The local volatility model is a celebrated model widely used for pricing and hedging financial derivatives. While the model’s main appeal is its capability of reproducing any given surface of observed option prices—it provides a perfect fit—the essential component of the model is a latent function which can only be unambiguously determined in the limit of infinite data. To (re)construct this function, numerous calibration methods have been suggested involving steps of interpolation and extrapolation, most often of parametric form and with point-estimates as result. We seek to look at the calibration problem in a probabilistic framework with a nonparametric approach based on Gaussian process priors. This immediately gives a way of encoding prior believes about the local volatility function, and a hypothesis model which is highly flexible whilst being prone to overfitting. Besides providing a method for calibrating a (range of) point-estimate, we seek to draw posterior inference on the distribution over local volatility to better understand the uncertainty attached with the calibration. Further, we seek to understand dynamical properties of local volatility by augmenting the hypothesis space with a time dimension. Ideally, this gives us means of inferring predictive distributions not only locally, but also for entire surfaces forward in time.

Leandro Sánchez Betancourt
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The Cost of Latency: Improving Fill Ratios in Foreign Exchange Markets

Latency is the time delay between an exchange streaming market data to a trader, the trader processing information and deciding to trade, and the exchange receiving the order from the trader.  Liquidity takers  face  a  moving target problem as a consequence of their latency in the marketplace -- they send marketable orders that aim at a price and quantity they observed in the LOB, but by the time their order was processed by the Exchange, prices (and/or quantities) may have worsened, so the  order  cannot  be  filled. If liquidity taking orders can walk the limit order book (LOB), then orders that arrive late may still be filled at worse prices. In this paper we show how to optimally choose the discretion of liquidity taking orders to walk the LOB. The optimal strategy balances the tradeoff between the costs of walking the LOB and targeting  a desired percentage of filled orders over a period of time.  We employ a proprietary data set of foreign exchange trades to analyze the performance of the strategy. Finally, we show the relationship between latency and the percentage of filled orders, and showcase the optimal strategy as an alternative investment to reduce latency.

Jasdeep Kalsi
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An SPDE model for the Limit Order Book

I will introduce a microscopic model for the Limit Order Book in a static setting i.e. in between price movements. Here, order flow at different price levels is given by Poisson processes which depend on the relative price and the depth of the book. I will discuss how reflected SPDEs can be obtained as scaling limits of such models. This motivates an SPDE with reflection and a moving boundary as a model for the dynamic Order Book. An outline for how to prove existence and uniqueness for the equation will be presented, as well as some simple simulations of the model.

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)

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. 

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.

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.

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.