# Professor Erik Schlogl

### 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.

**Professor,**Finance Discipline Group

**Core Member,**QFRC - Quantitative Finance

**Director,**QFRC - Quantitative Finance

DipVw (Bonn), PhD (Bonn)

Member, Bachelier Finance Society

**Phone**

+61 2 9514 7785

**ORCID**

### Research Interests

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

**Can supervise:**Yes

**Postgraduate research degree students supervised:**

Samson Assefa

King Ming Chan

In Hwan (David) Chung

Du Ke

Troy Morgan

Tao Peng

Liang Zhao

## Books

Schlogl, E. 2014,

*Quantitative finance: An object-oriented approach in C++*, 1st, Taylor and Francis, Florida, USA. 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.

## Chapters

Schlogl, L. & Schlogl, E. 2010, 'Duffie-Singleton Model' in al, R.C.E. (ed),

View/Download from: UTS OPUS

*Encyclopedia of Quantitative Finance*, Wiley, US, pp. 499-501.View/Download from: UTS OPUS

NA

Chung, I., Dun, T. & Schlogl, E. 2010, 'Lognormal forward market model (LFM) volatility function approximation' in Chiarella, C. & Novikov, A. (eds),

View/Download from: UTS OPUS or Publisher's site

*Contemporary Quantitative Finance: Essays in Honour of Eckhard Platen*, Springer, Germany, pp. 369-405.View/Download from: UTS OPUS or Publisher's site

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 Schlögl 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. (ed),

View/Download from: UTS OPUS

*Frontiers in Quantitative Finance*, John Wiley and Sons, New Jersey, USA, pp. 217-234.View/Download from: UTS OPUS

NA

Schlogl, E. 2008, 'Markov Models for CDOs' in Meissner, G. (ed),

View/Download from: UTS OPUS

*The Definitive Guide to CDOs: Market, Application, Valuation and Hedging*, Risk Books, Cambridge, UK, pp. 319-340.View/Download from: UTS OPUS

NA

Choy, B., Dun, T. & Schlogl, E. 2005, 'Correlating market models' in Dunbar, N. (ed),

*Derivatives Trading and Option Pricing*, Risk Books, London, UK, pp. 303-322. Schlogl, E. 2002, 'Arbitrage-free interpolation in models of market observable interest rates' in Sandmann, K. & Schonbucher, P.J. (eds),

*Advances in Finance and Stochastics: essays in honour of Dieter Sondermann*, Springer-Verlag Berlin Heidelberg, Berlin, Germany, pp. 197-218.## Conferences

Cheng, B., Nikitopoulos Sklibosios, C. & Schlogl, E. 2016, 'Empirical pricing performance on long-dated crude oil derivatives: Do stochastic interest rates matter?', Energy and Commodity Finance Conference, Paris, France.

Cheng, B., Nikitopoulos Sklibosios, C. & Schlogl, E. 2016, 'Empirical Hedging Performance of Long dated Commodity Derivatives', Quantitative Methods in Finance 2016, Sydney, Australia.

Schlogl, E. & Chang, Y. 2012, 'Carry trade and liquidity risk: Evidence from forward and cross-currency swap markets', 2012 Auckland Finance Meeting, Auckland, New Zealand.

Pilz, K. & Schlogl, E. 2012, 'Calibration of multi-currency LIBOR market model: An orthonormal procrustes problem', Seminar Presentation, Imperial College LOndon, London, UK.

Pilz, K. & Schlogl, E. 2012, 'Calibration of multi-currency LIBOR market model: An orthonormal procrustes problem', Seminar Presentation, Rheinische-Friedrich-Wilhelms-University, Bonn, Germany.

Schlogl, E., Nielsen, J. & Sandman, K. 2010, 'Equity-linked pension schemes with guarantees', 14th International Congress on Insurance: Mathematics and Economics, Toronto, Canada.

Pilz, K. & Schlogl, E. 2010, 'A hybrid commodity and interest rate market model', 6th World Congress of the Bachelier Finance Society, Toronto, Canada.

Schlogl, E. 2010, 'CalibrationÂ ofÂ LIBORÂ marketÂ modelsÂ incorporatingÂ multipleÂ sourcesÂ ofÂ riskÂ', Quantitative Methods in Finance 2010 Conference, Sydney, Australia.

Bruti Liberati, N., Nikitopoulos Sklibosios, C., Platen, E. & Schlogl, E. 2009, 'Alternative defaultable term structure models', X Workshop on Quantitative Finance to the Memory of Nicola Bruti-Liberati, Milan, Italy.

Schlogl, E. 2009, 'Quantitative finance before and after the crisis', Seminar Presentation, Sim Corp, Sydney, Australia.

Peng, T. & Schlogl, E. 2008, 'Dynamic default correlation models: Binomial lattices, cross entropy and perfect match', Bachelier Finance Society 5th World Congress, Lindon, UK.

Peng, T. & Schlogl, E. 2008, 'Dynamic default correlation models: Binomial lattices, cross entropy and perfect match', Seminar, Lehman Brothers Investment Bank, London, UK.

Schlogl, E. 2008, 'Option pricing where the underlying assets follow a Gram/Charlier density of arbitrary order', Third International Conference on Mathematics in Finance, Kruger National Park, South Africa.

Nikitopoulos Sklibosios, C., Bruti Liberati, N., Platen, E. & Schlogl, E. 2008, 'Real-world pricing for defaultable term structure models', Bachelier Finance Society 5th World Congress, London, UK.

Schlogl, E. 2008, 'Option pricing where assets follow a Gram-Charlier density of arbitrary order', Bachelier Finance Society 5th World Congress, London, UK.

Schlogl, E. 2008, 'Design patterns and objects in monte carlo simulation', Quantitative Methods in Finance 2008 Conference, Sydney, Australia.

Schlogl, E. 2008, 'Option Pricing where Assets Follow a Gram-Charlier Density of Arbitrary Order', Seminar, Lehman Brothers Investment Bank, London, UK.

Bruti Liberati, N., Nikitopoulos Sklibosios, C., Platen, E. & Schlogl, E. 2007, 'Real-World Pricing for Defaultable Term Structure Models', CREDIT 2007, Venice, Italy.

Peng, T. & Schlogl, E. 2007, 'Default correlation modelling: Binomial lattices, cross entropy and perfect match', CREDIT 2007 Conference, Venice, Italy.

Schlogl, E. 2007, 'Option pricing where the underlying assets follow a Gram/Charlier density of arbitrary order', Q Group Australia 2007 Colloquium, Sydney, Australia.

Bruti Liberati, N., Nikitopoulos Sklibosios, C., Platen, E. & Schlogl, E. 2007, 'Defaultable term structure models under the benchmark approach', Quantitative Methods in Finance 2007 Conference, Sydney, Australia.

Schlogl, E. 2006, 'Fitting the market: Tractable approximations and calibrating models to multiple volatility smiles',

*Quantitative Methods in Finance 2006 Conference*, Quantitative Methods in Finance 2006 Conference, Sydney, Australia. Schlogl, E. 2006, 'Generic implementation of control variates in option pricing',

*5th National Symposium on Financial Mathematics*, 5th National Symposium on Financial Mathematics, Melbourne, Australia. Schlogl, E. & Schlogl, L. 2006, 'Fitting CDO factor distributions to quoted synthetic tranche spreads',

*2006 Symposium on Credit Risk, Extreme Values and Actural Studies*, Symposium on Credit Risk, Extreme Values and Actural Studies, Canberra, Austalia. Schlogl, E. 2005, 'Factor distributions and correlations implied by market quotes for synthetic CDO',

*4th National Symposium on Financial Mathematics*, 4th National Symposium on Financial Mathematics, -, Day Dream Island, Australia. Schlogl, E. 2005, 'Spoken and implied: factor distributions implied by quotes CDO spreads and the pricing of bespoke tranches',

*Quantitative Methods in Finance 2005 Conference*, Quantitative Methods in Finance 2005 Conference, -, Sydney, Australia. Kazakov, V., Schlogl, E. & Schlogl, L. 2004, 'Gram-charlier expansions, edgeworth expansions and multivariate distributions implied by options prices.',

*3rd National symposium on financial mathematics*, 3rd National symposium on financial mathematics, -, Melbourne, Australia. Schlogl, E. 2004, 'Modelling default correlation for portfolio credit risk',

*Derivatives and risk management*, Derivatives and risk mamagement, -, Sydney, Australia. Schlogl, E. 2004, 'Default correlation modelling',

*Sydney financial mathematics workshop*, Sydney financial mathematics workshop, -, Sydney, Australia. Schlogl, E. 2004, 'Advance credit risk measurement and modelling techniques for effective portfolio credit risk management',

*Risk magazine workshop*, Risk magazine workshop, -, Hong Kong, China. Schlogl, E. 2004, 'Understanding the key issues and concerns in modelling portfolio credit risk',

