Paper Info
Title
Fuzzy pricing of geometric Asian options and its algorithm.
Abstract
This paper considers the problem of pricing the geometric Asian option in the fuzzy environment. The fuzzy pattern of Kemma-Vorst formula is proposed under the assumption that the stock price, the risk-free interest rate and the volatility are all fuzzy numbers. An interpolation search algorithm is designed to solve the proposed pricing model. Furthermore, a numerical example is presented to show the rationality for the algorithm. Finally, an empirical study is also provided to indicate the practicability of the proposed fuzzy pricing model. From the empirical study, we can see that the market prices of E0015 option lay in the closed interval with belief degree 90% while the Kemma-Vorst model tends to underprice E0015 option. A general fuzzy pattern of geometric Asian option pricing is given.The specific fuzzy formulae of the Asian option pricing are obtained.The interpolation search algorithm is designed to solve the proposed pricing model. Owing to the fluctuations of the financial market, input data in the options pricing formula cannot be expected to be precise. This paper discusses the problem of pricing geometric Asian options under the fuzzy environment. We present the fuzzy price of the geometric Asian option under the assumption that the underlying stock price, the risk-free interest rate and the volatility are all fuzzy numbers. This assumption makes the financial investors to pick any geometric Asian option price with an acceptable belief degree. In order to obtain the belief degree, the interpolation search algorithm has been proposed. Some numerical examples are presented to illustrate the rationality and practicability of the model and the algorithm. Finally, an empirical study is performed based on the real data. The empirical study results indicate that the proposed fuzzy pricing model of geometric Asian option is a useful tool for modeling the imprecise problem in the real world.
Year
DOI
Venue
2015
10.1016/j.asoc.2014.12.008
Appl. Soft Comput.
Keywords
Field
DocType
fuzzy number
Monte Carlo methods for option pricing,Mathematical optimization,Valuation of options,Rational pricing,Fuzzy logic,Algorithm,Finite difference methods for option pricing,Asian option,Fuzzy number,Trinomial tree,Mathematics
Journal
Volume
Issue
ISSN
28
C
1568-4946
Citations 
PageRank 
References 
4
0.43
14
Authors
4
Name
Order
Citations
PageRank
Wei-Guo Zhang155739.22
Weilin Xiao2685.19
Wen-Tao Kong340.43
Yue Zhang418453.93