Past Mathematical Finance Internal Seminar

9 February 2018
13:00
Athena Picarelli
Abstract

This work deals with a class of stochastic optimal control problems in the presence of state constraints. It is well known that for such problems the value function is, in general, discontinuous, and its characterisation by a Hamilton-Jacobi equation requires additional assumptions involving an interplay between the boundary of the set of constraints and the dynamics
of the controlled system. Here, we give a characterization of the epigraph of the value function without assuming the usual controllability assumptions. To this end, the stochastic optimal control problem is first translated into a state-constrained stochastic target problem. Then a level-set approach is used to describe the backward reachable sets of the new target problem. It turns out that these backward reachable sets describe the value function. The main advantage of our approach is that it allows us to easily handle the state constraints by an exact penalisation. However, the target problem involves a new state variable and a new control variable that is unbounded.
 

  • Mathematical Finance Internal Seminar
26 January 2018
13:00
Abstract


In the 12 months from the middle of June 2016 to the middle of June 2017, a number of events occurred in a relatively short period of time, all of which either had, or had the potential to have,  a considerably volatile impact upon financial markets. The events referred to here are the Brexit  referendum (23 June 2016), the US election (8 November 2016), the 2017 French elections (23 April and 7 May 2017) and the surprise 2017 UK parliamentary election (8 June 2017). 
All of these events - the Brexit referendum and the Trump election in particular - were notable both for their impact upon financial markets after the event and the degree to which the markets failed to anticipate these events. A natural question to ask is whether these could have been predicted, given information freely available in the financial markets beforehand. In this talk, we focus on market expectations for price action around Brexit and the Trump election, based on information available in the traded foreign exchange options market. We also investigate the horizon date of 30 March 2019, when the two year time window that started with the Article 50 notification on 29 March 2017 will terminate.
Mathematically, we construct a mixture model corresponding to two scenarios for the GBPUSD exchange rate after the referendum vote, one scenario for “remain” and one for “leave”. Calibrating this model to four months of market data, from 24 February to 22 June 2016, we find that a “leave” vote was associated with a predicted devaluation of the British pound to approximately 1.37 USD per GBP, a 4.5% devaluation, and quite consistent with the observed post-referendum exchange rate move down from 1.4877 to 1.3622. We find similar predictive power for USDMXN in the case of the 2016 US presidential election. We argue that we can apply the same bimodal mixture model technique to construct two states of the world corresponding to soft Brexit (continued access to the single market) and hard Brexit (failure of negotiations in this regard).
 

  • Mathematical Finance Internal Seminar
1 December 2017
13:00
Alexander Cox (University of Bath)
Abstract

In this paper, we consider the pricing and hedging of a financial derivative for an insider trader, in a model-independent setting. In particular, we suppose that the insider wants to act in a way which is independent of any modelling assumptions, but that she observes market information in the form of the prices of vanilla call options on the asset. We also assume that both the insider’s information, which takes the form of a set of impossible paths, and the payoff of the derivative are time-invariant. This setup allows us to adapt recent work of Beiglboeck, Cox, and Huesmann [BCH16] to prove duality results and a monotonicity principle, which enables us to determine geometric properties of the optimal models. Moreover, we show that this setup is powerful, in that we are able to find analytic and numerical solutions to certain pricing and hedging problems. (Joint with B. Acciaio and M. Huesmann)

  • Mathematical Finance Internal Seminar
3 November 2017
13:00
tba
Rita Maria del Rio Chanona and Johannes Wiesel
Abstract

Rita Maria del Rio Chanona:

Global financial contagion on a Multiplex Network

We explore the global financial system, in particular the risk of global financial contagion through network theory. Although there is extensive literature on contagion in networks, we argue that it is important to consider different channels of contagion. Therefore we deem into the multilayer framework, where nodes are countries and each layer represents a different type of financial obligation. The multiplex network is built using data provided by collaborators in the IMF. We study contagion with a percolation model and conclude that financial shocks can be amplified considerably when the multilayer structure is taken into account.


Johannes Wiesel:

Robust Superhedging vs Robust Statistics

In this talk I try to reconcile the different understanding of robustness in mathematical finance and statistics. Motivated by recent advances in the estimation of risk measures, I present estimators for the superhedging price of a claim given a history of observed prices. I discuss weak efficiency and convergence speed of these estimators. Besides I explain how to apply classical notions of sensitivity for the estimation procedure. This talk is based on ongoing work with Jan Obloj.

 

  • Mathematical Finance Internal Seminar

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