# 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

**Director,**Quantitative Finance Research Centre

**Core Member,**Quantitative Finance Research Centre

DipVw (Bonn), PhD (Bonn)

Member, Bachelier Finance Society

**Phone**

+61 2 9514 7785

**Room**

CB08.07.15

### 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

Schlögl, E. & Schlögl, L. 2012, 'Factor Distributions Implied by Quoted CDO Spreads' in

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

*Frontiers in Quantitative Finance: Volatility and Credit Risk Modeling*, John Wiley and Sons, pp. 217-234.View/Download from: UTS OPUS or Publisher's site

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. 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. Schlögl, E. 2001, 'Arbitrage-Free Interpolation in Models of Market Observable Interest Rates'.

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.

## Conferences

Schlögl, E. 2013, 'Option pricing where the underlying assets follow a Gram/Charlier density of arbitrary order',

View/Download from: Publisher's site

*Journal of Economic Dynamics and Control*, pp. 611-632.View/Download from: 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. © 2012 Elsevier B.V.

Pilz, K.F. & Schloegl, E. 2013, 'A hybrid commodity and interest rate market model',

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*QUANTITATIVE FINANCE*, pp. 543-560.View/Download from: Publisher's site

Schlogl, E. & Chang, Y. 2012, 'Carry Trade and Liquidity Risk: Evidence from Forward and Cross-Currency Swap Markets'.

This study empirically examines the effect of foreign exchange (FX) market liquidity risk and volatility on the excess returns of currency carry trades. In contrast to the existent literature, we construct an alternative
proxy of liquidity risk - violations of no arbitrage bounds in the forward and currency swap markets. We also use volatility smile data to capture FX-market specific volatility. The sample data cover periods both before and after the
Global Financial Crisis (GFC). Both proxies are significant in explaining the abnormal returns of carry trades, particularly after the GFC. Our findings provide substantial evidence that uncovered interest parity (UIP) puzzle can
be resolved after controlling for liquidity risk and market volatility.

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.

Nielsen, J.A., Sandmann, K. & Schlögl, E. 2011, 'Equity-linked pension schemes with guarantees',

View/Download from: Publisher's site

*Insurance: Mathematics and Economics*, pp. 547-564.View/Download from: 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 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. © 2011 Elsevier B.V.

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. & Schlögl, E. 2009, 'Alternative defaultable term structure models',

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*Asia-Pacific Financial Markets*, pp. 1-31.View/Download from: 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. © 2009 Springer Science+Business Media, LLC.

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.

Chiarella, C., Sklibosios, C.N. & Schlögl, E. 2007, 'A Markovian defaultable term structure model with state dependent volatilities',

View/Download from: Publisher's site

*International Journal of Theoretical and Applied Finance*, pp. 155-202.View/Download from: Publisher's site

The defaultable forward rate is modelled as a jump diffusion process within the Schönbucher [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. © World Scientific Publishing Company.

CHIARELLA, C.A.R.L., SKLIBOSIOS, C.H.R.I.S.T.I.N.A.N.I.K.I.T.O.P.O.U.L.O.S. & SCHLÖGL, E.R.I.K. 2007, 'A MARKOVIAN DEFAULTABLE TERM STRUCTURE MODEL WITH STATE DEPENDENT VOLATILITIES',

*International Journal of Theoretical and Applied Finance*, pp. 155-202. The defaultable forward rate is modelled as a jump diffusion process within the Schönbucher [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.

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.

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. Mahayni, A. & Schlögl, E. 2003, 'The Risk Management of Minimum Return Guarantees'.

We analyse contracts which pay out a guaranteed minimum rate of return and a fraction of a positive excess rate, which is specified on the basis of a benchmark portfolio. These contracts are
closely related to unit-linked life-insurance/savings plans products and can be considered as alternatives to a direct investment in the underlying benchmark portfolio. The option embedded into the
savings plan is in fact a power option, and thus the specification of the "fair" contract parameters is closely related to well known features of these financial derivatives. The key issue,
both in order to rigorously justify valuation by arbitrage arguments and to prevent the guarantees from becoming uncontrollable liabilities to the issuer, is the risk management of the embedded options by
a tractable and realistic hedging strategy. The long maturity of life-insurance products makes it necessary to lift Black/Scholes assumptions and consider an uncertain volatility scenario, thus explicitly
taking into account "model risk". In this context, we show how to determine the contract parameters conservatively and implement robust risk management strategies. This highlights the necessity of a
careful choice of guarantees which are granted to the insurance customer and suggests a new role for a type of "bonus account" customary in many life-insurance contracts.

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

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. & Schlögl, E. 2008, 'The Risk Management of Minimum Return Guarantees',

View/Download from: UTS OPUS

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

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',

View/Download from: UTS OPUS

*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, 'Response to comments by Stephen Blyth and Maciej Sawicki',

*Risk*, vol. 17, no. 11, p. 118. Choy, B., Dun, T. & Schlögl, E. 2003, 'Correlating Market Models'.

View/Download from: UTS OPUS

View/Download from: UTS OPUS

Schlö & gl, 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

Dunn, T., Schlögl, E. & Barton, G. 2000, 'Simulated Swaption Delta-Hedging in the Lognormal Forward Libor Model'.

View/Download from: UTS OPUS

View/Download from: UTS OPUS

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.

## Other

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'.

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.

Schlögl, E. & Schlögl, L. 2007, 'Factor Distributions Implied by Quoted CDO Spreads Tranche Pricing'.

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 'smiles' and 'skews'. 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'.

This paper examines the pricing of interest rate derivatives when the interest rate dynamics experience infrequent jump shocks modelled as a Poisson process and within the Markovian HJM framework
developed in Chiarella & Nikitopoulos (2003). Closed form 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, we provide a novel perspective on the control variate
methods by going outside a given complex model to a simpler more tractable setting to provide the control variates.

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.

Schlögl, E. & Schlögl, L. 1999, 'A Square-Root Interest Rate Model Fitting Discrete Initial Term Structure Data'.

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.

## Reports

Schlögl, E. 2002,

*Extracting the Joint Volatility Structure of Foreign Exchange and Interest Rates from Option Prices*, no. 79.**Selected Peer-Assessed Projects**