Closed‐form lower bounds for the price of arithmetic average Asian options by multiple conditioning

2021 ◽  
Author(s):  
Geon Ho Choe ◽  
Minseok Kim
Keyword(s):  
Closed Form ◽  
Lower Bounds ◽  
Asian Options ◽  
Arithmetic Average

scholarly journals Expected Logarithm and Negative Integer Moments of a Noncentral χ2-Distributed Random Variable

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1048
Author(s):  
Stefan Moser
Keyword(s):  
Closed Form ◽  
Lower Bounds ◽  
Degrees Of Freedom ◽  
Random Variable ◽  
Negative Integer ◽  
Upper And Lower Bounds ◽  
Basic Properties

Closed-form expressions for the expected logarithm and for arbitrary negative integer moments of a noncentral χ2-distributed random variable are presented in the cases of both even and odd degrees of freedom. Moreover, some basic properties of these expectations are derived and tight upper and lower bounds on them are proposed.

scholarly journals Transforming Arithmetic Asian Option PDE to the Parabolic Equation with Constant Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Zieneb Ali Elshegmani ◽  
Rokiah Rozita Ahmad ◽  
Saiful Hafiza Jaaman ◽  
Roza Hazli Zakaria
Keyword(s):  
Parabolic Equation ◽  
Analytical Solution ◽  
Heat Equation ◽  
Numerical Solution ◽  
Closed Form ◽  
Asian Option ◽  
Asian Options ◽  
New Approach ◽  
Constant Coefficients ◽  
Closed Form Analytical Solution

Arithmetic Asian options are difficult to price and hedge, since at present, there is no closed-form analytical solution to price them. Transforming the PDE of the arithmetic the Asian option to a heat equation with constant coefficients is found to be difficult or impossible. Also, the numerical solution of the arithmetic Asian option PDE is not very accurate since the Asian option has low volatility level. In this paper, we analyze the value of the arithmetic Asian option with a new approach using means of partial differential equations (PDEs), and we transform the PDE to a parabolic equation with constant coefficients. It has been shown previously that the PDE of the arithmetic Asian option cannot be transformed to a heat equation with constant coefficients. We, however, approach the problem and obtain the analytical solution of the arithmetic Asian option PDE.

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.

Commodity Asian Options: A Closed-Form Formula

2007 ◽  
Author(s):  
Gianluca Fusai ◽  
Marina Marena ◽  
Andrea Roncoroni
Keyword(s):  
Closed Form ◽  
Asian Options ◽  
Closed Form Formula

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.

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