*Credit risk forum 2004*, Credit risk forum 2004, -, Sydney, Australia. Schlogl, E. 2004, 'Factor distribution and correlations implied by market quotes for synthetic CDO tranches',

*-*, Quantitative methods in finance 2004 conference, -, Sydney, Australia. Frishling, V. & Schlogl, E. 2004, 'Credit derivatives pricing models: Overview and firm value models',

*Sydney financial mathematics workshop*, Sydney Financial Mathematics Workshop, -, Sydney, Australia. Mahayni, A.B. & Schlogl, E. 2003, 'The risk management of power options embedded in life-insurance products',

*20th AFFI International Conference*, AFFI International Conference, The Association Francaise de Finance, Lyon, France, pp. 1-27. Chiarella, C., Schlogl, E. & Nikitopoulos Sklibosios, C. 2003, 'A Markovian defaultable term structure model with state dependent volatilities',

*CREDIT 2003 Conference on Dependence Modelling for Credit Portfolios*, --, Venice, Italy. Chiarella, C., Nikitopoulos Sklibosios, C. & Schlogl, E. 2003, 'A Markovian defaultable term structure model with state dependent volatilities',

*Quantitative Methods in Finance 2003 Conference*, Quantitative Methods in Finance 2003 Conference, --, Sydney, Australia. Schlogl, E. 2003, 'The risk management of minimum return guarantees',

*Quantitative Methods in Finance 2003 Conference*, Quantitative Methods in Finance 2003 Conference, --, Sydney. Schlogl, E. & Kazakov, V. 2003, 'Implied volatilities, implied correlations, implied distributions: Information contained in options prices',

*2nd National Symposium on Financial Markets*, 2nd National Symposium on Financial Markets, --, Sydney. Schlogl, E. & Mahayni, A.B. 2003, 'The risk management of minimum return guarantees: Retirement provision in scary markets',

*11th Australian Colloquium of Superannuation Researchers*, 11th Australian Colloquium of Superannuation Researchers, --, Sydney. Schlogl, E. 2002, 'Arbitrage-free interpolation in models of market observable interest rates',

*2nd World Congress of the Bachelier Finance Society*. Schlogl, E. 2002, 'Integration of interest rate and currency risk across markets: model calibration, derivatives pricing & risk management',

*RISK 2002 Conference*, RISK 2002 Conference, Sydney, Australia. Schlogl, E. 2002, 'Joint calibration of volatilities & correlations in interest rate and FX markets',

*Quantitative Methods in Finance 2002 Conference*, Quantitative Methods in Finance 2002 Conference, Sydney and Cairns, Australia.## Journal articles

Karlsson, P., Pilz, K. & Schlogl, E. 2017, 'Calibrating a Market Model with Stochastic Volatility to Commodity and Interest Rate Risk',

*Quantitative Finance*, vol. 17, no. 6, pp. 907-925. Pilz, K. & Schlogl, E. 2013, 'A hybrid commodity and interest rate market model',

View/Download from: UTS OPUS or Publisher's site

*Quantitative Finance*, vol. 13, no. 4, pp. 543-560.View/Download from: UTS OPUS or Publisher's site

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-interpretation½ 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',

View/Download from: UTS OPUS or Publisher's site

*Journal of Economic Dynamics and Control*, vol. 37, no. 3, pp. 611-632.View/Download from: UTS OPUS or Publisher's site

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',

View/Download from: UTS OPUS or Publisher's site

*Insurance: Mathematics and Economics*, vol. 49, no. 3, pp. 547-564.View/Download from: UTS OPUS or Publisher's site

This paper analyses the relationship between the level of a return guarantee in an equity-linked pension scheme and the proportion of an investors 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',

View/Download from: UTS OPUS or Publisher's site

*Asia - Pacific Financial Markets*, vol. 16, no. 1, pp. 1-31.View/Download from: UTS OPUS or Publisher's site

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',

View/Download from: UTS OPUS or Publisher's site

*BuR - Business Research*, vol. 1, no. 1, pp. 55-76.View/Download from: UTS OPUS or Publisher's site

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 Markovian Defaultable Term Structure Model with State Dependent Volatilities',

View/Download from: UTS OPUS or Publisher's site

*International Journal of Theoretical and Applied Finance*, vol. 10, no. 1, pp. 155-202.View/Download from: UTS OPUS or Publisher's site

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.

