High Performance American Option Pricing

Andersen, Leif; Lake, Mark; Offengenden, Dimitri

doi:10.2139/ssrn.2547027

Cited by 12 publications

(57 citation statements)

References 61 publications

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“…In this section, the pricing of an American put option will be considered. Note that the price of the corresponding American call could be found by put‐call symmetry . It could easily be seen that as soon as the early exercise boundary is determined, the option price could then be obtained by employing an appropriate quadrature rule applied to the integral terms in Equation .…”

Section: Approximation Of the American Option Pricementioning

confidence: 99%

A product integration method for the approximation of the early exercise boundary in the American option pricing problem

Nedaiasl

Bastani

Rafiee

2019

Math Methods in App Sciences

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Integral equation methods are now becoming well‐established tools in the study of financial models used in theory and practice. In this paper, we investigate the fully nonlinear weakly singular nonstandard Volterra integral equations representing the early exercise boundary of American option contracts, which gained popularity in recent years. We propose a product integration approach based on linear barycentric rational interpolation to solve the problem. The price of the option will then be computed using the obtained approximation of the early exercise boundary and a barycentric rational quadrature. The convergence of the approximation scheme will also be analyzed. Finally, some numerical experiments based on the introduced method are presented and compared with some exiting approaches.

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Section: Approximation Of the American Option Pricementioning

confidence: 99%

A product integration method for the approximation of the early exercise boundary in the American option pricing problem

Nedaiasl

Bastani

Rafiee

2019

Math Methods in App Sciences

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“…For the reference solver, we used option pricing libraries from the Financial Toolbox in MATLAB R2016a. Tree sizes reported in the literature to provide highly accurate results included values of 10000 [17] and 15000 [2] time steps. We also used 15000 time-step trees in the reference program, using double-precision arithmetic.…”

Section: B Accuracy Analysismentioning

confidence: 99%

A High-Level Design Framework for the Automatic Generation of High-Throughput Systolic Binomial-Tree Solvers

Tavakkoli¹,

Thomas²

2018

IEEE Trans. VLSI Syst.

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Abstract-The binomial-tree model is a numerical method widely used in finance with a computational complexity which is quadratic with respect to the solution accuracy. Existing research has employed reconfigurable computing to provide faster solutions compared to general-purpose processors, but they require low-level manual design by a hardware engineer, and can only solve American options. This paper presents a formal mathematical framework that captures a large class of binomial-tree problems, and provides a systolic data-movement template that maps the framework into digital hardware. The article also presents a fully-automated design flow, which takes C-level user descriptions of binomial trees, with custom data types and tree operations, and automatically generates fullypipelined reconfigurable hardware solutions in FPGA bit-stream files. On a Xilinx Virtex-7 xc7vx980t FPGA at a 100-MHz clock frequency, we require 54-µs latency to solve three 876-step 32-bit fixed-point American option binomial trees, with a pricing rate of 114k trees/s. From the same device and in comparison to existing solutions with equivalent FPGA technology, we always achieve better throughput. This ranges from 1.4× throughput compared to a hand-tuned register-transfer level systolic design, to 9.1× and 5.6× improvement with respect to scalar and vector architectures, respectively.

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“…In Andersen et al [1], we introduced a fast, and very accurate, numerical technique for American option prices. Loosely, the method involves fixed-point iterations for the early-exercise boundary of the option, aided by a Chebyshev collocation scheme and high-performance quadrature routines.…”

Section: Introductionmentioning

confidence: 99%

“…Working primarily in a Black-Scholes setting, we develop new results and completely characterize the topology of the optimal exercise region; establish short-and long-term asymptotics for all possible configurations of the signs of rates and dividend yields; and provide a complete numerical algorithm for the pricing of American puts and calls with a double exercise boundary. The algorithm is carefully formulated such that each of the two exercise boundaries can be computed separately from each other, which not only simplifies implementation but also allows us to retain the high accuracy of the work in [1].…”

mentioning

confidence: 99%