An Asian option (or average value 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 maturity.

One advantage of Asian options is that these reduce the risk of market manipulation of the underlying instrument at maturity.

Payout of Asian call options with arithmetic average

We describe the payout of some Asian call options.

The continuous case gives the payout:

where T is the time to maturity, S is the price and K is the strike price.

For the case of discrete monitoring (with monitoring at the times ) we have the payout:

The examples above involve Asian options with arithmetic average. There also exists Asian options with geometric average.

Pricing of Asian options

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 is solved via the Effective Classical

potential

of Feynman and Kleinert, as shown in .

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.

Asian option Topic - Options

In finance, an option is a contract between a buyer and a seller that gives the buyer the right, but not the obligation, to buy or to sell a particular asset (the underlying asset) on or before the option's expiration time, at an agreed price, the strike price. In return for granting the option, the seller collects a payment (the premium) from the buyer. A call option gives the buyer the right to buy the underlying asset and a put option gives the buyer of the option the right to sell the underlying asset. If the buyer chooses to exercise this right, the seller is obliged to sell or buy the asset at the agreed price. The buyer may choose not to exercise the right and let it expire. The underlying asset can be a piece of property, a security (stock or bond), or a derivative instrument, such as a futures contract.