London/Oxford/Warwick Financial Mathematics Workshop

Entry 

Attendees must first register at Strand reception and then will be able to access the Mcadam building using the entrance on Surrey Street.  

 

 

 

Registration

If you wish to attend the event, registration is free but is required as places are limited.

 

Schedule

Wednesday, 12 July

09:45 Registration
10:15 - 11:15 Ryan Donnelly - Exploratory Control with Tsallis Entropy for Latent Factor Models
11:15 - 11:30 Coffee
11:30 - 12:15 Svetlana Malysheva - Application of random matrices theory to short-period stock log-returns
12:15 - 13:00 Álvaro Arroyo - Deep Attentive Survival Analysis in Limit Order Books: Estimating Fill Probabilities with Convolutional-Transformers
13:00 - 14:00 Lunch
14:00 - 15:00 Carol Alexander - : Arbitrage Opportunities and Efficiency Tests in Crypto Options
15:00 - 15:15 Coffee
15:15 - 16:00 Zi Li - Dynamic Inventory Management with Mean-Field Competition
16:00 - 16:45 Micha Bender - Lead-Lag Relationships in Market Microstructure

19:30 Conference Dinner – Brasserie Blanc, Southbank

 

Thursday, 13 July

10:15 - 11:15 Andreas Søjmark - From the supercooled Stefan problem to financial contagion: a forward-looking indicator of systemic risk
11:15 - 11:30 Coffee
11:30 - 12:15 Peter Vodicka - Probability Hedging Investment Strategy in Deterministic and Stochastic Settings
12:15 - 13:00 Lionel Sopgoui - Propagation of carbon tax in credit portfolio through macroeconomic factors
13:00 - 14:00 Lunch
14:00 - 15:00 Katia Babbar - Characteristics of Automated Market Makers (AMMs) in Decentralized Finance (DeFi) - a look at Uniswap

15:00 - 15:15 Coffee
15:15 - 16:00 Edward Wang - Callable convertible bonds under liquidity constraints and hybrid priorities
16:00 - 16:45 Shijie Xu - Statistically consistent term structures have affine geometry

 

Abstracts

Carol Alexander

Title: Arbitrage Opportunities and Efficiency Tests in Crypto Options
Abstract: For liquidity providers in the rapidly-growing crypto options market as well as potential institutional investors in crypto options, we test the joint efficiency of the bitcoin options and perpetual futures markets, and likewise for ether, and identify the frequency and magnitude of arbitrage opportunities. We introduce the necessary (fiat-currency-free) put-call parity relationship, including transaction costs, and thereafter develop a variety of strong and weak arbitrage boundaries for crypto option prices. Novel empirical analysis concludes that both bitcoin and ether derivatives markets are broadly evolving to a more efficient state. Longer-dated options (with maturity ≥ 15 days) are notable in that their price efficiency has improved very significantly over time. Bitcoin markets are more efficient than ether and efficiency of both markets shifts closely with prices of perpetual futures. Hence, periods of extreme volatility can result in highly profitable arbitrage opportunities.

 

Ryan Donnelly

Title: Exploratory Control with Tsallis Entropy for Latent Factor Models

Abstract: We study optimal control in models with latent factors where the agent controls the distribution over actions, rather than actions themselves, in both discrete and continuous time. To encourage exploration of the state space, we reward exploration with Tsallis Entropy and derive the optimal distribution over states – which we prove is q-Gaussian distributed with location characterised through the solution of a backward stochastic difference equation and backward stochastic differential equation discrete and continuous time, respectively. Finally, we discuss the relation between the solutions of the optimal exploration problems and the standard dynamic optimal control solution.

 

Katia Babbar

Title: Characteristics of Automated Market Makers (AMMs) in Decentralized Finance (DeFi) - a look at Uniswap

Abstract: Crypto assets have developed over the last 14 years in parallel to mainstream finance. An ecosystem has flourished of projects/'protocols' to address some of the challenges within that system. One of the key drivers for Crypto was the concept of decentralisation, yet, many of the earlier crypto exchanges offered centralised solutions for trading in Crypto. The concept of decentralized exchanges (or DEX's) then flourished with the advent to the Ethereum network, but it was (and still is) too computationally expensive to offer the mechanics of limit order books on-chain. A solution was then proposed to replace the limit order book with an Automated Market-Maker (AMM) dynamics and the most successful DEX became Uniswap. Here we explore the AMMs dynamics and understand how to assess value for makers and takers in Uniswap.

 

Andrea Sojmark

Title: From the supercooled Stefan problem to financial contagion: a forward-looking indicator of systemic risk

Abstract: In this talk, we will explore a Brownian perturbation of the supercooled Stefan problem which turns out to arise naturally as a structural mean-field model of financial contagion, conditional on the market risk that remains after full diversification. We begin by introducing a probabilistic formulation of the problem and discussing the precise connection with contagion in a given financial system. Next, we show how, under a simple condition, the problem must involve jump discontinuities, corresponding to the wipe-out of a macroscopic proportion of the financial system. Finally, we will discuss how this problem may serve as the basis for a forward-looking systemic risk indicator, aiming to capture the current market sentiment on systemic risk, as implied by CDS index prices.

 

Svetlana Malysheva

Title: Application of random matrices theory to short-period stock log-returns

Abstract: Cubic law for the stock log-returns is well known. We study the spectrum of the log-returns covariance matrix and compare it to the limiting distribution of a specific matrix ensemble, different from the Wishart ensemble.

The spectrum of the covariance matrix is highly affected by the presence of the common multiplication factor with a tail exponent approximately equal to -3.

 

Álvaro Arroyo

Title: Deep Attentive Survival Analysis in Limit Order Books: Estimating Fill Probabilities with Convolutional-Transformers

Abstract: One of the key decisions in execution strategies is the choice between a passive (liquidity providing) or an aggressive (liquidity taking) order to execute a trade in a limit order book (LOB). Essential to this choice is the fill probability of a passive limit order placed in the LOB. This paper proposes a deep learning method to estimate the filltimes of limit orders posted in different levels of the LOB. We develop a novel model for survival analysis that maps time-varying features of the LOB to the distribution of filltimes of limit orders. Our method is based on a convolutionalTransformer encoder and a monotonic neural network decoder. We use proper scoring rules to compare our method with other approaches in survival analysis, and perform an interpretability analysis to understand the informativeness of features used to compute fill probabilities. Our method significantly outperforms those typically used in survival analysis literature. Furthermore, we carry out a detailed statistical analysis of the fill probability of orders placed in the order book, including within the bid-ask spread, for assets with different queue dynamics and trading activity.

 

Zi Li

Title: Dynamic Inventory Management with Mean-Field Competition

Abstract: Agents attempt to maximize expected profits earned by selling multiple units of a perishable product where their revenue streams are affected by the prices they quote as well as the distribution of other prices quoted in the market by other agents. We propose a model which captures this competitive effect and directly analyse the model in the mean-field limit as the number of agents is very large. We classify mean-field Nash equilibrium in terms of the solution to a Hamilton-Jacobi-Bellman equation and a consistency condition and use this to motivate an iterative numerical algorithm to compute equilibrium. Properties of the equilibrium pricing strategies and overall market dynamics are then investigated, in particular how they depend on the strength of the competitive interaction and the ability to oversell the product.

 

Micha Bender

Title: Lead-Lag Relationships in Market Microstructure

Abstract: We investigate high-frequency cross-asset lead-lag relationships using various market microstructure measures capturing price, liquidity, depth, and volatility dimensions. Using historical trade and order book data from stocks, futures, and exchange-traded products, we find that information from one asset’s transaction prices and order book imbalance at the best quotes provides information about the future behaviour of another asset’s midpoint. We also discover lead-lag relationships between different volatility measures. Most of the lead-lag relationships in our sample exist between fundamentally related instruments. With respect to the determinants of lead-lag effects, we find that trading activity and liquidity strengthen the lead of equity- related instruments. However, this does not hold true for bond futures and exchange-traded products.

 

Peter Vodicka

Title: Probability Hedging Investment Strategy in Deterministic and Stochastic Settings

Abstract: In this talk, I present a probability hedging investment strategy which is designed for a long-term investor who wish to invest their wealth in stocks but have concerns about potential losses, such jeopardising their retirement income. I demonstrate that our strategy can be derived by considering different utility functions, and its choice directly impacts the probability measure. In particular, with the logarithmic utility it results in an intuitive probability hedge under physical measure. This facilitates effective communication without compromising the accuracy of theoretical results or misrepresenting their realism, thereby safeguarding the integrity of financial advice. In the case of a constant market risk premium, I explain an explicit formula which serves as a natural bridge between unconstrained and constrained optimal strategies. Additionally, I discuss probability hedging in multi-stochastic environment, and I show how our strategy generates a more favourable distribution of terminal wealth compared to traditional hedging approaches.

 

Lionel Sopgoui

Title: Propagation of carbon tax in credit portfolio through macroeconomic factors

Abstract: We study how the introduction of carbon taxes in a closed economy propagate in a credit portfolio and precisely describe how carbon taxes dynamics affect the firm value and credit risk measures. In a first step, we adapt a stochastic multisectoral model to take into account carbon taxes on both sectoral firms’ production and household’s consumption. Carbon taxes are calibrated on carbon prices, on sectoral households’ consumption and firms’ production, together with their related greenhouse gases emissions. For each sector, this yields the sensitivity of firms’ production and households’ consumption to carbon taxes and the relationships between sectors. In a second step, we adapt a Discounted Cash Flows methodology to compute firms’ values which we then use in the Merton model to describe how the introduction of carbon taxes impacts credit risk measures. We obtain and quantify how the introduction of carbon taxes distorts the distribution of the firm’s value, increases banking fees charged to clients, and reduces banks’ profitability. In addition, the randomness introduced in our model provides extra flexibility to take into account uncertainties on productivity and on the different transition scenarios by sector.

 

Edward Wang

Title: Callable convertible bonds under liquidity constraints and hybrid priorities

Abstract: We investigate the callable convertible bond problem in the presence of a liquidity constraint modeled by Poisson signals, where neither the bondholder nor the firm has priority when they stop the game simultaneously. Instead, a proportion m in [0,1] of the bond is converted to the firm's stock and the rest is called by the firm. The paper thus generalizes the special case studied in [Liang and Sun, Dynkin games with Poisson random intervention times, SIAM Journal on Control and Optimization, 57(4): 2962–2991, 2019] where the bondholder has priority so m=1, and presents a complete solution to the callable convertible bond problem. The callable convertible bond is an example of a Dynkin game, but falls outside the standard paradigm since the payoffs do not depend in an ordered way upon which agent stops the game. We show how to deal with this non-ordered situation by introducing a new technique which may of interest in its own right, and then apply it to the bond problem. Joint work with David Hobson, Gechun Liang and Haodong Sun.

 

Shijie Xu

Title: Statistically consistent term structures have affine geometry

Abstract: This paper is concerned with finite dimensional models for the entire term structure for energy futures. As soon as a finite dimensional set of possible yield curves is chosen, one likes to estimate the dynamic behaviour of the yield curve evolution from data. The estimated model should be free of arbitrage which is known to result in some drift condition. If the yield curve evolution is modelled by a diffusion, then this leaves the diffusion coefficient open for estimation. From a practical perspective, this requires that the chosen set of possible yield curves is compatible with any obtained diffusion coefficient. In this paper, we show that this compatibility enforces an affine geometry of the set of possible yield curves.