Chiarella, C., Nikitopoulos Sklibosios, C. & Schlogl, E. 2007, 'A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton Models with Jumps',

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*Applied Mathematical Finance*, vol. 14, no. 5, pp. 365-399.View/Download from: UTS OPUS

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.

Choy, B., Dun, T. & Schlogl, E. 2004, 'Correlating market models',

View/Download from: UTS OPUS

*Asia Risk*, vol. October, pp. 53-59.View/Download from: UTS OPUS

Choy, B., Dun, T. & Schlogl, E. 2004, 'Response to comments by Stephen Blyth and Maciej Sawicki',

*Risk*, vol. 17, no. 11, p. 118. Schlogl, E. 2002, 'A multicurrency extension of the lognormal interest rate market models',

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*Finance and Stochastics*, vol. 6, no. 2, pp. 173-196.View/Download from: UTS OPUS or Publisher's site

Dun, T., Barton, G.W. & Schlogl, E. 2001, 'Simulated Swaption Delta-Hedging in the Lognormal Forward Libor Model',

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*International Journal of Theoretical & Applied Finance*, vol. 4, no. 4, pp. 677-709.View/Download from: UTS OPUS or Publisher's site

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 prot 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.

Schlogl, E. & Sommer, D. 1998, 'Factor Models and the Shape of the Term Structure',

*The Journal of Financial Engineering*, vol. 7.## Other

Chiarella, C., Nikitopoulos-Sklibosios, C., Schlogl, E. & Yang, H. 2016, 'Pricing American Options under Regime Switching Using Method of Lines'.

This paper considers the American option pricing problem under regime-switching by using the method-of-lines (MOL) scheme. American option prices in each regime involve prices
in all other regimes. We treat the prices from other regimes implicitly, thus guaranteeing consistency. Iterative procedures are required but very few iterative steps are needed in
practice. Numerical tests demonstrate the robustness, accuracy and efficiency of the proposed numerical scheme. We compare our results with Buffington and Elliott (2002)'s analytical
approximation under two regimes. Our MOL scheme provides improved results especially for out-of-the money options, possibly because they use a separation of variable approach to the PDEs
which cannot hold around the early exercise region. We also compare our results with those of Khaliq and Liu (2009) and suggest that their implicit scheme can be improved.

Karlsson, P., Pilz, K.F. & Schlogl, E. 2016, 'Calibrating Market Model to Commodity and Interest Rate Risk'.

Based on the multi-currency LIBOR Market Model (LMM) this paper constructs a hybrid commodity interest rate market model with a time-dependent stochastic local volatility function allowing the model to simultaneously fit the
implied volatility surfaces of commodity and interest rate options. Since liquid market prices are only available for options on commodity futures, rather than forwards, a convexity correction formula for the model is derived to
account for the difference between forward and futures prices. A procedure for efficiently calibrating the model to interest rate and commodity volatility smiles is constructed. Finally, the model is fitted to an exogenously given
correlation structure between forward interest rates and commodity prices (cross–correlation). When calibrating to options on forwards (rather than futures), the fitting of cross–correlation preserves the (separate) calibration in the
two markets (interest rate and commodity options), while in the case of futures a (rapidly converging) iterative fitting procedure is presented. The fitting of cross–correlation is reduced to finding an optimal rotation of volatility
vectors, which is shown to be an appropriately modified version of the 'orthonormal Procrustes problem in linear algebra. The calibration approach is demonstrated in an application to market data for oil futures.

Cheng, B., Nikitopoulos Sklibosios, C. & Schlogl, E. 2016, 'Empirical Hedging Performance of Long dated Commodity Derivatives',

*Research Paper: 376, Quantitative Finance Research Centre, University of Technology Sydney*. Cheng, B., Nikitopoulos Sklibosios, C. & Schlogl, E. 2016, 'Hedging Futures Options with Stochastic Interest Rates',

*Research Paper: 375, Quantitative Finance Research Centre, University of Technology Sydney*. Cheng, B., Nikitopoulos Sklibosios, C. & Schlogl, E. 2016, 'Empirical Pricing Performance on Long Dated Crude Oil Derivatives: Do Models with Stochastic Interest Rates Matter?',

*Research Paper: 367, Quantitative Finance Research Centre, University of Technology Sydney*. Cheng, B., Nikitopoulos-Sklibosios, C. & Schlogl, E. 2015, 'Pricing of Long-dated Commodity Derivatives with Stochastic Volatility and Stochastic Interest Rates'.

