Thu, 12 Mar 2015
16:00
L4

Implied Volatility of Leveraged ETF Options: Consistency and Scaling​

Tim Siu-Tang Leung
(Colombia University)
Abstract

The growth of the exchange-traded fund (ETF) industry has given rise to the trading of options written on ETFs and their leveraged counterparts (LETFs). Motivated by a number of empirical market observations, we study the relationship between the ETF and LETF implied volatility surfaces under general stochastic volatility models. Analytic approximations for prices and implied volatilities are derived for LETF ​options, along with rigorous error bounds. In these price and IV expressions, we identify their non-trivial dependence on the leverage ratio. Moreover, we introduce a "moneyness scaling" procedure to enhance the comparison of implied volatilities across leverage ratios, and test it with empirical price data.

Thu, 05 Mar 2015
16:00
L4

Measures of Systemic Risk

Stefan Weber
(Leibniz Universität Hannover)
Abstract
Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of this type of risk requires the design and implementation of tools for the efficient macroprudential regulation of financial institutions. We propose a novel approach to measuring systemic risk.

Key to our construction is a rigorous derivation of systemic risk measures from the structure of the underlying system and the objectives of a financial regulator. The suggested systemic risk measures express systemic risk in terms of capital endowments of the financial firms. Their definition requires two ingredients: first, a random field that assigns to the capital allocations of the entities in the system a relevant stochastic outcome. The second ingredient is an acceptability criterion, i.e. a set of random variables that identifies those outcomes that are acceptable from the point of view of a regulatory authority. Systemic risk is measured by the set of allocations of additional capital that lead to acceptable outcomes. The resulting systemic risk measures are set-valued and can be studied using methods from set-valued convex analysis. At the same time, they can easily be applied to the regulation of financial institutions in practice.
 
We explain the conceptual framework and the definition of systemic risk measures, provide an algorithm for their computation, and illustrate their application in numerical case studies. We apply our methodology to systemic risk aggregation as described in Chen, Iyengar & Moallemi (2013) and to network models as suggested in the seminal paper of Eisenberg & Noe (2001), see also Cifuentes, Shin & Ferrucci (2005), Rogers & Veraart (2013), and Awiszus & Weber (2015). This is joint work with Zachary G. Feinstein and Birgit Rudloff
Tue, 24 Feb 2015
12:30
Oxford-Man Institute

Measuring and predicting human behaviour using online data

Tobias Preis
(University of Warwick)
Abstract

In this talk, I will outline some recent highlights of our research, addressing two questions. Firstly, can big data resources provide insights into crises in financial markets? By analysing Google query volumes for search terms related to finance and views of Wikipedia articles, we find patterns which may be interpreted as early warning signs of stock market moves. Secondly, can we provide insight into international differences in economic wellbeing by comparing patterns of interaction with the Internet? To answer this question, we introduce a future-orientation index to quantify the degree to which Internet users seek more information about years in the future than years in the past. We analyse Google logs and find a striking correlation between the country's GDP and the predisposition of its inhabitants to look forward. Our results illustrate the potential that combining extensive behavioural data sets offers for a better understanding of large scale human economic behaviour.
Thu, 19 Feb 2015
16:00
L1

Optimal casino betting: why lucky coins and good memory are important

Sang Hu
(National University of Singapore)
Abstract

We consider the dynamic casino gambling model initially proposed by Barberis (2012) and study the optimal stopping strategy of a pre-committing gambler with cumulative prospect theory (CPT) preferences. We illustrate how the strategies computed in Barberis (2012) can be strictly improved by reviewing the entire betting history or by tossing random coins, and explain that such improvement is possible because CPT preferences are not quasi-convex. Finally, we develop a systematic and analytical approach to finding the optimal strategy of the gambler. This is a joint work with Prof. Xue Dong He (Columbia University), Prof. Jan Obloj, and Prof. Xun Yu Zhou.

Thu, 12 Feb 2015
16:00
L4

Discrete time approximation of HJB equations via BSDEs with nonpositive jumps

Idris Kharroubi
(Université Paris Dauphine)
Abstract
We propose a new probabilistic numerical scheme for fully nonlinear equations of Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problems, which is based on the a recent Feynman-Kac representation by means of control randomization and backward stochastic differential equation with nonpositive jumps. We study a discrete time approximation for the minimal solution to this class of BSDE when the time step goes to zero, which provides both an approximation for the value function and for an optimal control in feedback form. We obtained a convergence rate without any ellipticity condition on the controlled diffusion coefficient.
Thu, 05 Feb 2015
16:00
L1

Bridge Simulation and Estimation for Multivariate Stochastic Differential Equations

Michael Sørensen
(University of Copenhagen)
Abstract

New simple methods of simulating multivariate diffusion bridges, approximately and exactly, are presented. Diffusion bridge simulation plays a fundamental role in simulation-based likelihood inference for stochastic differential equations. By a novel application of classical coupling methods, the new approach generalizes the one-dimensional bridge-simulation method proposed by Bladt and Sørensen (2014) to the multivariate setting. A method of simulating approximate, but often very accurate, diffusion bridges is proposed. These approximate bridges are used as proposal for easily implementable MCMC algorithms that produce exact diffusion bridges. The new method is more generally applicable than previous methods because it does not require the existence of a Lamperti transformation, which rarely exists for multivariate diffusions. Another advantage is that the new method works well for diffusion bridges in long intervals because the computational complexity of the method is linear in the length of the interval. The usefulness of the new method is illustrated by an application to Bayesian estimation for the multivariate hyperbolic diffusion model.

 

The lecture is based on joint work presented in Bladt, Finch and Sørensen (2014).References:

Bladt, M. and Sørensen, M. (2014): Simple simulation of diffusion bridges with application to likelihood inference for diffusions. Bernoulli, 20, 645-675.

Bladt, M., Finch, S. and Sørensen, M. (2014): Simulation of multivariate diffusion bridges. arXiv:1405.7728, pp. 1-30.

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