# Workshop on Mathematical Finance

## China Academy of Research for Finance (SAIF)

Following the annual International Problem Solving Workshop 2018 taking place this year at Shanghai University of Finance and Economics, this workshop aims at presenting and exchanging ideas on modern quantitative financial questions. It ranges from topics about algorithmic trading, energy markets, systemic risk and network, credit derivative pricing, to change point detection. This event is organized by the China Academy of Research for Finance (CAFR) from Shanghai Advanced Institute for Finance (SAIF) at Shanghai Jiao Tong University.

Attendance is open to any interested participants.

Place:
Shanghai Advanced Institute for Finance (SAIF)
Shanghai Jiao Tong University
211 West Huaihai Road, Shanghai, 200030 China
Date and time:
May 14th 2018 from 2pm to 6pm
Room:
903
Contact:
The workshop is organized by the Chinese Academy of Research for Finance (CAFR/SAIF) in Shanghai. For any question do not hesitate to contact CAFR or Samuel Drapeau.
Program:
Time Speaker Affiliation
14:00-14:05 Welcome
14:05-14:45 Tom Salisbury York University and Fields Institute
14:50-15:30 Matheus Grasselli McMaster University
15:30-16:00 Nathan Gold York University
16:00-16:20 Tea Break
16:20-16:50 Andrew Day Western University
16:50-17:30 Sebastian Jaimungal University of Toronto
Registration:
Attendance is free and open to everyone. Please send a mail to CAFR or Samuel Drapeau to notify your presence in order to estimate the capacity and keep you informed about eventual program changes.

## Overview

### Titles and Abstracts

#### Tom Salisbury

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

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

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

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

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 $\epsilon$-Nash equilibrium for the finite player game. We conclude by illustrating the behaviour of agents using the optimal MFG strategy through simulated examples.