Talks (titles and abstracts)

Matheus Grasselli: Macroeconomic modelling with heterogeneous agents: the master equation approach

We propose a mean-field approximation to a stock-flow consistent agent-based macroeconomic model with heterogeneous firms and households. Depending on their investment elasticity to past profits, firms can be either aggressive or conservative.
Conversely, households are divided into investor and non-investor groups, depending on whether or not they invest a portion of their wealth in the stock market. Both firms and households dynamically change their type according to transition probabilities specified exogenously. The mean-field approximation consists of homogenizing the balance-sheet variables for agents (firms or households) of the same type and compute the time evolution of the corresponding average as a combination of the deterministic dynamic, derived from investment and consumption decisions before a change of type, and the probabilistic change in type, with an appropriate rebalancing to take stock-flow consistency into account. The last step of the approximation consists in replacing the underlying Markov chain with a continuous-time diffusive limit. We present numerical experiments showing the accuracy of the approximation and the sensitivity of the model with respect to several discretionary parameters. We then use the model to investigate the relationship between stock markets with low returns and high volatility and the proportion of firms with fragile financial positions. (joint work with Patrick X. Li, available at https://ms.mcmaster.ca/~grasselli/Grasselli_Li_2017_submitted_JNTF.pdf)

Andrea Macrina: Across-Curve Pricing

In this talk we shall share with our friends some results on the development of a novel formalism for what we term across-curve pricing. The proposed approach is presented in the context of fixed-income pricing where emphasis is put on multi-curve interest rate modelling, inflation-linked pricing, exchange to foreign currencies, and the valuation of inflation-linked foreign exchange hybrid securities. We show how a conversion formula, which relies on the concept of a multiplicative spread, in principle allows for a unified modelling approach with a high level of flexibility and transparence.

Tom McWalter

TBA

Erik Schlögl: A Consistent Stochastic Model of the Term Structure of Interest Rates for Multiple Tenors

Explicitly taking into account the risk incurred when borrowing at a shorter tenor versus lending at a longer tenor ("roll-over risk"), we construct a stochastic model framework for the term structure of interest rates in which a frequency basis (i.e. a spread applied to one leg of a swap to exchange one floating interest rate for another of a different tenor in the same currency) arises endogenously. This roll-over risk consists of two components, a credit risk component due to the possibility of being downgraded and thus facing a higher credit spread when attempting to roll over short-term borrowing, and a component reflecting the (systemic) possibility of being unable to roll over short-term borrowing at the reference rate (e.g., LIBOR) due to an absence of liquidity in the market. The modelling framework is of "reduced form" in the sense that (similar to the credit risk literature) the source of credit risk is not modelled (nor is the source of liquidity risk). However, the framework has more structure than the literature seeking to simply model a different term structure of interest rates for each tenor frequency, since relationships between rates for all tenor frequencies are established based on the modelled roll-over risk. We proceed to consider a specific case within this framework, where the dynamics of interest rate and roll-over risk are driven by a multifactor Cox/Ingersoll/Ross-type process, show how such model can be calibrated to market data, and used for relative pricing of interest rate derivatives, including bespoke tenor frequencies not liquidly traded in the market. (joint work with Mesias Alfeus and Martino Grasselli, available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2972428)

Rodrigo Targino: Bayesian Modelling, Monte Carlo Sampling and Capital Allocation of Insurance Risks

The main objective of this work is to develop a detailed step-by-step guide to the development and application of a new class of efficient Monte Carlo methods to solve practically important problems faced by insurers under the new solvency regulations. In particular, a novel Monte Carlo method to calculate capital allocations for a general insurance company is developed, with focus on coherent capital allocation that is compliant with the Swiss Solvency Test. The data used is based on the balance sheet of a representative stylized company. For each line of business in that company, allocations are calculated for the one-year risk with dependencies based on correlations given by the Swiss Solvency Test. Two different approaches for dealing with parameter uncertainty are discussed and simulation algorithms based on (pseudo-marginal) Sequential Monte Carlo algorithms are described and their efficiency is analysed. (joint work with Gareth W. Peters, Rodrigo S. Targino, Mario V. Wüthrich, available at http://dx.doi.org/10.2139/ssrn.2961888)

Josef Teichmann: Universal approximation theorems

Some ideas related to universal approximation theorems which constitute the core of many machine learning algorithms are presented.