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.

Long memory stochastic volatility in option pricing

The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range dependence. We consider the option price as a sum of classical Black-Scholes price and random deviation describing the risk from the random volatility. By using the fact the option price and random volatility change on different time scales, we find the asymptotic equation for the derivation involving fractional Brownian motion. The solution to this equation allows us to find the pricing bands for options

The Local Fractional Bootstrap

We introduce a bootstrap procedure for high-frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an estimator based on a ratio of realized power variations. Our new resampling method, the local fractional bootstrap, relies on simulating an auxiliary fractional Brownian motion that mimics the fine properties of high frequency differences of the Brownian semistationary process under the null hypothesis. We prove the first order validity of the bootstrap method and in simulations we observe that the bootstrap-based hypothesis test provides considerable finite-sample improvements over an existing test that is based on a central limit theorem. This is important when studying the roughness properties of time series data; we illustrate this by applying the bootstrap method to two empirical data sets: we assess the roughness of a time series of high-frequency asset prices and we test the validity of Kolmogorov's scaling law in atmospheric turbulence data

Option pricing for Fractal Activity Time Geometric Brownian Motion (FATGBM)

This thesis examines option pricing for a Long Range Dependent (LRD) stochastic process with student marginal distributions called Fractal Activity Time Geometric Brownian Motion (FATGBM), introduced in Heyde (1999). We address four separate problems involving the pricing of options under FATGBM and other LRD stochastic processes. Following an introduction into the mechanics of derivative pricing, the thesis begins by addressing the problem of derivative pricing under FATGBM. We first develop the properties of FATGBM and show that the market is arbitrage-free but incomplete under this model. We then prove that there is no replicating strategy for this model except under special circumstances. We show that those special circumstances lead to the hedging of a Timer Option where interest rates are zero and we conclude by discussing the issue of completing the market by calibrating FATGBM to liquid risky assets such as European Options, as discussed in Carr et al. (2001). We then describe how to price path dependent options under FATGBM. We first propose a non-recombining tree that is used to then construct a recombining tree to price path dependent options. Further, we prove that our discrete time model converges to the continuous time one, resulting in a discrete approximation scheme for path dependent options. We then prove that the discrete approximation scheme results in an upper bound for the price of an American put. The next chapter addresses the problem of sampling from the distribution of FATGBM conditional on price history. Given that FATGBM is a LRD process, it is imperative to be able to simulate future price paths given a price path history. We propose a Markov Chain Monte Carlo (MCMC) approach to develop two algorithms for two different LRD processes, one FATGBM and one similar to FATGBM that we call FATGBM 2. We prove that the algorithms result in a Markov chain with a stationary distribution identical to the conditional distribution from which we wish to sample. We then discuss the implementation of both algorithms and compare the mixing times and features of the resultant conditional distribution. The final chapter combines the themes and results of the preceding chapters by using the MCMC algorithm in conjunction with the recombining tree developed in Chapter 2. The result is an analysis of the effect of long range dependence on option prices, the most compelling finding being that LRD has more of an impact on the option price than the impact of heavy tails alone, a phenomenon that has thus far been overlooked by the literature on option pricing. We conclude with an analysis of the implied volatility surface arising from FATGBM and discuss the implications of our research in the context of the existing literature

From Random Walks to Chaotic Crashes: The Linear Genealogy of the Efficient Capital Market Hypothesis

This Article argues that chaos theory, noise theory and behavioral finance mandate opening a new chapter in a voluminous corporate and securities law debate revolving around the efficient capital market hypothesis (ECMH), which for decades has been the context for debating corporate and securities law and policy. The debate has been defined by interpretations of the semi-strong form of the ECMH - the claim that security prices fully reflect all publicly available information. As such, the debate has assumed as true and built upon the weak form of the ECMH - the claim that security prices fully reflect all information consisting of past security prices. This Article analyzes the historical development of the ECMH, showing that the weak and semi-strong forms of the ECMH are based on linear methodology and thought that have been rendered obsolete by chaos models applying nonlinear techniques. This obsolescence renders the ECMH false in all its forms, rendering it moot for purposes of policy formulation on topics ranging from such basic corporate and securities law doctrines as mandatory disclosure rules and mandatory fiduciary obligation, which neither the ECMH nor noise theory can do to the capital market circuit breakers and relational investing