Conditional sampling for barrier option pricing under the LT method

We develop a conditional sampling scheme for pricing knock-out barrier options under the Linear Transformations (LT) algorithm from Imai and Tan (2006). We compare our new method to an existing conditional Monte Carlo scheme from Glasserman and Staum (2001), and show that a substantial variance reduction is achieved. We extend the method to allow pricing knock-in barrier options and introduce a root-finding method to obtain a further variance reduction. The effectiveness of the new method is supported by numerical results

Accelerating Reconfigurable Financial Computing

This thesis proposes novel approaches to the design, optimisation, and management of reconfigurable computer accelerators for financial computing. There are three contributions. First, we propose novel reconfigurable designs for derivative pricing using both Monte-Carlo and quadrature methods. Such designs involve exploring techniques such as control variate optimisation for Monte-Carlo, and multi-dimensional analysis for quadrature methods. Significant speedups and energy savings are achieved using our Field-Programmable Gate Array (FPGA) designs over both Central Processing Unit (CPU) and Graphical Processing Unit (GPU) designs. Second, we propose a framework for distributing computing tasks on multi-accelerator heterogeneous clusters. In this framework, different computational devices including FPGAs, GPUs and CPUs work collaboratively on the same financial problem based on a dynamic scheduling policy. The trade-off in speed and in energy consumption of different accelerator allocations is investigated. Third, we propose a mixed precision methodology for optimising Monte-Carlo designs, and a reduced precision methodology for optimising quadrature designs. These methodologies enable us to optimise throughput of reconfigurable designs by using datapaths with minimised precision, while maintaining the same accuracy of the results as in the original designs

Efficient hierarchical approximation of high-dimensional option pricing problems

A major challenge in computational finance is the pricing of options that depend on a large number of risk factors. Prominent examples are basket or index options where dozens or even hundreds of stocks constitute the underlying asset and determine the dimensionality of the corresponding degenerate parabolic equation. The objective of this article is to show how an efficient discretisation can be achieved by hierarchical approximation as well as asymptotic expansions of the underlying continuous problem. The relation to a number of state-of-the-art methods is highlighted

Lower Precision calculation for option pricing

The problem of options pricing is one of the most critical issues and fundamental building blocks in mathematical finance. The research includes deployment of lower precision type in two options pricing algorithms: Black-Scholes and Monte Carlo simulation. We make an assumption that the shorter the number used for calculations is (in bits), the more operations we are able to perform in the same time. The results are examined by a comparison to the outputs of single and double precision types. The major goal of the study is to indicate whether the lower precision types can be used in financial mathematics. The findings indicate that Black-Scholes provided more precise outputs than the basic implementation of Monte Carlo simulation. Modification of the Monte Carlo algorithm is also proposed. The research shows the limitations and opportunities of the lower precision type usage. In order to benefit from the application in terms of the time of calculation improved algorithms can be implemented on GPU or FPGA. We conclude that under particular restrictions the lower precision calculation can be used in mathematical finance.

Efficient Procedure for Valuing American Lookback Put Options

Lookback option is a well-known path-dependent option where its payoff depends on the historical extremum prices. The thesis focuses on the binomial pricing of the American floating strike lookback put options with payoff at time $t$ (if exercise) characterized by $$\max_{k=0, \ldots, t} S_k - S_t,$$ where $S_t$ denotes the price of the underlying stock at time $t$. Build upon the idea of \hyperlink{RBCV}{Reiner Babbs Cheuk and Vorst} (RBCV, 1992) who proposed a transformed binomial lattice model for efficient pricing of this class of option, this thesis extends and enhances their binomial recursive algorithm by exploiting the additional combinatorial properties of the lattice structure. The proposed algorithm is not only computational efficient but it also significantly reduces the memory constraint. As a result, the proposed algorithm is more than 1000 times faster than the original RBCV algorithm and it can compute a binomial lattice with one million time steps in less than two seconds. This algorithm enables us to extrapolate the limiting (American) option value up to 4 or 5 decimal accuracy in real time

Quasi-Monte Carlo in finance: extending for problems of high effective dimension

Neste artigo mostramos que é possível usar métodos de simulação quase-Monte Carlo em problemas de alta dimensão efetiva. Isto é feito por meio de uma combinação de uma cuidadosa construção das seqüências de Sobol e de uma decomposição apropriada da matriz de covariância dos fatores de risco. A eficácia do método é ilustrada por meio da precificação de opções que envolve a solução de problemas com dimensão nominal da ordem de 550 (e dimensão efetiva da ordem de 300). Acreditamos que o método apresentado seja de fácil implementação e de grande interesse para os participantes do mercado financeiro.In this paper we show that it is possible to extend the use of quasi-Monte Carlo for applications of high effective dimension. This is achieved through a combination of a careful construction of the Sobol sequence and an appropriately chosen decomposition of a covariance matrix. The effectiveness of this procedure is demonstrated as we price average options with nominal dimensions ranging up to 550 (effective dimension around 300). We believe the method we present is easy to implement and should be of great interest to practitioners

Assessing investment strategies in mining projects in the Asia-Pacific region

The Asia-Pacific region has experienced a significant period of development over the last four decades. Rapid urbanisation has resulted in an increased demand for mineral resources indicating the resource industry has contributed the primary income to the economies of many Asia-Pacific countries. The objective of this thesis is to shed light on investment opportunity using the strategy of timing flexibility. This thesis uses two methodologies, namely Net Present value (NPV) and real options valuation (ROV), to conduct an investment analysis assessing timing flexibility. This thesis finds that commodity prices affect the mining investors’ decisions. However, the impact of tax policy uncertainty is quite subtle

\u3ci\u3eThe Conference Proceedings of the 2003 Air Transport Research Society (ATRS) World Conference, Volume 1\u3c/i\u3e

UNOAI Report 03-5https://digitalcommons.unomaha.edu/facultybooks/1131/thumbnail.jp