Rainbow
FinPricing offers:
Four user interfaces:
- Data API.
- Excel Add-ins.
- Model Analytic API.
- GUI APP.
Rainbow Option Valuation
FinPricing provides valuation models for:
- Rainbow Option (call, put, binary call, binary put)
- Rainbow Asian Option
- Best of Option
- Worst of Option
- Forward Start Rainbow Option
- Rainbow Option with Bucketing
- Rainbow Option with Floors
- Rainbow Option with Management Fees
- Autocallable Rainbow Payout
| 1. Rainbow Option Introduction |
A rainbow option is an option on a basket that gives the holder the right to buy or sell assets according to their performance. The number of assets is called the number of colours of the rainbow. Each asset is referred to as a colour of the rainbow that is associated with the percentage growth of returns.
Rainbow option consists of a combination of various assets just like a rainbow is a combination of various colours. The assets are sorted by their performance at payment date. There are weights applied to the assets according to their performance. The final payout is the sum of the weighted returns of all the assets in the basket.
The weights are dynamically assigned to the assets in the basket according to their relative growths. Therefore, rainbow can be seen as a dynamic basket option with dynamic allocation of weigths. For example, a rainbow option has 3 assets with weights 50%, 30%, and 20%. At maturity, the option pays 50% of the best return, 30% of the second best, and 20% of the third best.
Rainbow option is a correlation and basket product that gives investors portfolio diversification. It is cheaper than the sum of individual options. Rainbow option is also an excellent tool for hedging the risk of multiple assets and portfolio.
| 2. Rainbow Option Payoff |
The payoff function can be specified in the form of a put, call or forward. The structure is unique in the way the weights are applied to assets in computing the payment. First, assets may be grouped into buckets (bucketing). Each bucket containing one or more asset. A vector of weights is then applied to the ranked bucket returns based on performance.
A rainbow option may have a barrier provision. If all the assets are above or equal to the strike price. The option pays out a predefined payoff structure.
A Reference Asset Level is defined as the level of an underlying asset post-fees, and is equal at any given time to the underlying asset’s actual level times its Multiplier. The multiplier initially begins at one (no fees accrued), and is adjusted downwards as fees are accrued.
The returns of the assets in the basket are ranked according to the overall performance:
in order from k = 1,...,n; such that
There are several sub-types of rainbow options:
- Maximum options: Like simple Vanilla options, except that the payoff is based upon the maximum price of two possible underlyings on the expiry date.
- Minimum options: Like simple Vanilla options, except that the payoff is based upon the minimum price of two possible underlyings on the expiry date.
- Receive Best: Pay the maximum of two possible underlyings on the expiry date (are not really options).
- Receive Worst: pay the minimum of two possible underlyings on the expiry date (are not really options).
- Spread options: Pay the difference between the price of the two underlyings on the expiry date.
- Sum options: Like simple Vanilla options, except that the payoff is based on the sum of two underlying prices on the expiry date.
- Product options: Like simple Vanilla options, except that the payoff is based on the product of two underlying prices on the expiry date.
- Quotient options: Like simple Vanilla options, except that the payoff is based on the ratio of two underlying prices on the expiry date.
The payoffs of best of, worst of, maximum, minimum are given by
| 3. Rainbow Option Valuation |
Weights to be applied to bucket returns, sorted in order of best-performing to worst-performing. Each bucket’s return is the average return of its component stocks. For avoidance of doubt, W_1 will be applied to the highest bucket return while W_n will be applied to the lowest bucket’s return..
Final Averaging Dates can be different for each bucket. One could specify a matrix of Final Averaging Dates with each row containing the final averaging dates for each bucket. The first index corresponds to the bucket number while the second index corresponds to the index of the averaging date for that bucket. This matrix must have a number of rows equal to nBuckets.
A single date may be specified in place of the Final Averaging Dates matrix, in which case it is assumed that all stocks have one and the same final averaging date.
Compute the weighted return, relative to an initial level in the basket ranked according to the overall performance, adjusted by the Individual Floors:
Rainbow option can be seen as a dynamic basket as the relative weight of each underlyer can change with relative levels. A static hedge with a basket option may perform poorly because of the various switch options.
Another way of looking at it is to see the Rainbow as a basket option with known weights that are effective according to the relative performance of the underlying assets. This can be seen as the product of a basket option time digital options. The digital options indicate that we are sensitive to the spread volatility between the various underlying assets.
| 4. Related Topics |