CAFR Workshop on Mathematical Finance

The CAFR Workshop on Mathematical Finance will be held from 2-5:30 pm, 14 May 2018 at Room 903, SAIF. Aiming at presenting and exchanging ideas on modern quantitative financial questions, the workshop will cover topics ranging from algorithmic trading, energy markets, systemic risk and network, credit derivative pricing, to change point detection. Further details about the workshop can be found below.

Registration is free and seats are limited on a first-come-first-serve basis. Confirmation of attendance is expected via email at cafr@saif.sjtu.edu.cn by May 9, 2018.

CAFR Workshop on Mathematical Finance

Time: 14:00-18:00, May 14, 2018

Venue: Room 903, Shanghai Advanced Institute for Finance (SAIF)

MAY 14 (Monday)
14:00-14:05	Welcome address
14:05-14:45	Uncertain correlation and credit derivatives
	Tom Salisbury, York University and Fields Institute
14:50-15:30	Banking networks and the circuit theory of money
	Matheus Grasselli, McMaster University
15:30-16:00	Change-Point Detection and Forecasting of the U.S. Dollar Index and Equity Markets
	Nathan Gold, York University
16:00-16:20	Tea Break
16:20-16:50	Connection between flux/slope limiter methods and simulation based approaches for optimal control of energy storage
	Andrew Day, Western University
16:50-17:30	Algorithmic Trading with Partial Information: A Mean Field Game Approach
	Sebastian Jaimungal, University of Toronto

Session Information:

Tom Salisbury

Paper Title

Uncertain correlation and credit derivatives

Abstract

Consider a credit derivative involving two stocks whose marginal laws are known, but whose correlation is uncertain. How large a spread can there be in price, and what are the best-case or worst-case scenarios? I’ll illustrate this numerically in some generality, and will discuss particular payoffs for which we can find closed form solutions. The most interesting of these involves rapid switching of correlations and leads to a new characterization of skew Brownian motion. This is joint work with Yang Fenghao and Alexey Kuznetsov.

Matheus Grasselli

Paper Title

Banking networks and the circuit theory of money

Abstract

We consider a network of banks with interconnected balance sheets coupled with a macroeconomic model for households, firms, and the government sector. The key feature of the model is that money is created endogenously by the banking sector to satisfy the demand for loans and deposits of the other economic agents. The macroeconomic core model is driven by stochastic consumption, with firms adjusting investment according to realized profits and capacity utilization. Stock-flow consistent between savings of the different sectors in turn give the total amount of external loans and deposits for the banking sector. We then assume that these aggregate quantities are distributed among the banks using a preferential attachment mechanism and study the stability of the resulting network. Crucially, the amplification of shocks within the banking network can, by rationing of available credit, drive the macroeconomic model away from its stable equilibrium and provoke an economic crisis. This is joint work with Alex Lipton.

Nathan Gold

Paper Title

Change-Point Detection and Forecasting of the U.S. Dollar Index and Equity Markets

Abstract

While the commonality of liquidity between foreign exchange and equity markets has recently been studied, less attention has been paid to common structural breaks in both markets. Common structural breaks are suggestive of a dominant common risk factor between these different markets, similar to risk factors found between equity markets. Such structural breaks violate the assumption of stationary return distributions, leaving fixed parametric models unable to generalize over different temporal regions, and voiding forecasts. To study these effects and detect changes in real time, we apply a Bayesian online change-point detection algorithm to determine economic regime changes in the returns of the U.S. Dollar Index and the S\&P 500 from 2005-2015. Using a nonlinear Gaussian process time series model to forecast future observations and detect regime changes, we are able to link worldwide economic and political events to regime changes in both the U.S. Dollar Index and the S\&P 500, and find commonality in periods of high volatility between these markets. We will also talk about some interesting questions arising from these findings.

Andrew Day

Paper Title

Connection between flux/slope limiter methods and simulation based approaches for optimal control of energy storage

Abstract

Energy storage is a key problem facing society as we make the transition to the new “green” energy economy. Determining optimal control strategies for storage facilities in the face of market determined prices for electricity requires the numerical solution of partial differential equations (PDEs). In this talk we will highlight the various difficulties arising from numerically solving this PDE along with an alternative approach based on the least squares Monte Carlo method.

Sebastian Jaimungal

Paper Title

Algorithmic Trading with Partial Information: A Mean Field Game Approach

Abstract

Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform statistical arbitrage, where all agents filter the latent states of the world, and their trading actions have permanent and temporary price impact. This leads to a large stochastic game with heterogeneous agents. We solve the stochastic game by investigating its mean-field game (MFG) limit, with sub-populations of heterogeneous agents, and, using a convex analysis approach, we show that the solution is characterized by a vector-valued forward-backward stochastic differential equation (FBSDE). We demonstrate that the FBSDE admits a unique solution, obtain it in closed-form, and characterize the optimal behaviour of the agents in the MFG equilibrium. Moreover, we prove the MFG equilibrium provides an ?-Nash equilibrium for the finite player game. We conclude by illustrating the behaviour of agents using the optimal MFG strategy through simulated examples.