Aiming to study pricing of long-dated commodity derivatives, this paper presents a class of models within the Heath, Jarrow, and Morton (1992) framework for commodity futures
prices that incorporates stochastic volatility and stochastic interest rate and allows a correlation structure between the futures price process, the futures volatility process and the
interest rate process. The functional form of the futures price volatility is specified so that the model admits finite dimensional realisations and retains affine representations,
henceforth quasi-analytical European futures option pricing formulae can be obtained. A sensitivity analysis reveals that the correlation between the interest rate process and the futures
price process has noticeable impact on the prices of long-dated futures options, while the correlation between the interest rate process and the futures price volatility process does not
impact option prices. Furthermore, when interest rates are negatively correlated with futures prices then option prices are more sensitive to the volatility of interest rates, an effect
that is more pronounced with longer maturity options.

Chang, Y. & Schlogl, E. 2014, 'A Consistent Framework for Modelling Basis Spreads in Tenor Swaps'.

The phenomenon of the frequency basis (i.e. a spread applied to one leg of a swap to exchange one
oating interest rate for another of a different tenor in the same currency) contradicts textbook no-arbitrage conditions and
has become an important feature of interest rate markets since the beginning of the Global Financial Crisis (GFC) in 2008. Empirically, the basis spread cannot be explained by transaction costs alone, and therefore must be due to a
new perception by the market of risks involved in the execution of textbook "arbitrage" strategies. This has led practitioners to adopt a pragmatic "multi-curve" approach to interest rate modelling, which leads to a proliferation of
term structures, one for each tenor. We take a more fundamental approach and explicitly model liquidity risk as the driver of basis spreads, reducing the dimensionality of the market for the frequency basis from observed spread term
structures for every frequency pair down to term structures of two factors characterising liquidity risk. To this end, we use an intensity model to describe the arrival time of (possibly stochastic) liquidity shocks with a Cox Process.
The model parameters are calibrated to quoted market data on basis spreads, and the improving stability of the calibration suggests that the basis swap market has matured since the turmoil of the GFC.

Nielsen, J.A., Sandman, K. & Schlogl, E. 2010, 'Equity-linked pension schemes with guarantees',

*Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney*. Research Paper Number: 270 Abstract: 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 participation surplus. 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 contracts pecifications 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 a 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.

Nielsen, J., Sandmann, K. & Schlogl, E. 2010, 'Equity-Linked Pension Schemes with Guarantees',

*QFRC*. This paper demonstrates an efficient numerical (semi-analytical) method for valuing return guarantees embedded in equity-linked pension schemes and analyses the qualitative properties of such contracts. We study and compare the pricing of three types of pension schemes with guarantees. These are long term investment plans, in which the investor typically puts in periodic payments of cash over a long time. The possibility of early contract termination is modelled by a mortality distribution. These schemes are closely related to equity-linked life insurance contracts, and the results presented here are also applicable to the latter.

Pilz, K. & Schlogl, E. 2010, 'Calibration of Multicurrency LIBOR Market Models'.

This paper presents a methodf or calibrating a multi currency lognormal LIBOR Market Model to market data of at-the-money caps, swaptions and FX options. By exploiting the fact that multivariate
normal distributions are invariant under orthonormal transformations, the calibration problem is decomposed into manageable stages, while maintaining the ability to achieve realistic correlation structures
between all modelled market variables.

Bruti Liberati, N., Nikitopoulos Sklibosios, C., Platen, E. & Schlogl, E. 2009, 'Alternative Defaultable Term Structure Models',

*Quantitative Finance Research Paper Series*. 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.

Pilz, K. & Schlogl, E. 2009, 'A hybrid commodity and interest rate',

*Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney*. Research Paper Number: 261 Abstract: 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 âre-interpretationâ 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. & SchlÃ¶gl, L. 2007, 'Factor distributions implied by quoted CDO spreads tranche pricing',

*Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney*. Research Paper Number: 190 Abstract: The rapid pace of innovation in the market for credit risk has given rise to a liquid market in synthetic collateralised debt obligation (CDO) tranches on standardised portfolios. To the extent that tranche spreads depend on default dependence between different obligors in the reference portfolio, quoted spreads can be seen as aggregating the market views on this dependence. In a manner reminiscent of the volatility smiles found in liquid option markets, practitioners speak of implied correlation âsmilesâ and âskewsâ. We explore how this analogy can be taken a step further to extract implied factor distributions from the market quotes for synthetic CDO tranches.

