Parallel Computation in Econometrics: A Simplified Approach

Parallel computation has a long history in econometric computing, but is not at all wide spread. We believe that a major impediment is the labour cost of coding for parallel architectures. Moreover, programs for specific hardware often become obsolete quite quickly. Our approach is to take a popular matrix programming language (Ox), and implement a message-passing interface using MPI. Next, object-oriented programming allows us to hide the specific parallelization code, so that a program does not need to be rewritten when it is ported from the desktop to a distributed network of computers. Our focus is on so-called embarrassingly parallel computations, and we address the issue of parallel random number generation.Code optimization; Econometrics; High-performance computing; Matrix-programming language; Monte Carlo; MPI; Ox; Parallel computing; Random number generation.

High dimensional American options

Pricing single asset American options is a hard problem in mathematical finance. There are no closed form solutions available (apart from in the case of the perpetual option), so many approximations and numerical techniques have been developed. Pricing multi–asset (high dimensional) American options is still more difficult. We extend the method proposed theoretically by Glasserman and Yu (2004) by employing regression basis functions that are martingales under geometric Brownian motion. This results in more accurate Monte Carlo simulations, and computationally cheap lower and upper bounds to the American option price. We have implemented these models in QuantLib, the open–source derivatives pricing library. The code for many of the models discussed in this thesis can be downloaded from quantlib.org as part of a practical pricing and risk management library. We propose a new type of multi–asset option, the “Radial Barrier Option” for which we find analytic solutions. This is a barrier style option that pays out when a barrier, which is a function of the assets and their correlations, is hit. This is a useful benchmark test case for Monte Carlo simulations and may be of use in approximating multi–asset American options. We use Laplace transforms in this analysis which can be applied to give analytic results for the hitting times of Bessel processes. We investigate the asymptotic solution of the single asset Black–Scholes–Merton equation in the case of low volatility. This analysis explains the success of some American option approximations, and has the potential to be extended to basket options

Parallel Monte Carlo Methods for Derivative Security Pricing

Monte Carlo (MC) methods have proved to be flexible, robust and very useful techniques in computational finance. Several studies have investigated ways to achieve greater efficiency of such methods for serial computers. In this paper, we concentrate on the parallelization potentials of the MC methods. While MC is generally thought to be "embarrassingly parallel", the results eventually depend on the quality of the underlying parallel pseudo-random number generators. There are several methods for obtaining pseudo-random numbers on a parallel computer and we briefly present some alternatives. Then, we turn to an application of security pricing where we empirically investigate the pros and cons of the different generators. This also allows us to assess the potentials of parallel MC in the computational finance framework