Minicourses

References

1. Ackerer, D., & Filipović, D. (2016). Linear Credit Risk Models. Swiss Finance Institute Research Paper No. 16-34.
2. Ackerer, D., Filipović, D., & Pulido, S. (2016). The Jacobi Stochastic Volatility Model. Swiss Finance Institute Research Paper No. 16-35.
3. Filipović, D., Gourier, E., & Mancini, L. (2016). Quadratic Variance Swap Models. Journal of Financial Economics 119, 44-68.
4. Filipović, D., & Larsson, M. (2016). Polynomial Diffusions and Applications in Finance. Finance and Stochastics 20, 931-972.
5. Filipović, D., Larsson, M., & Trolle, A. (2016). Linear-Rational Term Structure Models. Journal of Finance, forthcoming.

Jan Kallsen: Portfolio choice, pricing, and hedging under small frictions

Real markets are facing bid-ask spreads, transaction costs and related kinds of market imperfections. These affect the performance of investment strategies, the trading volume, the cost of hedging and hence derivative prices. In this minicourse we study market frictions from the perspective of stochastic control. The main idea is to consider imperfections as small perturbations of the simpler frictionless model. This often allows us to quantify their leading-order effect surprisingly explicitly. We discuss a formal heuristic derivation of the asymptotic solution as well as rigorous verification strategies, based on both classical dynamic programming and dual approaches to stochastic control.

References
On this page (will be updated) a number of background papers can be found.

Special invited lectures

References

1. Erhan Bayraktar and Zhou Zhou (2016), Arbitrage, hedging and utility maximization using semi-static trading strategies with American options, (with ), Annals of Applied Probability 26(6), 3531-3558. [article], [SSRN] and [ArXiv].
2. Erhan Bayraktar, Yu-Jui Huang and Zhou Zhou (2015), On hedging American options under model uncertainty, SIAM Journal on Financial Mathematics 6(1), 425-447. [article], [SSRN] and [ArXiv]].
3. Erhan Bayraktar and Zhou Zhou (2016), No-arbitrage and hedging with liquid American options. [SSRN], [ArXiv].
4. Erhan Bayraktar and Zhou Zhou (2016), Super-hedging American Options with Semi-static Trading Strategies under Model Uncertainty. [SSRN], [ArXiv].

Thorsten Schmidt : A new perspective on multiple curve models

We consider a general representation of markets with multiple yield curves and provide a characterization of absence of arbitrage via techniques from large financial markets. In particular, we allow for stochastic discontinuities of the associated bond prices, incorporating recent results in term structure theory. The interesting point is that this setup allows us to consider market models as a special case. The obtained drift conditions build the foundation for the development of affine models which turn out to be significantly more complicated than in the classical on-curve markets. This is joint work with Zorana Grbac and Claudio Fontana. (slides)

References

1. Gehmlich, F. and T. Schmidt (2016), Dynamic defaultable term structure modelling beyond the intensity paradigm, forthcoming in Mathematical Finance. Also available as arXiv:1411.4851, and doi:10.1111/mafi.12138
2. Fontana, C. and T. Schmidt. General term structures under default risk, submitted.
3. Gehmlich, F. and T. Schmidt (2016), A generalized intensity based framework for single-name credit risk, in: Innovations in Derivatives Markets ? Fixed Income Modeling, Valuation Adjustments, Risk Management, and Regulation, 267-284, edited by Zorana Grbac, Kathrin Glau, Matthias Scherer, and Rudi Zagst, Springer.

Wim Schoutens: Applied conic finance

We give an introduction to conic finance. Conic Finance is a brand new quantitative finance theory incorporating in a fundamental way bid and ask pricing. We provide the basics and its connection with the concept of acceptability and coherent risk measures. Distorted expectations are employed to actually calculate bid and ask prices. We elaborate on various applications of the theory such as conic hedging, conic portfolio theory, conic trading and show how conic finance can be used for systemic risk measurement, liquidity measurement and how the counter-intuitive effects of booking profits due to your own credit deterioration (also referred to as Debt Valuation Adjustment or DVA) are mitigated under the conic bid and ask pricing theory. (slides)

References

1. Dilip Madan and Wim Schoutens (2016), Applied Conic Finance. Cambridge University Press
2. Dilip Madan and Wim Schoutens (2015), Conic CVA and DVA
3. José Manuel Corcuera, Florence Guillaume, Dilip B. Madan and Wim Schoutens (2010), Implied Liquidity - Towards Stochastic Liquidity Modeling and Liquidity Trading
4. Dilip B. Madan, Ernst Eberlein and Wim Schoutens (2011), Capital Requirements, the Option Surface, Market, Credit and Liquidity Risk
5. Dilip Madan and Wim Schoutens (2013), Two Processes for Two Prices
6. Florence Guillaume, Wim Schoutens and Hansjoerg Albrecher (2012), Implied Liquidity: Model Sensitivity
7. Ernst Eberlein, Dilip B. Madan, Martijn Pistorius, Wim Schoutens and Marc Yor (2013), Two Price Economies in Continuous Time
8. Dilip B. Madan, Peter Carr, Wim Schoutens and Michael Melamed (2015), Hedging Insurance Books
9. Dilip B. Madan, Martijn Pistorius and Wim Schoutens (2015), Dynamic Conic Hedging for Competitiveness

