General optimized lower and upper bounds for discrete and continuous arithmetic Asian options

We propose an accurate method for pricing arithmetic Asian options on the discrete or continuous average in a general model setting by means of a lower bound approximation. In particular, we derive analytical expressions for the lower bound in the Fourier domain. This is then recovered by a single univariate inversion and sharpened using an optimization technique. In addition, we derive an upper bound to the error from the lower bound price approximation. Our proposed method can be applied to computing the prices and price sensitivities of Asian options with fixed or floating strike price, discrete or continuous averaging, under a wide range of stochastic dynamic models, including exponential Lévy models, stochastic volatility models, and the constant elasticity of variance diffusion. Our extensive numerical experiments highlight the notable performance and robustness of our optimized lower bound for different test cases

Moment-matching approximations for stochastic sums in non-Gaussian Ornstein-Uhlenbeck models

In this paper, we recall actuarial and financial applications of sums of dependent random variables that follow a non-Gaussian mean-reverting process and contemplate distribution approximations. Our work complements previous related studies restricted to lognormal random variables; we revisit previous approximations and suggest new ones. We then derive moment-based distribution approximations for random sums attuned to Asian option pricing and computation of risk measures of random annuities. Various numerical experiments highlight the speed–accuracy benefits of the proposed methods

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

Jumps and stochastic volatility in crude oil prices and advances in average option pricing

Crude oil derivatives form an important part of the global derivatives market. In this paper, we focus on Asian options which are favoured by risk managers being effective and cost-saving hedging instruments. The paper has both empirical and theoretical contributions: we conduct an empirical analysis of the crude oil price dynamics and develop an accurate pricing setup for arithmetic Asian options with discrete and continuous monitoring featuring stochastic volatility and discontinuous underlying asset price movements. Our theoretical contribution is applicable to various commodities exhibiting similar stylized properties. We here estimate the stochastic volatility model with price jumps as well as the nested model with omitted jumps to NYMEX WTI futures vanilla options. We find that price jumps and stochastic volatility are necessary to fit options. Despite the averaging effect, we show that Asian options remain sensitive to jump risk and that ignoring the discontinuities can lead to substantial mispricings

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

Technical Note. On Matrix Exponential Differentiation with Application to Weighted Sum Distributions

In this note, we revisit the innovative transform approach introduced by Cai, Song, and Kou [(2015) A general framework for pricing Asian options under Markov processes. Oper. Res. 63(3):540–554] for accurately approximating the probability distribution of a weighted stochastic sum or time integral under general one-dimensional Markov processes. Since then, Song, Cai, and Kou [(2018) Computable error bounds of Laplace inversion for pricing Asian options. INFORMS J. Comput. 30(4):625–786] and Cui, Lee, and Liu [(2018) Single-transform formulas for pricing Asian options in a general approximation framework under Markov processes. Eur. J. Oper. Res. 266(3):1134–1139] have achieved an efficient reduction of the original double to a single-transform approach. We move one step further by approaching the problem from a new angle and, by dealing with the main obstacle relating to the differentiation of the exponential of a matrix, we bypass the transform inversion. We highlight the benefit from the new result by means of some numerical examples

General lattice methods for arithmetic Asian options

In this research, we develop a new discrete-time model approach with flexibly changeable driving dynamics for pricing Asian options, with possible early exercise, and a fixed or floating strike price. These options are ubiquitous in financial markets but can also be recast in the framework of real options. Moreover, we derive an accurate lower bound to the price of the European Asian options under stochastic volatility. We also survey theoretical aspects; more specifically, we prove that our tree method for the European Asian option in the binomial model is unconditionally convergent to the continuous-time equivalent. Numerical experiments confirm smooth, monotonic convergence, highly precise performance, and robustness with respect to changing driving dynamics and contract features