An Asian option (or ''average value'' option) is a special type of
option contract
An option contract, or simply option, is defined as "a promise which meets the requirements for the formation of a contract and limits the promisor's power to revoke an offer". Option contracts are common in relation to property (see below) and ...
. For Asian options, the payoff is determined by the average underlying price over some pre-set period of time. This is different from the case of the usual
European option
In finance, the style or family of an option is the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American (style) options. These options ...
and
American option
In finance, the style or family of an option is the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American (style) options. These options ...
, where the payoff of the option contract depends on the price of the
underlying instrument at exercise; Asian options are thus one of the basic forms of
exotic option
In finance, an exotic option is an option which has features making it more complex than commonly traded vanilla options. Like the more general exotic derivatives they may have several triggers relating to determination of payoff. An exotic op ...
s.
There are two types of Asian options: Average Price Option (fixed strike), where the strike price is predetermined and the averaging price of the underlying asset is used for payoff calculation; and Average Strike Option (floating strike), where the averaging price of the underlying asset over the duration becomes the strike price.
One advantage of Asian options is that these reduce the risk of
market manipulation
In economics and finance, market manipulation occurs when someone intentionally alters the supply or demand of a security to influence its price. This can involve spreading misleading information, executing misleading trades, or manipulating ...
of the underlying instrument at maturity. Another advantage of Asian options involves the relative cost of Asian options compared to European or American options. 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. This can be an advantage for corporations that are subject to the
Financial Accounting Standards Board
The Financial Accounting Standards Board (FASB) is a private standard-setting body whose primary purpose is to establish and improve Generally Accepted Accounting Principles (GAAP) within the United States in the public's interest. The Secur ...
revised Statement No. 123, which required that corporations expense employee stock options.
Etymology
In the 1980s Mark Standish was with the London-based Bankers Trust working on fixed income derivatives and proprietary arbitrage trading. David Spaughton worked as a systems analyst in the financial markets with Bankers Trust since 1984 when the Bank of England first gave licences for banks to do foreign exchange options in the London market. In 1987 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." They called this exotic option the Asian option because they were in Asia.
Permutations of Asian option
There are numerous permutations of Asian option; the most basic are listed below:
* Fixed
strike
Strike may refer to:
People
*Strike (surname)
* Hobart Huson, author of several drug related books
Physical confrontation or removal
*Strike (attack), attack with an inanimate object or a part of the human body intended to cause harm
* Airstrike, ...
(or average rate) Asian
call
Call or Calls may refer to:
Arts, entertainment, and media Games
* Call (poker), a bet matching an opponent's
* Call, in the game of contract bridge, a bid, pass, double, or redouble in the bidding stage
Music and dance
* Call (band), from L ...
payout
::
: where A denotes the average price for the period
, T and K is the strike price.
The equivalent
put option
In finance, a put or put option is a derivative instrument in financial markets that gives the holder (i.e. the purchaser of the put option) the right to sell an asset (the ''underlying''), at a specified price (the ''strike''), by (or on) a ...
is given by
::
* Floating strike (or floating rate) Asian call option payout
::
: where S(T) is the price at maturity and k is a weighting, usually 1 so often omitted from descriptions.
The equivalent put option payoff is given by
::
Types of averaging
The Average
may be obtained in many ways. Conventionally, this means an
arithmetic average. In the ''continuous'' case, this is obtained by
:
For the case of ''discrete monitoring'' (with monitoring at the times
and
) we have the average given by
:
There also exist Asian options with
geometric average; in the continuous case, this is given by
:
Pricing of Asian options
A discussion of the problem of pricing Asian options with
Monte Carlo method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be ...
s 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.
A Variance Gamma model can be efficiently implemented when pricing Asian-style options. Then, using the Bondesson series representation to generate the
variance gamma process can increase the computational performance of the Asian option pricer.
[Mattias Sander. Bondesson's Representation of the Variance Gamma Model and Monte Carlo Option Pricing. Lunds Tekniska Högskola 2008]
Within jump diffusions and stochastic volatility models, the pricing problem for geometric Asian options can still be solved.
For the arithmetic Asian option in Lévy models, one can rely on numerical methods
or on analytic bounds.
European Asian call and put options with geometric averaging
We are able to derive a closed-form solution for the geometric Asian option; when used in conjunction with
control variates in
Monte Carlo
Monte Carlo ( ; ; or colloquially ; , ; ) is an official administrative area of Monaco, specifically the Ward (country subdivision), ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is located. Informally, the name also refers to ...
simulations, the formula is useful for deriving fair values for the arithmetic Asian option.
Define the continuous-time geometric mean
as: