# Dr Christina Nikitopoulos Sklibosios

### Biography

Dr Christina Nikitopoulos joined the School of Finance and Economics in July 2003 and she has been a Senior Lecturer at the UTS Business School since July 2011. She had been with the School for several years before this undertaking her PhD on developing Markovian models for the term structure of interest rates under jump-diffusions. Christina has an extensive experience in teaching within Quantitative Finance with specialization in derivative securities pricing, derivatives and risk management, investments as well as interest rate modelling.

Her research interests include derivative securities pricing, modelling of term structure of interest rates, credit risk modelling, and more recently modelling of commodity futures markets. Christina has published in leading finance journals including Energy Economics, The Journal of Futures Markets, Quantitative Finance and Applied Mathematical Finance.

**Senior Lecturer,**Finance Discipline Group

**Core Member,**Quantitative Finance Research Centre

MBus(UTS), PhD (UTS)

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**Phone**

+61 2 9514 7768

**Room**

CB08.07.01

### Research Interests

Derivative securities pricing, modelling of term structure of interest rates, credit risk modelling, modelling of commodity prices.

Derivative securities pricing, Interest rate modelling and derivatives

## Chapters

Clewlow, L., Kang, B. & Nikitopoulos Sklibosios, C. 2014, 'On the Volatility of Commodity Futures Prices' in Dieci, R., He, X. & Hommes, C. (eds),

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*Nonlinear Economic Dynamics and Financial Modelling: Essays in Honour of Carl Chiarella*, Springer, pp. 315-334.View/Download from: Publisher's site

## Conferences

Chiarella, C., Kang, B., Nikitopoulos, C.S. & Tô, T.-.D. 2015, 'The Return-Volatility Relation in Commodity Futures Markets',

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*Journal of Futures Markets*, Wiley-Liss Inc..View/Download from: Publisher's site

By employing a continuous time multi-factor stochastic volatility model, the dynamic relation between returns and volatility in the commodity futures markets is analyzed. The model is estimated by using an extensive database of gold and crude oil futures and futures options. A positive relation in the gold futures market and a negative relation in the crude oil futures market subsist, especially over periods of high volatility principally driven by market-wide shocks. The opposite relation holds over quiet periods typically driven by commodity-specific effects. According to the proposed convenience yield effect, normal (inverted) commodity futures markets entail a negative (positive) relation.

Nikitopoulos Sklibosios, C., Squires, M., Thorp, S. & Yeung, D.C. 2014, 'The spread seesaw: How consumption, inventory and expected volatility affect the oik forward curve', Frontiers in Financial Econometrics, Brisbane, Australia.

Chiarella, C., Kang, B., Nikitopoulos Sklibosios, C. & To, T. 2014, 'The return-volatility relation in commodity futures markets', Performance of Financial Markets and Credit Derivatives, Geelong, Australia.

Chiarella, C., Kang, B., Nikitopoulos, C.S. & TÔ, T.-.D. 2013, 'Humps in the volatility structure of the crude oil futures market: New evidence',

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*Energy Economics*, pp. 989-1000.View/Download from: Publisher's site

This paper analyses the volatility structure of commodity derivatives markets. The model encompasses hump-shaped, unspanned stochastic volatility, which entails a finite-dimensional affine model for the commodity futures curve and quasi-analytical prices for options on commodity futures. Using an extensive database of crude oil futures and futures options spanning 21. years, we find the presence of hump-shaped, partially spanned stochastic volatility in the crude oil market. The hump shaped feature is more pronounced when the market is more volatile, and delivers better pricing as well as hedging performance under various dynamic factor hedging schemes. © 2013 Elsevier B.V.

Nikitopoulos-Sklibosios, C. & Platen, E. 2012, 'Alternative Term Structure Models for Reviewing Expectations Puzzles'.

According to the expectations hypothesis, the forward rate is equal to the expected future short rate, an argument that is not supported by most empirical studies that demonstrate the existence
of term premiums. An alternative arbitrage-free term structure model for reviewing the expectations hypothesis is presented and tractable expressions for time-varying term premiums are obtained. The model
is constructed under the real-world probability measure and depends on two stochastic factors: the short rate and the market price of risk. The model suggests that for short maturities the short rate
contribution determines the term premiums, while for longer maturities, the contribution of the market price of risk dominates.

Chiarella, C., Kang, B., Nikitopoulos Sklibosios, C. & To, T. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence', 18th International Conference Computing in Economics and Finance, Prague, Czech Republic.

Chiarella, C., Kang, B., Nikitopoulos Sklibosios, C. & To, T. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence', 29th Spring International Conference of the French Finance Association, Strasbourg, France.

