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supersharesensbybls

Determine price or sensitivities of supershare digital options using Black-Scholes model

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Syntax

PriceSens = supersharesensbybls(RateSpec,StockSpec,Settle,Maturity,StrikeLow,StrikeHigh)
PriceSens = supersharesensbybls(___,Name,Value)

Description

PriceSens = supersharesensbybls(RateSpec,StockSpec,Settle,Maturity,StrikeLow,StrikeHigh) computes price or sensitivities of supershare digital options using the Black-Scholes option pricing model.

example

PriceSens = supersharesensbybls(___,Name,Value) specifies options using one or more name-value pair arguments in addition to the input arguments in the previous syntax.

example

Examples

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Open Live Script

This example shows how to compute price and sensitivities of supershare digital options using a 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 and sensitivity 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;

% define 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

% compute the delta and theta of the supershare option
OutSpec = { 'delta';'theta'};
[Delta, Theta]= supersharesensbybls(RateSpec, StockSpec, Settle,...
Maturity, StrikeLow, StrikeHigh, 'OutSpec', OutSpec)
Delta = 
-0.0010

Theta = 
-1.0102

Input Arguments

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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

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

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, supersharesensbybls also accepts serial date numbers as inputs, but they are not recommended.

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, supersharesensbybls also accepts serial date numbers as inputs, but they are not recommended.

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

Data Types: double

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

Data Types: double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: [Gamma,Theta,Price] = supersharesensbybls(RateSpec,StockSpec,Settle,Maturity,StrikeLow,StrikeHigh,'OutSpec',{'gamma';'theta';'price'})

Define outputs, specified as the comma-separated pair consisting of 'OutSpec' and a NOUT- by-1 or a 1-by-NOUT cell array of character vectors with possible values of 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All'.

OutSpec = {'All'} specifies that the output is Delta, Gamma, Vega, Lambda, Rho, Theta, and Price, in that order. This is the same as specifying OutSpec to include each sensitivity.

Example: OutSpec = {'delta','gamma','vega','lambda','rho','theta','price'}

Data Types: char | cell

Output Arguments

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

More About

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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

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See Also

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