The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Mean-Variance Hedging under Additional Market Information

In this paper we analyse the mean-variance hedging approach in an incomplete market under the assumption of additional market information, which is represented by a given, finite set of observed prices of non-attainable contingent claims. Due to no-arbitrage arguments, our set of investment opportunities increases and the set of possible equivalent martingale measures shrinks. Therefore, we obtain a modified mean-variance hedging problem, which takes into account the observed additional market information. Solving this by means of the techniques developed by Gourieroux, Laurent and Pham (1998), we obtain an explicit description of the optimal hedging strategy and an admissible, constrained variance-optimal signed martingale measure, that generates both the approximation price and the observed option prices.option pricing, mean variance hedging, incomplete markets, varianceoptimal martingale measure

Utility based pricing of contingent claims

In a discrete setting, we develop a model for pricing a contingent claim. Since the presence of hedging opportunities influences the price of a contingent claim, first we introduce the optimal hedging strategy assuming a contingent claim has been issued: a strategy implemented by investing the budget plus the selling price is optimal if it maximizes the expected utility of the agent's revenue, which is the difference between the outcome of the hedging portfolio and the payoff of the claim. Next, we introduce the `reservation price' as a subjective valuation of a contingent claim. This is defined as the minimum price to be added to the initial budget that makes the issue of the claim more preferable than optimally investing in the available securities. We define the reservation price both for a short position (reservation selling price) and for a long position (reservation buying price) in the contingent claim. When the contingent claim is redundant, both the selling and the buying price collapse in the usual Arrow-Debreu price. We develop a numerical procedure to evaluate the reservation price and two applications are provided. Different utility functions are used and some qualitative properties of the reservation price are shown.Incomplete markets, reservation price, expected utility, optimization

Arbitrage and Control Problems in Finance. Presentation.

The theory of asset pricing takes its roots in the Arrow-Debreu model (see,for instance, Debreu 1959, Chap. 7), the Black and Scholes (1973) formula,and the Cox and Ross (1976) linear pricing model. This theory and its link to arbitrage has been formalized in a general framework by Harrison and Kreps (1979), Harrison and Pliska (1981, 1983), and Du¢e and Huang (1986). In these models, security markets are assumed to be frictionless: securities can be sold short in unlimited amounts, the borrowing and lending rates are equal, and there is no transaction cost. The main result is that the price process of traded securities is arbitrage free if and only if there exists some equivalent probability measure that transforms it into a martingale, when normalized by the numeraire. Contingent claims can then be priced by taking the expected value of their (normalized) payo§ with respect to any equivalent martingale measure. If this value is unique, the claim is said to be priced by arbitrage and it can be perfectly hedged (i.e. duplicated) by dynamic trading. When the markets are dynamically complete, there is only one such a and any contingent claim is priced by arbitrage. The of each state of the world for this probability measure can be interpreted as the state price of the economy (the prices of $1 tomorrow in that state of the world) as well as the marginal utilities (for consumption in that state of the world) of rational agents maximizing their expected utility.arbitrage, control problem

A Benchmark Approach to Investing and Pricing

This paper introduces a general market modeling framework, the benchmark approach, which assumes the existence of the numeraire portfolio. This is the strictly positive portfolio that when used as benchmark makes all benchmarked nonnegative portfolios supermartingales, that is intuitively speaking downward trending or trendless. It can be shown to equal the Kelly portfolio which maximizes expected logarithmic utility. In several ways the Kelly or numeraire portfolio is the "best" performing portfolio and can not be out performed systematically by any other nonnegative portfolio. Its use in pricing as numeraire leads directly to the real world pricing formula, which employs the real world probability when calculating conditional expectations. In a large regular financial market, the Kelly portfolio is shown to be approximated by well diversified portfolios.Kelly portfolio; real world pricing; numeraire portfolio; strong arbitrage; diversification

Markov-Switching models and resultant equity implied volatility surfaces: a South African application

Includes bibliographical references.Standard Geometric Brownian Motion is the stock model underlying Black-Scholes famous option pricing formula. There are however numerous problems with this stock model as certain features do not follow some empirical stylised facts we see from the observation of actual asset prices. In particular, the constant parameter idea behind Geometric Brownian Motion is flawed. It is argued that information flow dictates stock price movements and information is a function macro-economic regimes shifts. As such, we propose an alternative model, one in which the parameters in the Standard Geometric Brownian Motion change according to an underlying Hidden Markov Process. This new model, termed a Markov-Switching model, is presented in extensive detail. Parameter Estimation methods, Simulation Methods and Option Pricing Theory are explored. Summary algorithms are presented so that this dissertation may be used as a good reference guide for those wishing to apply Markov-Switching Models. The model is tested by fitting the model on South African data and using the discussed option theory to create various implied volatility surfaces. The surfaces produced appear to obey some of the empirical observations and theoretical ideas around expected implied volatility surfaces, indicating that the Markov-Switching model has some value for option pricing