A basket option is a

financial derivative In finance, a derivative is a contract that ''derives'' its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be u ...

, more specifically an

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 opt ...

, whose

underlying In finance, a derivative is a contract that ''derives'' its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be use ...

is a weighted sum or average of different assets that have been grouped together in a

basket A basket is a container that is traditionally constructed from stiff fibers and can be made from a range of materials, including wood splints, runners, and cane. While most baskets are made from plant materials, other materials such as horsehai ...

. A basket option is similar to an index option, where a number of stocks have been grouped together in an index and the option is based on the price of the

index Index (or its plural form indices) may refer to: Arts, entertainment, and media Fictional entities * Index (''A Certain Magical Index''), a character in the light novel series ''A Certain Magical Index'' * The Index, an item on a Halo megastru ...

, but differs in that the members and weightings of an

can change over time while those in a basket option do not. Unlike a

rainbow option Rainbow option is a derivative exposed to two or more sources of uncertainty, as opposed to a simple option that is exposed to one source of uncertainty, such as the price of underlying asset. The name of ''rainbow'' comes from Rubinstein (1991), ...

which considers a group of assets but ultimately pays out on the level of one, a basket option is written on a basket of underlying assets but will pay out on a weighted average gain of the basket as a whole. Like

s basket options are most commonly written on a basket of equity indices, though they are frequently written on a basket of individual equities as well. For example, a call option could be written on a basket of ten healthcare stocks, where the basket was composed of ten stocks in weighted proportions. The strike price X is usually set at the current value of the basket (

at-the-money In finance, moneyness is the relative position of the current price (or future price) of an underlying asset (e.g., a stock) with respect to the strike price of a derivative, most commonly a call option or a put option. Moneyness is firstly a thr ...

), and the payoff profile will be ''max''(S − X, 0) where S is a weighted average of n asset prices at maturity, and each weight represents the percentage of total investment in that asset.

Pricing and valuation

Basket options are usually priced using an appropriate industry-standard model (such as Black–Scholes) for each individual basket component, and a matrix of correlation coefficients applied to the underlying

stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...

drivers for the various models. While there are some closed-form solutions for simpler cases (e.g. two-color European rainbows),Rubinstein, Mark. "Exotic options." No. RPF-220. University of California at Berkeley, 1991. URL:http://www.haas.berkeley.edu/groups/finance/WP/rpf220.pdf semi-analytic solutions, analytical approximations, and numerical quadrature integrations, the general case must be approached with

Monte Carlo Monte Carlo (; ; french: Monte-Carlo , or colloquially ''Monte-Carl'' ; lij, Munte Carlu ; ) is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is ...

or binomial lattice methods.

Lognormality

Problems in hedging basket options can be of some significance when dealing with markets that exhibit a strong skew. Many operators price basket options as if the underlying basket were a single commodity following its own stochastic process with its volatility derived from its own time series. This however conflicts with a fact that an average (or any linear combination) of assets with lognormal distribution does not follow lognormal distribution.Taleb, Nassim. ''Dynamic hedging: managing vanilla and exotic options''. Vol. 64. John Wiley & Sons, 1997. p.391 This problem arises in swaps and Eurodollar strips (baskets of Eurodollar options) but in equities and fixed income it is mitigated by the fact that when correlation between assets is high, the sum would come closer to a lognormally distributed asset.

References

External links

FiNCAD - Basket options
{{Derivatives market Derivatives (finance) Options (finance)

Pricing and valuation

Lognormality

See also

References

External links