# 2014-15

**Summer Term**

### Week 1: Friday 15th May, 2-3pm, A1.01

Spectral risk measures form a family of static risk measures which is widely deployed in risk analysis due to their intuitive and explicit form. Such risk measures are coherent in the sense of Artzner et al. (1999) and stand in one-to-one relation to distorted expectations or distortion operators, a class of Choquet expectations proposed by Wang and co-authors. In this talk we present a new class of dynamic risk-measures which may be regarded as a dynamic extension of static spectral risk-measures and which are given in terms of Peng's g-expectations driven by Levy processes, with driver functions g of certain shape. We discuss properties of such dynamic risk-measures, and show that such continuous-time risk-measures arise in the limit of discrete time spectral risk-measures under vanishing time-step. This involves a certain non-standard scaling of the corresponding spectral weight-measures that we identify explicitly. This talk is based on joint work with M. Stadje and D. Madan.

### Week 7: Friday 5th June, 2-3pm, A1.01

Antoine Jacquier (Imperial) Martingale information of the implied volatility smile

Given an implied volatility smile at some fixed maturity, we wish to answer the following questions regarding the underlying stock price process:

- is it a true martingale?

- Does it have a strictly positive mass at zero?

We shall see that the answers to these two questions can be quantified precisely in terms of the tails of the implied volatility smile. In doing so, we shall revisit some of the model-free asymptotic behaviours of the implied volatility smile developed by Roger Lee and Shalom Benaim and Peter Friz, and discuss the translation of the results by Alex Cox and David Hobson into implied volatility statements . These results also provide a new testable characterisation of bubbles. This talk is based on joint works with Stefano de Marco and Caroline Hillairet, and Martin Keller-Ressel.

**Spring Term**

#### Week 4: Wednesday 28th January, A1.01

Rama Cont (Imperial College) Pathwise analysis and robustness of hedging strategies** **

We develop a pathwise framework for analyzing the performance and robustness of delta hedging strategies for path-dependent derivatives across a given set of scenarios. Our setting allows for general path-dependent payoffs and does not require any probabilistic assumption on the dynamics of the underlying asset, thereby extending previous results on robustness of hedging strategies in the setting of diffusion models.

We obtain a pathwise formula for the hedging error for a general path-dependent derivative and provide sufficient conditions ensuring the robustness of the delta hedge. We show in particular that robust hedges may be obtained in a large class of continuous exponential martingale models under a directional convexity condition on the payoff functional. Under the same conditions, we show that discontinuities in the underlying asset always deteriorate the hedging performance. These results are illustrated in the case of Asian options and barrier options.

#### Week 10: Wednesday 11th March, C0.08

Tim Leung (Columbia) Optimal Mean Reversion Trading with Transaction Costs

We study the optimal timing of trades under mean-reverting price dynamics subject to fixed transaction costs. We first consider an optimal double stopping approach to determine the optimal times to enter and subsequently exit the market when prices are driven by an Ornstein-Uhlenbeck (OU), exponential OU, or CIR process. In addition, we analyze a related optimal switching problem with an infinite sequence of trades, and identify the conditions under which the double stopping and switching problems admit the same optimal entry and/or exit timing strategies. Among our results, we find that the investor generally enters when the price is low, but may find it optimal to wait if the current price is sufficiently close to zero, leading to a disconnected continuation (waiting) region for entry. Numerical results are provided to illustrate the dependence of timing strategies on model parameters and transaction costs.

**Autumn Term**

#### Week 9: Friday 28th November

Jun Maeda (Warwick)

**Derivatives in Practice: From a Trader's Point of View**

#### Week 10: Friday 5th December

Matthew Burgess (Warwick)

**The Disposition effect in financial data **

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Week 1: Friday 3 Oct: Tony He (UTS, Sydney)

*Tony is a Professor in the Finance Group at UTS with research interests in financial market modelling, heterogeneous expectations and learning, nonlinear economic dynamics and bounded rationality, behavioural finance and asset pricing.*

**Social Interaction and Financial Market Anomalies**

We develop a simple asset pricing model with differences in opinion and social interaction and show that the model is able to explain many important financial market anomalies, including excess volatility, volatility clustering, bubbles, crashes, and time series momentum in short-run and reversal in long run.

Week 2: Friday 10th Oct: Vicky Henderson (Warwick)

**Prospect Theory, Liquidation and the Disposition Effect **

Week 3: Friday 17th Oct: Sebastian Gryglewicz (Erasmus University Rotterdam)

*Sebastian is an Associate Professor in the Erasmus School of Economics. His research interests are in dynamic real options models in corporate finance. He has recently been working on decision making under prospect theory and has run experiments to validate his theory.*

**Exit in Good and Bad Times: Prospect Theory and Timing Decisions**

Week 4: Friday 24th October: Daniel Read (Behavioural Science Group, WBS) Daniel is a Professor of Behavioural Science at WBS and his research interests include: judgment and decision making including intertemporal choice, choice under uncertainty and risk, heuristics and biases.

**The Behavioural Economics of Time**

Week 5: Friday 31st October Alex Tse (Statistics)

**Prospect Theory & Probability Weighting**

Alex will give us an introduction to prospect theory and probability weighting based on Kahneman and Tversky (1979, 1992)

Week 6: Friday 7th November OxWasp seminars - Saul Jacka (Warwick) & Peter Moerters (Bath)

Week 8: Friday 21st November:

Hanqing Jin (Mathematical Institute, University of Oxford)Hanqing is an Associate Professor in the Mathematical Institute at Oxford. His research interests include portfolio selection, behavioural finance, applied stochastic analysis and optimisation.

**Mean-Risk Portfolio Choice with Weighted VaR and Law-Invariant Coherent Risk Measure**s

We study a continuous-time mean-risk portfolio choice problem in which an agent, with or without the bankruptcy constraint, chooses among the portfolios that achieve an exogenously given expected terminal wealth target with the objective of minimizing the risk of his portfolio. The risk is measured either by a so-called weighted value-at-risk risk measure, which is a generalization of value-at-risk and conditional value-at-risk, or by a law-invariant coherent risk measure.