Chiarella, C., Kang, B., Nikitopoulos Sklibosios, C. & To, T. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence', Seminar Presentation, University of Cyprus, Cyprus.

Chiarella, C., Kang, B., Nikitopoulos Sklibosios, C. & To, T. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence', Asian Finance Association and Taiwan Finance Association 2012 Joint International Conference, Taipei, Taiwan.

Chiarella, C., Kang, B. & Nikitopoulos Sklibosios, C. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence', Seminar Presentation, Sydney Institute of Language and Commerce, Shanghai University, Shanghai, China.

Chiarella, C., Kang, B. & Nikitopoulos Sklibosios, C. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence"', Seminar Presentation, School of Commerce and the Centre for Applied Financial Studies, University of South Australia, Adelaide, 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.

Bruti Liberati, N., Nikitopoulos Sklibosios, C. & Platen, E. 2008, 'Monte-Carlo simulations of alternative defaultable term structure models', Bachelier Finance Society 5th World Congress, London, UK.

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.

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

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*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.

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.

Bruti Liberati, N., Nikitopoulos Sklibosios, C. & Platen, E. 2006, 'Heath Jarrow Morton equation for jump-diffusions under the benchmark approach',

*2nd International Symposium on Economic Theory, Policy & Applications*, 2nd International Symposium on Economic Theory, Policy & Applications, -, Athens, Greece. Bruti Liberati, N., Nikitopoulos Sklibosios, C. & Platen, E. 2006, 'On the strong approximation of jump-diffusion processes', Stochastic Calculus and its Applications to Quantitative Finance and Electrical Engineering, Calgary, Canada.

Nikitopoulos Sklibosios, C. 2006, 'Real-world pricing for the HJM framework with jumps',

*Quantitative Methods in Finance 2006 Conference*, Quantitative Methods in Finance 2006 Conference, Sydney, Australia. Nikitopoulos Sklibosios, C. 2006, 'Markovian HJM term structure models under jump-diffusions', Seminar Presentation, Department of Mathematics, University of Patras, Patras, Greece.

Nikitopoulos Sklibosios, C. 2006, 'Benchmark term structure of interest rates under jump-diffusions', Seminar Presentation, Department of Mathematics, University of Patras, Patras, Greece.

Chiarella, C. & Nikitopoulos-Sklibosios, C. 2004, 'A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework'.

This paper considers a class of term structure models that is a parameterisation of the Shirakawa (1991) extension of the Heath, Jarrow and Morton (1992) model to the case of jump-diffusions. We
consider specific forward rate volatility structures that incorporate state dependent Wiener volatility functions and time dependent Poisson volatility functions. Within this framework, we discuss the
Markovianisation issue, and obtain the corresponding affine term structure of interest rates. As a result we are able to obtain a broad tractable class of jump-diffusion term structure models. We
relate our approach to the existing class of jump-diffusion term structure models whose starting point is a jump-diffusion process for the spot rate. In particular we obtain natural jump-diffusion
versions of the Hull and White (1990, 1994) one-factor and two-factor models and the Ritchken and Sankarasubramanian (1995) model within the HJM framework. We also give some numerical simulations to gauge
the effect of the jump-component on yield curves and the implications of various volatility specifications for the spot rate distributions.

Chiarella, C. & Nikitopoulos Sklibosios, C. 2003, 'A jump-diffusion bond pricing model within the HJM frame work',

*Japanese Association Financial Econometrics and Engineering Meeting*, --, Tokyo, Japan. Chiarella, C. & Nikitopoulos Sklibosios, C. 2003, 'An implementation of the Shirakawa jump-diffusion term structure model',

*9th International Conference on Computing in Economics and Finance*, --, Seattle, USA. Nikitopoulos Sklibosios, C. 2003, 'Defaultable HJM term structure models', Quantitative Methods in Finance 2003 Conference, Sydney, Australia.

Nikitopoulos Sklibosios, C. 2002, 'A jump diffusion derivative pricing model arising within the Heath-Jarrow-Morton framework',

*Quantitative methods in Finance 2002 Conference*, Quantitative Methods in Finance 2002 Conference, Sydney and Cairns, Australia. Nikitopoulos Sklibosios, C. & Chiarella, C. 2002, 'A jump diffusion derivative pricing model arising within the Heath-Jarrow-Morton framework',

*2nd World Congress of the Bachelier Finance Society*, 2nd World Congress of the Bachelier Finance Society, Knossos,Crete.## Journal articles

Nikitopoulos Sklibosios, C. & Platen, E. 2013, 'Alternative term structure models for reviewing the expectations puzzle',

