Past Mathematical and Computational Finance Seminar

14 June 2018
16:00
to
17:30
Josef Teichmann
Abstract

We present several instances of applications of machine
learning technologies in mathematical Finance including pricing,
hedging, calibration and filtering problems. We try to show that
regularity theory of the involved equations plays a crucial role
in designing such algorithms.

(based on joint works with Hans Buehler, Christa Cuchiero, Lukas
Gonon, Wahid Khosrawi-Sardroudi, Ben Wood)

  • Mathematical and Computational Finance Seminar
7 June 2018
16:00
to
17:30
Goncalo dos Reis
Abstract


We discuss two Freidlin-Wentzell large deviation principles for McKean-Vlasov equations (MV-SDEs) in certain path space topologies. The equations have a drift of polynomial growth and an existence/uniqueness result is provided. We apply the Monte-Carlo methods for evaluating expectations of functionals of solutions to MV-SDE with drifts of super-linear growth.  We assume that the MV-SDE is approximated in the standard manner by means of an interacting particle system and propose two importance sampling (IS) techniques to reduce the variance of the resulting Monte Carlo estimator. In the "complete measure change" approach, the IS measure change is applied simultaneously in the coefficients and in the expectation to be evaluated. In the "decoupling" approach we first estimate the law of the solution in a first set of simulations without measure change and then perform a second set of simulations under the importance sampling measure using the approximate solution law computed in the first step. 

  • Mathematical and Computational Finance Seminar
24 May 2018
16:00
to
17:30
Michael Kupper
Abstract

We present a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network with smooth objective function. We present numerical examples from optimal transport, and bounds on the distribution of a sum of dependent random variables. As an application we focus on the problem of risk aggregation under model uncertainty. The talk is based on joint work with Stephan Eckstein and Mathias Pohl.

  • Mathematical and Computational Finance Seminar
17 May 2018
16:00
to
17:30
Abstract

High-frequency realized variance approaches offer great promise for 
estimating asset prices’ covariation, but encounter difficulties 
connected to the Epps effect. This paper models the Epps effect in a 
stochastic volatility setting. It adds dependent noise to a factor 
representation of prices. The noise both offsets covariation and 
describes plausible lags in information transmission. Non-synchronous 
trading, another recognized source of the effect, is not required. A 
resulting estimator of correlations and betas performs well on LSE 
mid-quote data, lending empirical credence to the approach.

  • Mathematical and Computational Finance Seminar
10 May 2018
16:00
to
17:30
Abstract

Abstract:
Highlights:

•We increasingly live in a digital world and commercial companies are not the only beneficiaries. The public sector can also use data to tackle pressing issues.
•Machine learning is starting to make an impact on the tools regulators use, for spotting the bad guys, for estimating demand, and for tackling many other problems.
•The speech uses an array of examples to argue that much regulation is ultimately about recognising patterns in data. Machine learning helps us find those patterns.
 
Just as moving from paper maps to smartphone apps can make us better navigators, Stefan’s speech explains how the move from using traditional analysis to using machine learning can make us better regulators.
 
Mini Biography:
 
Stefan Hunt is the founder and Head of the Behavioural Economics and Data Science Unit. He has led the FCA’s use of these two fields and designed several pioneering economic analyses. He is an Honorary Professor at the University of Nottingham and has a PhD in economics from Harvard University.
 

  • Mathematical and Computational Finance Seminar
3 May 2018
16:00
to
17:30
Beatrice Acciaio
Abstract

Title: Generalized McKean-Vlasov stochastic control problems.

Abstract: I will consider McKean-Vlasov stochastic control problems 
where the cost functions and the state dynamics depend upon the joint 
distribution of the controlled state and the control process. First, I 
will provide a suitable version of the Pontryagin stochastic maximum 
principle, showing that, in the present general framework, pointwise 
minimization of the Hamiltonian with respect to the control is not a 
necessary optimality condition. Then I will take a different 
perspective, and present a variational approach to study a weak 
formulation of such control problems, thereby establishing a new 
connection between those and optimal transport problems on path space.

The talk is based on a joint project with J. Backhoff-Veraguas and R. Carmona.

  • Mathematical and Computational Finance Seminar
26 April 2018
16:00
to
17:30
Zorana Grbac
Abstract

In this talk we present a framework for discretely compounding
interest rates which is based on the forward price process approach.
This approach has a number of advantages, in particular in the current
market environment. Compared to the classical Libor market models, it
allows in a natural way for negative interest rates and has superb
calibration properties even in the presence of persistently low rates.
Moreover, the measure changes along the tenor structure are simplified
significantly. This property makes it an excellent base for a
post-crisis multiple curve setup. Two variants for multiple curve
constructions will be discussed.

As driving processes we use time-inhomogeneous Lévy processes, which
lead to explicit valuation formulas for various interest rate products
using well-known Fourier transform techniques. Based on these formulas
we present calibration results for the two model variants using market
data for caps with Bachelier implied volatilities.

  • Mathematical and Computational Finance Seminar
8 March 2018
16:00
Abstract


We consider calculation of VaR/TVaR capital requirements when the underlying economic scenarios are determined by simulatable risk factors. This problem involves computationally expensive nested simulation, since evaluating expected portfolio losses of an outer scenario (aka computing a conditional expectation) requires inner-level Monte Carlo. We introduce several inter-related machine learning techniques to speed up this computation, in particular by properly accounting for the simulation noise. Our main workhorse is an advanced Gaussian Process (GP) regression approach which uses nonparametric spatial modeling to efficiently learn the relationship between the stochastic factors defining scenarios and corresponding portfolio value. Leveraging this emulator, we develop sequential algorithms that adaptively allocate inner simulation budgets to target the quantile region. The GP framework also yields better uncertainty quantification for the resulting VaR/\TVaR estimators that reduces bias and variance compared to existing methods.  Time permitting, I will highlight further related applications of statistical emulation in risk management.
This is joint work with Jimmy Risk (Cal Poly Pomona). 
 

  • Mathematical and Computational Finance Seminar
1 March 2018
16:00
Cecilia Mancini
Abstract

Joint work with Josè E. Figueroa-Lòpez, Washington University in St. Louis

Abstract: We consider a univariate semimartingale model for (the logarithm 
of) an asset price, containing jumps having possibly infinite activity. The 
nonparametric threshold estimator\hat{IV}_n of the integrated variance 
IV:=\int_0^T\sigma^2_sds proposed in Mancini (2009) is constructed using 
observations on a discrete time grid, and precisely it sums up the squared 
increments of the process when they are below a  threshold, a deterministic 
function of the observation step and possibly of the coefficients of X. All the
threshold functions satisfying given conditions allow asymptotically consistent 
estimates of IV, however the finite sample properties of \hat{IV}_n can depend 
on the specific choice of the threshold.
We aim here at optimally selecting the threshold by minimizing either the 
estimation mean squared error (MSE) or the conditional mean squared error 
(cMSE). The last criterion allows to reach a threshold which is optimal not in 
mean but for the specific  volatility and jumps paths at hand.

A parsimonious characterization of the optimum is established, which turns 
out to be asymptotically proportional to the Lévy's modulus of continuity of 
the underlying Brownian motion. Moreover, minimizing the cMSE enables us 
to  propose a novel implementation scheme for approximating the optimal 
threshold. Monte Carlo simulations illustrate the superior performance of the 
proposed method.

  • Mathematical and Computational Finance Seminar

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