Asian option
Encyclopedia
An Asian option is a special type of option contract
. For Asian options the payoff is determined by the average underlying price over some pre-set period of time. This is different to the case of the usual European option and American option, 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
s.
One advantage of Asian options is that these reduce the risk of market manipulation
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 FASB revised Statement No. 123, which requires that corporations expense employee stock options.
Fixed strike (also known as an average rate) Asian call payout
where A denotes the average, and K the strike. The equivalent put option is given by
The floating strike (or floating rate) Asian call option has the payout
where k is a weighting, usually 1 so often omitted from descriptions. The equivalent put option payoff is given by
For the case of discrete monitoring (with monitoring at the times
) we have the average given by
There also exists Asian options with geometric average, in the continuous case this is given by
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
.
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 have some advantages when pricing this type of option.
Within Lévy models the pricing problem for geometrically Asian options can still be solved. For the arithmetic Asian option in Lévy models one can rely on numerical methods or on analytic bounds
.
Option contract
An option contract 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." Restatement of Contracts § 25 ....
. For Asian options the payoff is determined by the average underlying price over some pre-set period of time. This is different to the case of the usual European option and American option, 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
Exotic option
In finance, an exotic option is a derivative which has features making it more complex than commonly traded products . These products are usually traded over-the-counter , or are embedded in structured notes....
s.
One advantage of Asian options is that these reduce the risk of market manipulation
Market manipulation
Market manipulation describes a deliberate attempt to interfere with the free and fair operation of the market and create artificial, false or misleading appearances with respect to the price of, or market for, a security, commodity or currency...
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 FASB revised Statement No. 123, which requires that corporations expense employee stock options.
History
Asian options are so called because they were introduced in Tokyo, Japan, in 1987, at a branch of an American bank.Permutations of Asian option
There are numerous permutations of Asian option, the most basic are listed below:Fixed strike (also known as an average rate) Asian call payout
where A denotes the average, and K the strike. The equivalent put option is given by
The floating strike (or floating rate) Asian call option has the payout
where k is a weighting, usually 1 so often omitted from descriptions. The equivalent put option payoff is given by
Types of averaging
The Average A 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
) we have the average given by
There also exists 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 methodMonte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...
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
Hagen Kleinert
Hagen Kleinert is Professor of Theoretical Physics at the Free University of Berlin, Germany , at theWest University of Timişoara, at thein Bishkek. He is also of the...
.
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
Variance gamma process
In the theory of stochastic processes, a part of the mathematical theory of probability, the variance gamma process , also known as Laplace motion, is a Lévy process determined by a random time change. The process has finite moments distinguishing it from many Lévy processes. There is no diffusion...
shows to have some advantages when pricing this type of option.
Within Lévy models the pricing problem for geometrically Asian options can still be solved. For the arithmetic Asian option in Lévy models one can rely on numerical methods or on analytic bounds
.