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*International Journal of Economic Research*, vol. 10, no. 2, pp. 349-372.View/Download from: UTS OPUS

NA

Chiarella, C., Kang, B., Nikitopoulos Sklibosios, C. & To, T.D. 2013, 'Humps in the volatility structure of the crude oil futures market: New evidence',

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

*Energy Economics*, vol. 40, no. 1, pp. 989-1000.View/Download from: UTS OPUS or Publisher's site

This paper analyses the volatility structure of commodity derivatives markets. The model encompasses hump-shaped, unspanned stochastic volatility, which entails a finite-dimensional affine model for the commodity futures curve and quasi-analytical prices for options on commodity futures. Using an extensive database of crude oil futures and futures options spanning 21 years, we find the presence of hump-shaped, partially spanned stochastic volatility in the crude oil market. The hump shaped feature is more pronounced when the market is more volatile, and delivers better pricing as well as hedging performance under various dynamic factor hedging schemes.

Chiarella, C., Maina, S.C. & Nikitopoulos-Sklibosios, C. 2011, 'Credit Derivative Pricing with Stochastic Volatility Models'.

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View/Download from: UTS OPUS

This paper proposes a framework for pricing credit derivatives within the defaultable Markovian HJM framework featuring unspanned stochastic volatility. Motivated by empirical evidence,
hump-shaped level dependent stochastic volatility specifications are proposed, such that the model admits finite dimensional Markovian structures. The model also accommodates a correlation structure
between the stochastic volatility, default-free interest rates and credit spreads. Default free and defaultable bonds are explicitly priced and an approach for pricing credit default swaps and swaptions
is presented where the credit swap rates can be approximated by defaultable bond prices with varying maturities. A sensitivity analysis capturing the impact of the model parameters including correlations
and stochastic volatility, on the credit swap rate and the value of the credit swaption is also presented.

Bruti-Liberati, N., Nikitopoulos-Sklibosios, C. & Platen, E. 2010, 'Real-world jump-diffusion term structure models',

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*Quantitative Finance*, vol. 10, no. 1, pp. 23-37.View/Download from: UTS OPUS or Publisher's site

This paper considers interest rate term structure models in a market attracting both continuous and discrete types of uncertainty. The event-driven noise is modelled by a Poisson random measure. Using as numeraire the growth optimal portfolio, interest rate derivatives are priced under the real-world probability measure. In particular, the real-world dynamics of the forward rates are derived and, for specific volatility structures, finite-dimensional Markovian representations are obtained. Furthermore, allowing for a stochastic short rate in a non-Markovian setting, a class of tractable affine term structures is derived where an equivalent risk-neutral probability measure may not exist. © 2010 Taylor & Francis.

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.

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.

Bruti-Liberati, N., Nikitopoulos-Sklibosios, C. & Platen, E. 2006, 'First Order Strong Approximations of Jump Diffusions',

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*Monte Carlo Methods and Applications*, vol. 12, no. 3, pp. 191-209.View/Download from: UTS OPUS or Publisher's site

Chiarella, C. & Sklibosios, C.N. 2003, 'A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework',

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

*Asia-Pacific Financial Markets*, vol. 10, no. 2-3, pp. 87-127.View/Download from: UTS OPUS or Publisher's site

## Other

Chiarella, C., Maina, S.C. & Nikitopoulos-Sklibosios, C. 2010, 'Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility'.

This paper presents a class of defaultable term structure models within the HJM framework with stochastic volatility. Under certain volatility specifications, the model admits finite dimensional
Markovian structures and consequently provides tractable solutions for interest rate derivatives. We also investigate the effect of stochastic volatility and of correlation between the stochastic
volatility and credit spreads on the defaultable short rate and defaultable bond prices.

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.

Bruti-Liberati, N., Nikitopoulos-Sklibosios, C. & Platen, E. 2007, 'Pricing under the Real-World Probability Measure for Jump-Diffusion Term Structure Models'.

This paper considers interest rate term structure models in a market attracting both continuous and discrete types of uncertainty. The event driven noise is modelled by a Poisson random measure.
Using as numeraire the growth optimal portfolio, interest rate derivatives are priced under the real-world probability measure. In particular, the real-world dynamics of the forward rates are derived and,
for specific volatility structures, finite dimensional Markovian representations are obtained. Furthermore, allowing for a stochastic short rate, a class of tractable affine term structures is derived
where an equivalent risk-neutral probability measure does not exist.

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. & Nikitopoulos Sklibosios, C. 2004, 'A class of jump-diffusion bond pricing models within the HJM framework (QFRC paper #132)'.

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

**Selected Peer-Assessed Projects**