Simulation of financial asset returns for strategic asset allocation

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• Dr Joo Hee Lee, Invesco
• Tuesday 13 February 2018, 13:00-14:00
• MR3 Centre for Mathematical Sciences.

If you have a question about this talk, please contact Dr Vivien Gruar.

The simulation of stochastic differential equations for Geometric Brownian Motion by Monte Carlo methods is a well-established technique in pricing options and many other derivatives (see e.g. Paul Glasserman, 2004, Monte Carlo Methods in Financial Engineering (Springer)). This project is concerned with extending this framework to the field of strategic asset allocation (i.e. long-term investment decisions with typically more than one financial assets in the portfolio).

The aim of this project is to design a financial-returns simulator for several correlated assets, which is to generate a substantial number (>10,000) of statistically equivalent returns series in a multi-variate fashion. Using the setup, we aim to create a daily returns database that will exhibit properties obtained from the corresponding historical time-series data at different frequencies, e.g. monthly or yearly.

In the investment management industry, it is often observed that financial returns are expressed interchangeably in price ratios, i.e. simple returns, and in log price differences, i.e. compounded returns, between two evaluation points in time, i.e. investment horizons. While they are close enough to each other when the investment horizon is short, say 1 day, the differences grow significantly with longer horizons. In addition, these two measures have different properties in aggregation through time and across assets according to their mathematical properties (A. Meucci, Apr 2010, GARP Risk Professional, pp. 49-51). As the simulated data will be compounded returns through discretization of a stochastic differential equation but will be aggregated across different assets, we will adopt the solution Meucci (2010) put forward while making sure that the statistical properties between historical data and simulated data remain comparable at different frequency of data.

It is expected that the student to have some background knowledge on option pricing and numerical analysis, and programming skills in desirably R.

The project student will then learn more than the basic aspects of:

1. strategic asset allocation;
2. financial modelling;
3. connecting statistical and empirical data through mathematics.

Progress permitting, an opportunity to apply the outcome to a real-world case could also be possible.

This project is to be carried out in Frankfurt as part of a large quantitative strategies team at Invesco consisting of more than 10 PhDs, including the supervisor being a Cambridge alumna.

This talk is part of the Cambridge Mathematics Placements Seminars series.

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• MR3 Centre for Mathematical Sciences

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