Asian option calculator
In general they do not differ in definition, only in how the pay-off is calculated. Because of the averaging feature, Asian options reduce the volatility inherent in the option; therefore, Asian options are typically cheaper than European or American options.
In the s Mark Standish was with the London-based Bankers Trust working on fixed income derivatives and proprietary arbitrage trading.
David Spaughton worked as systems analyst in the financial markets with Bankers Trust since when the Bank of England first gave licences for banks to do foreign exchange options in the London market.
In Standish and Spaughton were in Tokyo on business when "they developed the first commercially used pricing formula for options linked to the average price of crude oil. Conventionally, this means an arithmetic average. In the continuous case, this is obtained by. There also exist Asian options with geometric average ; in the continuous case, this is given by.
A discussion of the problem of pricing Asian options with Monte Carlo methods is given in a paper by Kemna and Vorst. In the path integral approach to option pricing ,  the problem for geometric average can be solved via the Effective Classical potential  of Feynman and Kleinert.
Rogers and Shi solve the pricing problem with a PDE approach. Variance Gamma model can be efficiently implemented when pricing Asian style options. Then using the Bondesson series representation for generating the variance gamma process shows to increase performance when pricing this type of option.
Currently, the stock market has numerous types of options: European, American, barrier, Exotic, etc. This article focuses on evaluating the Asian option. The mathematical model of considered problem is represented by the Black — Scholes model , which is a parabolic partial differ ential equation in relation to the price of Asian option. The use of implicit difference schemes for solving the problem can produce a stable numerical solution for different values of volatility, risk — free rate and the time of option exercise [1—3; 9].
These calculations for the analysis of the results are generated in the form of tables and graphs in spread sheet format and Excelcharts. Consider the example of the program of Asian put option.