Chiarella, C., Nikitopoulos Sklibosios, C. & Schlogl, E. 2005, 'A control variate method for Monte Carlo simulations of Heath-Jarrow-Morton with jumps (QFRC paper #167)'.

ISSN 1441-8010 www.business.uts.edu.au/qfrc/research/research_papers/rp167.pdf

Chiarella, C., Schlogl, E. & Nikitopoulos Sklibosios, C. 2004, 'A Markovian defaultable term structure model with state dependent volatilities (QFRC paper #135)'.

Choy, S., Dun, T. & Schlogl, E. 2003, 'Correlating market models (QFRC paper #105)'.

Mahayni, A.B. & Schlogl, E. 2003, 'The risk management of minimum return guarantees (QFRC paper #102)'.

Schlogl, E. 2001, 'Arbitrage-free interpolation in models of market observable interest rates',

*Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney*. Research Paper Number: 71 Abstract: Models which postulate lognormal dynamics for interest rates which are compounded according to market conventions, such as forward LIBOR or forward swap rates, can be constructed initially in a discrete tenor framework. Interpolating interest interest rates between maturities in the discrete tenor structure is equivalent to extending the model to continuous tenor. The present paper sets forth an alternative way of performing this extension; one which preserves the Markovian properties of the discrete tenor models and guarantees the positivity of all interpolated rates.

Dunne, T. & Schlogl, E. 2000, 'Simulated swaption delta-hedging in the lognormal forward Libor model',

*Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney*. Research Paper Number: 40 Abstract: Alternative approaches to hedging swaptions are explored and tested by simulation. Hedging methods implied by the Balck 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 profit 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 financial practitioners - it would be the preferred method in practice.

Schlogl, E. & Schlogl, L. 1999, 'A square-root interest rate model fitting discrete initial term structure data',

*Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney*. Research Paper Number: 24 Abstract: This paper presents the one- and the multifactor versions of a term structure model in which the factor dynamics are given by Cox/Ingersoll/Ross (CIR) type "square root" diffusions with piecewise constant parameters. This model is fitted to initial term structures given by a finite number of data points, interpolating endogenously. Closed form and near-closed form solutions for a large class of fixed income derivatives are derived in terms of a compound noncentral chi-square distribution. An implementation of the model is discussed where the initial term structure of volatility is fitted via cap prices.

Dudenhausen, A., Schlögl, E. & Schlögl, L. 1999, 'Robustness of Gaussian Hedges and the Hedging of Fixed Income Derivatives'.

The effect of model and parameter misspecification on the effectiveness of Gaussian hedging strategies for derivative financial instrumens is analyzed, showing that Gaussian hedges in the
"natural" hedging instruments are particularly robust. This is true for all models that imply Balck/Scholes - type formulas for option prices and hedging strategies. In this paper we focus on the hedging
of fixed income derivatives and show how to apply these results both within the framework of Gaussian term structure models as well as the increasingly popular market models where the prices for caplets
and swaptions are given by the corresponding Black formulas. By explicitly considering the behaviour of the hedging strategy under misspecification we also derive the El Karoui, Jeanblanc-Picque and
Shreve (1995, 1998) and Avellaneda, Levy and Paras (1995) results that a superhedge is obtained in the Black/Scholes model if the misspecified volatility dominates the true volatility. Furthermore, we
show that the robustness and superhedging result do not hold if the natural hedging instruments are unavailable. In this case, we study criteria for the optimal choice from the instruments that are
available.

Schlögl, E. 1999, 'A Multicurrency Extension of the Lognormal Interest Rate Market Models'.

The Market Models of the term structure of interest rates, in which forward LIBOR or forward swap rates are modelled to be lognormal under the forward probability measure of the corresponding
maturity, are extended to a multicurrency setting. If lognormal dynamics are assumed for forward swap rates in two currencies, for one maturity, with the dynamics for all other maturities given by
no-arbitage relationships. Alternatively, one could choose forward interest rates in only one currency, say the domestic, to be lognormal and postulate lognormal dynamics for all forward exchange rates,
with the dynamics of foreign interest rates determined by no-arbitrage relationships.

Schlogl, E. & Sommer, D. 1997, 'Factor Models and the Shape of the Term Structure'.

Schlogl, E. & Sommer, D. 1994, 'On Short Rate Processes and Their Implications for Term Structure Movements'.

## Reports

Schlogl, E. 2002,

*Extracting the joint volatility structure of foreign exchange & interest rates from option prices*.**Selected Peer-Assessed Projects**