Pricing of American-Style Fixed Strike Asian Options with Continuous Arithmetic Average

2004 ◽  
Author(s):  
Seung-Young Oh ◽  
Byung Chun Kim
Keyword(s):  
Asian Options ◽  
Arithmetic Average ◽  
American Style

AN ACCURATE VALUATION OF ASIAN OPTIONS USING MOMENTS

2002 ◽  
Vol 05 (02) ◽  
pp. 147-169 ◽  
Author(s):  
G. FUSAI ◽  
A. TAGLIANI
Keyword(s):  
Maximum Entropy ◽  
Option Price ◽  
High Accuracy ◽  
Great Accuracy ◽  
Entropy Density ◽  
Asian Option ◽  
Asian Options ◽  
True Density ◽  
Arithmetic Average ◽  
First Four Moments

We propose a new method for evaluating fixed strike Asian options using moments. In particular we show that the density of the logarithm of the arithmetic average is uniquely determined from its moments. Resorting to the maximum entropy density, we show that the first four moments are sufficient to recover with great accuracy the true density of the average. Then the Asian option price is estimated with high accuracy. We compare the proposed method with others based on the computation of moments.

A Dynamic Programming Procedure for Pricing American-Style Asian Options

2002 ◽  
Vol 48 (5) ◽  
pp. 625-643 ◽  
Author(s):  
Hatem Ben-Ameur ◽  
Michèle Breton ◽  
Pierre L'Ecuyer
Keyword(s):  
Dynamic Programming ◽  
Asian Options ◽  
American Style

PRICING ASIAN OPTIONS IN AFFINE GARCH MODELS

2011 ◽  
Vol 14 (02) ◽  
pp. 313-333 ◽  
Author(s):  
MERCURI LORENZO
Keyword(s):  
Monte Carlo ◽  
Analytical Procedure ◽  
Garch Models ◽  
Asian Options ◽  
Edgeworth Expansions ◽  
Arithmetic Average ◽  
Geometric Average ◽  
Low Order

We derive recursive relationships for the m.g.f. of the geometric average of the underlying within some affine Garch models [Heston and Nandi (2000), Christoffersen et al. (2006), Bellini and Mercuri (2007), Mercuri (2008)] and use them for the semi-analytical valuation of geometric Asian options. Similar relationships are obtained for low order moments of the arithmetic average, that are used for an approximated valuation of arithmetic Asian options based on truncated Edgeworth expansions, following the approach of Turnbull and Wakeman (1991). In both cases the accuracy of the semi-analytical procedure is assessed by means of a comparison with Monte Carlo prices. The results are quite good in the geometric case, while in the arithmetic case the proposed methodology seems to work well only in the Heston and Nandi case.

scholarly journals An Alternating-Direction Implicit Difference Scheme for Pricing Asian Options

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhongdi Cen ◽  
Anbo Le ◽  
Aimin Xu
Keyword(s):  
Difference Scheme ◽  
Numerical Method ◽  
Asset Price ◽  
Uniform Mesh ◽  
Asian Options ◽  
Central Difference ◽  
Alternating Direction Implicit ◽  
Arithmetic Average ◽  
Alternating Direction ◽  
Stable Numerical Method

We propose a fast and stable numerical method to evaluate two-dimensional partial differential equation (PDE) for pricing arithmetic average Asian options. The numerical method is deduced by combining an alternating-direction technique and the central difference scheme on a piecewise uniform mesh. The numerical scheme is stable in the maximum norm, which is true for arbitrary volatility and arbitrary interest rate. It is proved that the scheme is second-order convergent with respect to the asset price. Numerical results support the theoretical results.

scholarly journals Estimation of the Bid-Ask Prices for the European Discrete Geometric Average and Arithmetic Average Asian Options

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Xiankang Luo ◽  
Tao Chen
Keyword(s):  
Law Of One Price ◽  
Asian Options ◽  
European Options ◽  
Quantitative Finance ◽  
Arithmetic Average ◽  
Closed Form Solutions ◽  
Geometric Average ◽  
Conic Finance ◽  
The Law ◽  
Exciting Development

Conic finance is a new and exciting development in quantitative finance, which is widely applied to several topics in finance. The theory of conic finance extends the law of one price to the law of two prices, which yields closed forms for bid-ask prices of European options. In this paper, within the framework of conic finance, we derive effective, explicit, approximate formulas to estimate the bid-ask prices for the European discrete geometric average and arithmetic average Asian options. Finally, we give two examples to demonstrate and validate that the approximate closed-form solutions are efficient and accurate.

scholarly journals The Pricing of Asian Options in Uncertain Volatility Model

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Yulian Fan ◽  
Huadong Zhang
Keyword(s):  
Numerical Algorithms ◽  
Reduction Technique ◽  
Nonlinear Pdes ◽  
Asian Options ◽  
Two Dimensional ◽  
One Dimensional ◽  
Arithmetic Average ◽  
Volatility Model ◽  
Expectation Theory ◽  
Linear Pdes

This paper studies the pricing of Asian options when the volatility of the underlying asset is uncertain. We use the nonlinear Feynman-Kac formula in the G-expectation theory to get the two-dimensional nonlinear PDEs. For the arithmetic average fixed strike Asian options, the nonlinear PDEs can be transferred to linear PDEs. For the arithmetic average floating strike Asian options, we use a dimension reduction technique to transfer the two-dimensional nonlinear PDEs to one-dimensional nonlinear PDEs. Then we introduce the applicable numerical computation methods for these two classes of PDEs and analyze the performance of the numerical algorithms.

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