Friday 19 April 2023
10.00 - 10.30: welcome coffee
10.30 - 11.15: Eduardo Abi Jaber: From the Quintic model to signature volatility models: fast pricing and hedging with Fourier
11.15 - 12.00: Huy Ngoc Chau: Local market viability and superhedging under proportional transaction costs and model uncertainty
12.00 - 12.45: Blanka Horvath: Pathwise methods and generative models for pricing and trading
12.45 - 14.30: lunch break
14.30 - 15.15: Giulia Di Nunno: Lifting of Volterra processes: optimal control in UMD Banach spaces
15.15 - 16.00: Roxana Dumitrescu: A new Mertens decomposition of Y g,/xi-submartingale systems and applications
16.00 - 16.30: coffee break
16.30 - 17.15: David Skovmand: Term structure modeling of SOFR: evaluating the importance of scheduled jumps
17.15 - 18.00: Luca Taschini: Emission impossible: balancing environmental concerns and inflation
ABSTRACTS:
Eduardo Abi Jaber: From the Quintic model to signature volatility models: fast pricing and hedging with Fourier.
Abstract: We will introduce the Quintic Ornstein-Uhlenbeck model that jointly calibrates SPX-VIX options with a particular focus on its mathematical tractability namely for fast pricing SPX options using Fourier techniques. Then, we will consider the more general class of stochastic volatility models where the dynamics of the volatility are given by a possibly infinite linear combination of the elements of the time extended signature of a Brownian motion. First, we show that the model is remarkably universal, as it includes, but is not limited to, the celebrated Stein-Stein, Bergomi, and Heston models, together with some path-dependent variants. Second, we derive the joint characteristic functional of the log-price and integrated variance provided that some infinite-dimensional extended tensor algebra valued Riccati equation admits a solution. This allows us to price and (quadratically) hedge certain European and path-dependent options using Fourier inversion techniques. We highlight the efficiency and accuracy of these Fourier techniques in a comprehensive numerical study. Based on joint works with Louis-Amand Gérard, Camille Illand, Shaun Li and Xuyang Lin.
Huy Ngoc Chau: Local market viability and superhedging under proportional transaction costs and model uncertainty.
Abstract: In this talk, we present a new approach to study market viability under proportional transaction costs. We assume a Local No Free Lunch with Vanishing Risk condition, instead of the global one as in most of previous studies, and prove that it is equivalent to the existence of local consistent price systems. Superhedging duality and the existence of superhedging strategies are obtained even when wealth processes are negative. The new approach is compatible with the uncertainty modelling framework developed in Chau, Fukasawa and Rasonyi (2021) and hence, we provide a unified treatment for the two different settings. Joint with Claudio Fontana (University of Padova) and Masaaki Fukasawa (Osaka University)
Blanka Horvath: Pathwise methods and generative models for pricing and trading.
Abstract: The deep hedging framework as well as related deep trading setups have opened new horizons for solving hedging problems under a large variety of models and market conditions. In this setting, generative models and pathwise methods rooted in rough paths have proven to be a powerful tool from several perspectives. At the same time, any model – a traditional stochastic model or a market generator – is at best an approximation of market reality, prone to model-misspecification and estimation errors. In a data-driven setting, especially if sample sizes are limited by constraints, the latter issue becomes even more prevalent, which we demonstrate in examples. This raises the question, how to furnish a modelling setup (for deriving a strategy) with tools that can address the risk of the discrepancy between model and market reality, ideally in a way that is automatically built in the setting. A combination of classical and new tools yields insights into this matter.
Giulia Di Nunno: Lifting of Volterra processes: optimal control in UMD Banach spaces.
Abstract: We study a stochastic control problem for a Volterra-type controlled forward equation with past dependence obtained via convolution with a deterministic kernel. To be able to apply dynamic programming to solve the problem, we lift it to infinite dimensions and we formulate a UMD Banach-valued Markovian problem, which is shown to be equivalent to the original finite-dimensional non-Markovian one. We characterise the optimal control for the infinite dimensional problem and show that this in turns, also characterises the optimal control for the finite dimensional problem. An example of application is discussed.
Roxana Dumitrescu: A new Mertens decomposition of Y g,/xi-submartingale systems and applications.
Abstract: We introduce the concept of Y g,/xi-submartingale systems, where the nonlinear operator Y g,/xi corresponds to the first component of the solution of a reflected BSDE with generator g and lower obstacle /xi. We first show that, in the case of a left-limited right-continuous obstacle, any Y g,/xi-submartingale system can be aggregated by a process which is right-lower semicontinuous. We then prove a Mertens decomposition, by using an original approach which does not make use of the standard penalization technique. These results are in particular useful for the treatment of control/stopping game problems and, to the best of our knowledge, they are completely new in the literature. We finally present two applications in Finance (based on joint works with R. Elie, W. Sabbagh and C. Zhou).
David Skovmand: Term structure modeling of SOFR: evaluating the importance of scheduled jumps.
Abstract: As interest rate benchmarks move from LIBOR to overnight Risk-Free Rates (RFR), it has become increasingly important for models to accurately capture the interest rate dynamics at the overnight tenor. Overnight rates closely track central bank policy rate decisions resulting, in highly discontinuous dynamics around scheduled meeting dates. In this paper, we construct a dynamic term structure model, which accounts for the discontinuous short-rate dynamics. We show that the model is able to jointly fit the overnight US policy rate, SOFR and SOFR futures rates through the recent Fed hiking cycle. Comparing our model with a standard continuous time-homogeneous short-rate model, we find several indications that our model avoids the clear misspecification of the continuous model, in particular with regard to the short-rate dynamics around meeting dates of the Federal Open Market Committee (FOMC). This effect begins to disappear as the term of the rates under consideration is increased, suggesting that diffusive dynamics are a reasonably accurate reflection of the evolution of market expectations embodied in longer-term interest rates.
Luca Taschini: Emission impossible: balancing environmental concerns and inflation.
Abstract: This paper introduces a partial equilibrium model to explore how policy measures targeting emission reductions impact price levels (policy induced inflation). The model facilitates the quantification of the potential rise in inflation as a direct consequence of more ambitious environmental policies. We examine the trade-offs between environmental ambitions and economic stability, determining the extent to which inflation can be tolerated in the pursuit of enhanced environmental outcomes.