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Numerical Algorithm for Delta of Asian Option.

Boxiang Zhang1, Yang Yu1, Weiguo Wang1

  • 1School of Economics, Dongbei University of Finance and Economics, 217 Jianshan Street, Dalian, Liaoning 116023, China.

Thescientificworldjournal
|August 13, 2015
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Summary
This summary is machine-generated.

This study presents an efficient numerical method for calculating the Greeks of Asian options. The new approach improves hedging strategies by accurately pricing complex arithmetic Asian options.

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Area of Science:

  • Quantitative Finance
  • Computational Finance
  • Financial Derivatives

Background:

  • Asian options are complex derivatives whose pricing, particularly for arithmetic types, lacks a closed-form solution.
  • Accurate calculation of option Greeks (sensitivity measures) is crucial for effective risk management and hedging strategies.

Purpose of the Study:

  • To develop and validate an efficient numerical method for calculating the Greeks of Asian options.
  • To provide an analytical solution for the Delta of geometric Asian options to serve as a benchmark.
  • To improve the accuracy and efficiency of hedging strategies involving arithmetic Asian options.

Main Methods:

  • Derivation of a closed-form solution for the Delta of geometric Asian options.
  • Utilizing the analytical solution as a control variate for numerical pricing of arithmetic Asian options.
  • Implementation of a novel numerical method and comparison of its standard error against classical variance reduction techniques.

Main Results:

  • A closed-form solution for the Delta of geometric Asian options was successfully derived.
  • The proposed numerical method demonstrated efficiency in calculating the Delta of arithmetic Asian options.
  • The new method showed competitive or superior performance in terms of standard error compared to existing techniques.

Conclusions:

  • The developed numerical approach offers an efficient and accurate way to compute the Greeks for Asian options.
  • This advancement facilitates more robust hedging strategies for financial institutions trading these derivatives.
  • The study contributes a valuable tool for the quantitative analysis of exotic options.