supersharebybls

Determine price of supershare digital options using Black-Scholes model

Syntax

Price = supersharebybls(RateSpec,StockSpec,Settle,Maturity,StrikeLow,StrikeHigh)

Description

Price = supersharebybls(RateSpec,StockSpec,Settle,Maturity,StrikeLow,StrikeHigh) computes supershare digital options using the Black-Scholes option pricing model.

Examples

Compute the Price of Supershare Digital Options Using Black-Scholes Model

This example shows how to compute the price of supershare digital options using Black-Scholes model. Consider a supershare based on a portfolio of nondividend paying stocks with a lower strike of 350 and an upper strike of 450. The value of the portfolio on November 1, 2008 is 400. The risk-free rate is 4.5% and the volatility is 18%. Using this data, calculate the price of the supershare option on February 1, 2009.

Settle = datetime(2008,11,1);
Maturity = datetime(2009,2,1);
Rates = 0.045;
Basis = 1;
Compounding = -1;

% create the RateSpec
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,...
'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding, 'Basis', Basis);

% define the StockSpec
AssetPrice = 400;
Sigma = .18;
StockSpec = stockspec(Sigma, AssetPrice);

% define the high and low strike points
StrikeLow = 350;
StrikeHigh = 450;

% calculate the price
Pssh = supersharebybls(RateSpec, StockSpec, Settle, Maturity,...
StrikeLow, StrikeHigh)

Pssh = 0.9411

Input Arguments

RateSpec — Interest-rate term structure

structure

Interest-rate term structure (annualized and continuously compounded), specified by the RateSpec obtained from intenvset. For information on the interest-rate specification, see intenvset.

Data Types: struct

StockSpec — Stock specification for underlying asset

structure

Stock specification for the underlying asset. For information on the stock specification, see stockspec.

stockspec handles several types of underlying assets. For example, for physical commodities the price is StockSpec.Asset, the volatility is StockSpec.Sigma, and the convenience yield is StockSpec.DividendAmounts.

Data Types: struct

Settle — Settlement or trade date

datetime array | string array | date character vector

Settlement or trade date for the basket option, specified as an NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, supersharebybls also accepts serial date numbers as inputs, but they are not recommended.

Maturity — Maturity date

datetime array | string array | date character vector

Maturity date for the basket option, specified as an NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, supersharebybls also accepts serial date numbers as inputs, but they are not recommended.

StrikeLow — Low strike price values

vector

Low strike price values, specified as an NINST-by-1 vector.

Data Types: double

StrikeHigh — High strike price values

vector

High strike price values, specified as an NINST-by-1 vector.

Data Types: double

Output Arguments

Price — Expected prices for supershare option

vector

Expected prices for supershare option, returned as a NINST-by-1 vector.

More About

Supershare Option

A supershare option pays out a proportion of the assets underlying a portfolio if the asset lies between a lower and an upper bound at the expiry of the option.

For more information, see Digital Option.

Version History

Introduced in R2009a

R2022b: Serial date numbers not recommended

Although supersharebybls supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.