Reports and Records of Society Meetings
RECORDS OF PROCEEDINGS AT MEETINGS
ANNUAL GENERAL MEETING
held on Friday 21 November 2003 at University College London. About 70 members and visitors were present for all or part of the meeting.
The meeting began at 3:15 pm, with the President, Professor P. GODDARD, FRS, in the Chair. He reported that Professor A. Camina, who had been appointed a Scrutineer at the June Society meeting, had withdrawn when his daughter had been nominated for Council. Council had appointed Professor R.Y. Sharp as Assistant Scrutineer in his place. Members who had not yet voted were invited to hand their ballot papers to Dr D.J. Collins and Professor Sharp, as Scrutineers.
In the absence of the Treasurer, Professor N.L. Biggs (General Secretary), presented the Treasurers annual report, which is published in the Newsletter. Messrs Baker Tilly were appointed as auditors.
Four people were elected to Ordinary Membership: A. Charafi, G. Iori, T.S.H. Leinster, R. Ranman; six people were elected to Associate Membership: A.K. Bedi, J.R. Britnell, S. Gill, A. Roux, Y. Saltuk, D.N. Webdale. One member signed the book and was admitted to the Society.
The President, on Councils behalf, presented certificates to the 2003 Society Prizewinners: Polya Prize - Professor A.J. Macintyre; Berwick Prize - Professor T. Bridgeland; Senior Whitehead Prize - Dr P.M. Neumann; Whitehead Prizes - Dr N. Dorey, Dr T.D.H. Hall, Dr M. Lakenby, Dr M.L. Nazarov.
Professor L.C.G. Rogers gave a lecture entitled Monte Carlo valuation of American options.
After tea, Dr Collins announced the results of the ballot. The following Officers and Members of the Council were elected: President: F.C. Kirwan; Vice Presidents: A.G. Chetwynd, A.J. Scholl; Treasurer: N.M.J. Woodhouse; General Secretary: N.L. Biggs; Programme Secretary: S.A. Huggett; Publications Secretary: J. Howie; Education Secretary: B.W. Stewart; Members-at-Large of Council for two years: C.J. Budd, R.D. Camina, R.T. Curtis, P.J. Davies, A.M. Etheridge, J.F.C. Kingman. The members elected to the Nominating Committee for 2003 were R.A. Bailey, K.A. Brown, D.A. Rand. Council membership is completed by the following who were elected for two-year terms in 2002: I.D. Abrahams, M. Bridson, M.M. Dodson, K.J. Falconer, S.E. Rees, F.A. Rogers.
The newly-elected President, Professor F.C. KIRWAN, FRS, took the Chair. Professor M.H.A. Davis gave the Naylor Prize lecture on Optimal investment with randomly terminating income.
After the meeting, a reception was held at De Morgan House, followed by the Annual Dinner, which was held at The Montague on the Gardens Hotel, and attended by 65 people.
Friday 21 November 2003
Problems in mathematical finance are typically of two different types, called European and American. European-style problems involve random cash-flows that take place at one or more pre-designated times in the future; whereas American-style problems, which are usually more difficult, involve random cash-flows taking place at one or more random times in the future. One can also make a distinction between problems associated with (a) the pricing of derivatives, and (b) optimal portfolio investment. The two lectures, at the Societys Annual General Meeting on 21 November 2003, were both concerned with American style problems the first lecture being on a problem of type (a), and the second on a problem of type (b).
The first lecture, by Professor L.C.G. Rogers (Cambridge), presented a paper on Monte Carlo valuation of American options. The American style put option is a good example of a financial product that has a relatively simple structure, and is widely traded for many different classes of assets, and for which no exact solution is yet known even under the simplifying assumption of geometric Brownian motion for the price dynamics of the underlying asset. As a consequence the development of efficient numerical methods in connection with such problems for use in an investment banking context has been, and continues to be, of great significance, and this is especially the case for more exotic instruments involving several assets. The paper introduces a novel way to price American options by simulation of the path of (i) the option payoff and (ii) a cunning choice for a Lagrangian martingale. Taking the pathwise maximum of the option payoff minus the chosen Lagrangian martingale, and averaging over the simulated results, gives an upper bound for the price of the option. One of the surprising and significant features of this method is that its usefulness is not so much for the actual pricing of the option but rather the hedging of the position. This is of relevance particularly for the seller of the option (e.g. an investment bank), where hedging is of more importance than spot-on pricing (there is no risk involved in receiving the upper bound as payment rather than the unknown 'correct' price). A number of different structures were considered apart from the standard American put for example (to mention just one) the American min-put on n assets, which has a standard put-like payoff with a fixed strike, but where the payoff is calculated with respect to the particular asset, from amongst the given n, that has the lowest value at the random time of exercise.
The Naylor Lecture, presented by Professor M.H.A. Davis (Imperial College), had as its title Optimal investment with randomly terminating income. This is an American style problem of type (b). The problem of maximising utility of terminal wealth over a fixed time horizon (say, until retirement age) is well understood in so-called complete market situations, in which case the problem is essentially equivalent to that of derivative pricing (the relevant 'derivative payout' being the random terminal value of the investment portfolio that maximises the expected utility). This is often called the Merton problem. When consumption and income streams are included as well, then the picture does not fundamentally change if these cash flows are replicable through market investments. Such replicability is typically not the case in reality, however especially for income, which can for various reasons all too familiar be subject to unexpected randomly timed alterations (due to the termination of employment, the onset of chronic illness or disability, and so on). There are of course analogues in corporate finance as well e.g., the sudden loss of the income stream from a key client who decides to move their business to a competitor. In the lecture by Mark Davis a particular problem of this type was studied in detail, and solved, involving an income flow chosen to be constant up to a termination date modelled by an independent exponentially distributed random time. The applications of this path-breaking new line of research are potentially to a great variety of practical problems in finance, both in the public and the private sector.
A reception at De Morgan House then followed, and after that the Annual Dinner at The Montague on the Gardens Hotel. Along with the speakers and prize winners, guests of honour at the dinner included Professor Jocelyn Bell Burnell (President, Royal Astronomical Society), Professor John Enderby (Physical Secretary, The Royal Society), Professor John McWhirter (President, IMA), Professor John O'Reilly (Chief Executive, EPSRC), Professor John Toland (Director, ICMS), Peter Tompkins (Vice President, Institute of Actuaries), Sir Peter Williams (Chairman, Engineering & Technology Board) and Mr Tony McWalter, MP, who delivered an engaging after-dinner speech on the important issues facing us concerning the funding of mathematics education and research in the United Kingdom.