Topics in computational finance

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Computational Methods for Pricing and Hedging Derivatives

In this thesis, we propose three new computational methods to price financial derivatives and construct hedging strategies under several underlying asset price dynamics. First, we introduce a method to price and hedge European basket options under two displaced processes with jumps, which are capable of accommodating negative skewness and excess kurtosis. The new approach uses Hermite polynomial expansion of a standard normal variable to match the first m moments of the standardised basket return. It consists of Black-and-Scholes type formulae and its improvement on the existing methods is twofold: we consider more realistic asset price dynamics and we allow more flexible specifications for the basket. Additionally, we propose two methods for pricing and hedging American options: one quasi-analytic and one numerical method. The first approach aims to increase the accuracy of almost any existing quasi-analytic method for American options under the geometric Brownian motion dynamics. The new method relies on an approximation of the optimal exercise price near the beginning of the contract combined with existing pricing approaches. An extensive scenario-based study shows that the new method improves the existing pricing and hedging formulae, for various maturity ranges, and, in particular, for long-maturity options where the existing methods perform worst. The second method combines Monte Carlo simulation with weighted least squares regressions to estimate the continuation value of American-style derivatives, in a similar framework to the one of the least squares Monte Carlo method proposed by Longstaff and Schwartz. We justify the introduction of the weighted least squares regressions by numerically and theoretically demonstrating that the regression estimators in the least squares Monte Carlo method are not the best linear unbiased estimators (BLUE) since there is evidence of heteroscedasticity in the regression errors. We find that the new method considerably reduces the upward bias in pricing that affects the least squares Monte Carlo algorithm. Finally, the superiority of our new two approaches for American options are also illustrated over real financial data by considering S&P 100 options and LEAPS®, traded from 15 February 2012 to 10 December 2014

Evolutionary Algorithms and Computational Methods for Derivatives Pricing

This work aims to provide novel computational solutions to the problem of derivative pricing. To achieve this, a novel hybrid evolutionary algorithm (EA) based on particle swarm optimisation (PSO) and differential evolution (DE) is introduced and applied, along with various other state-of-the-art variants of PSO and DE, to the problem of calibrating the Heston stochastic volatility model. It is found that state-of-the-art DEs provide excellent calibration performance, and that previous use of rudimentary DEs in the literature undervalued the use of these methods. The use of neural networks with EAs for approximating the solution to derivatives pricing models is next investigated. A set of neural networks are trained from Monte Carlo (MC) simulation data to approximate the closed form solution for European, Asian and American style options. The results are comparable to MC pricing, but with offline evaluation of the price using the neural networks being orders of magnitudes faster and computationally more efficient. Finally, the use of custom hardware for numerical pricing of derivatives is introduced. The solver presented here provides an energy efficient data-flow implementation for pricing derivatives, which has the potential to be incorporated into larger high-speed/low energy trading systems

Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science

This volume is an eclectic mix of applications of Monte Carlo methods in many fields of research should not be surprising, because of the ubiquitous use of these methods in many fields of human endeavor. In an attempt to focus attention on a manageable set of applications, the main thrust of this book is to emphasize applications of Monte Carlo simulation methods in biology and medicine

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio