 'A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton Models with Jumps', Applied Mathematical Finance, vol. 14, no. 5, pp. 365-399.
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This paper examines the pricing of interest rate derivatives when the interest rate dynamics experience infrequent jump shocks modelled as a Poisson process. The pricing framework adapted was developed by Chiarella and Nikitopoulos to provide an extension of the Heath, Jarrow and Morton model to jump-diffusions and achieves Markovian structures under certain volatility specifications. Fourier Transform solutions for the price of a bond option under deterministic volatility specifications are derived and a control variate numerical method is developed under a more general state dependent volatility structure, a case in which closed form solutions are generally not possible. In doing so, a novel perspective is provided on control variate methods by going outside a given complex model to a simpler more tractable setting to provide the control variates.

Chiarella, C., Nikitopoulos Sklibosios, C. & Schlogl, E. 2007, 'A Markovian Defaultable Term Structure Model with State Dependent Volatilities', International Journal of Theoretical and Applied Finance, vol. 10, no. 1, pp. 155-202.
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The defaultable forward rate is modelled as a jump diffusion process within the Schonbucher [26,27] general Heath, Jarrow and Morton [20] framework where jumps in the defaultable term structure fd(t, T) cause jumps and defaults to the defaultable bond prices Pd(t, T). Within this framework, we investigate an appropriate forward rate volatility structure that results in Markovian defaultable spot rate dynamics. In particular, we consider state dependent Wiener volatility functions and time dependent Poisson volatility functions. The corresponding term structures of interest rates are expressed as finite dimensional affine realizations in terms of benchmark defaultable forward rates In addition, we extend this model to incorporate stochastic spreads by allowing jump intensities to follow a square-root diffusion process. In that case the dynamics become non-Markovian and to restore path independence we propose either an approximate Markovian scheme or, alternatively, constant Poisson volatility functions. We also conduct some numerical simulations to gauge the effect of the stochastic intensity and the distributional implications of various volatility specifications.

Choy, B., Dun, T. & Schlogl, E. 2004, 'Correlating market models', Asia Risk, vol. October, pp. 53-59.
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Schlogl, E. 2002, 'A multicurrency extension of the lognormal interest rate market models', Finance and Stochastics, vol. 6, no. 2, pp. 173-196.
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Dun, T., Barton, G.W. & Schlogl, E. 2001, 'Simulated Swaption Delta-Hedging in the Lognormal Forward Libor Model', International Journal of Theoretical & Applied Finance, vol. 4, no. 4, pp. 677-709.
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Alternative approaches to hedging swaptions are explored and tested by simulation. Hedging methods implied by the Black swaption formula are compared with a lognormal forward LIBOR model approach encompassing all the relevant forward rates. The simulation is undertaken within the LIBOR model framework for a range of swaptions and volatility structures. Despite incompatibilities with the model assumptions, the Black method performs equally well as the LIBOR method, yielding very similar distributions for the hedging pro t and loss even at high rehedging frequencies. This result demonstrates the robustness of the Black hedging technique and implies that being simpler and generally better understood by nancial practitioners it would be the preferred method in practice.

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