Short lectures

Anne Balter: Sets of indistinguishable models for robust optimisation

Models can be wrong and recognising their limitations is important in financial and economic decision making under uncertainty. Finding the explicit specification of the uncertainty set has been difficult so far. We develop a method that provides a plausible set of models to use in robust decision making. The choice of the specific size of the uncertainty region is what we will focus on. We use the Neyman-Pearson Lemma to characterise a set of models that cannot be distinguished statistically from a baseline model. The set of indistinguishable models can explicitly be obtained for a given probability for the Type I and II error. (slides)

References

1. Anne G. Balter and Antoon Pelsser (2015), Rectangular and Coherent Sets of Indistinguishable Models

Qian Feng: Efficient computation of exposure profiles under real-world and risk-neutral scenarios for Bermudan swaptions

This paper presents a computationally efficient technique for the computation of exposure distributions at any future time under the risk-neutral and some observed real-world probability measures, needed for computation of credit valuation adjustment (CVA) and potential future exposure (PFE). In particular, we present a valuation framework for Bermudan swaptions. The essential idea is to approximate the required value function via a set of risk-neutral scenarios and use this approximated value function on the set of observed real-world scenarios. This technique significantly improves the computational efficiency by avoiding nested Monte Carlo simulation and by using only basic methods such as regression. We demonstrate the benefits of this technique by computing exposure distributions for Bermudan swaptions under the Hull-White and the G2++ models. Joint work with S. Jain, P. Karlsson, B.D. Kandhai and C.W. Oosterlee.

References

1. Qian Feng, Shashi Jain, Patrik Karlsson, Drona Kandhai and Cornelis W. Oosterlee (2016), Efficient computation of exposure profiles on real-world and risk-neutral scenarios for Bermudan swaptions. Journal of Computational Finance 20(1), 139-172.

Rutger-Jan Lange: A new approach to filtering for non-linear state space models

This paper considers state space models with non-linear and non-Gaussian observation and state equations. We propose a new approximate filter, based on recursive on-line estimation of the posterior mode. The approximation error can be made arbitrarily small in some limit. For each new observation, the proposed filter uses multiple steps of an optimisation routine in order to update its estimate. These steps use the score of the predictive density, rather than the prediction error, making the filter robust and applicable to a wide class of models. Simulation studies reveal that the performance of the proposed filter in terms of RMSE is statistically indistinguishable from that of theoretically optimal methods. Furthermore, the proposed technique improves computational efficiency by several orders of magnitude. The method is illustrated by an application to stock returns subject to stochastic volatility and leverage.

References

1. Durbin, James, and Siem Jan Koopman (2000). Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 62.1 : 3-56.
2. Fahrmeir, Ludwig (1992). Posterior mode estimation by extended Kalman filtering for multivariate dynamic generalized linear models. Journal of the American Statistical Association 87.418: 501-509.

Anton van der Stoep: A novel Monte Carlo approach to hybrid local volatility models

We present in a Monte Carlo simulation framework a novel approach for the evaluation of hybrid local volatility models (Dupire 1994, Derman and Kani 1998). In particular, we consider the stochastic local volatility model - see e.g. Lipton et al. (2014), Piterbarg (2007), Tataru and Fisher (2010), Lipton (2002) - and the local volatility model incorporating stochastic interest rates - see e.g. Atlan (2006), Piterbarg (2006), Deelstra and Rayee (2012), Ren et al. (2007). For both model classes a particular (conditional) expectation must be evaluated, which cannot be extracted from the market and is expensive to compute. We establish accurate and 'cheap to evaluate' approximations for the expectations by means of the stochastic collocation method (Babuska et al. 2007, Xiu and Hesthaven 2005, Beck et al. 2012, Nobile et al. 2014, Sankaran and Marsden 2011), which was recently applied in a financial context (Grzelak et al. 2014, Grzelak and Oosterlee 2017), combined with standard regression techniques. Monte Carlo pricing experiments confirm that our method is highly accurate and fast.

References

1. Griselda Deelstra and Grégory Rayée, Local Volatility Pricing Models for Long-dated FX Derivatives (preprint)
2. L.A. Grzelak, J.A.S. Witteveen, M.Suarez-Taboada, C.W. Oosterlee, The Stochastic Collocation Monte Carlo Sampler: Highly efficient sampling from ?expensive? distributions
3. Vladimir Piterbarg, Modern Approaches to Stochastic Volatility Calibration (slides)
4. Yong Ren, Dilip Madan and Michael Qian Qian (2007), Calibrating and pricing with embedded local volatility models, Risk, 138-143
5. A.W. van der Stoep, L.A. Grzelak and C.W. Oosterlee (2017), A Novel Monte Carlo Approach to Hybrid Local Volatility Models, forthcoming in Quantitative Finance

Poster presentations

• Jakob Krause (Martin Luther University of Halle-Wittenberg): The role of liquidity in electricity markets
• Roland Seydel (German Finance Agency): Performance measures adjusted for the risk situation
• Anastasiia Zalashko (University of Vienna): Causal transport and applications