supersharesensbybls - Calculate price and sensitivities of supershare digital options using Black-Scholes model

Syntax

Arguments

RateSpec	The annualized, continuously compounded rate term structure. For information on the interest rate specification, see intenvset.
StockSpec	Stock specification. See stockspec.
Settle	NINST-by-1 vector of settlement or trade dates.
Maturity	NINST-by-1 vector of maturity dates.
StrikeLow	NINST-by-1 vector of low strike price values.
StrikeHigh	NINST-by-1 vector of high strike price values.
OutSpec	(Optional) All optional inputs are specified as matching parameter name/value pairs. The parameter name is specified as a character string, followed by the corresponding parameter value. You can specify parameter name/value pairs in any order. Names are case-insensitive and partial string matches are allowed provided no ambiguities exist. Valid parameter names are: NOUT-by-1 or 1-by-NOUT cell array of strings indicating the nature and order of the outputs for the function. Possible values are 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', or 'All'. For example, OutSpec = {'Price'; 'Lamba'; 'Rho'} specifies that the output should be Price, Lambda, and Rho, in that order. To invoke from a function: [Price, Lambda, Rho] = supersharesensbybls(..., 'OutSpec', {'Price', 'Lamba', 'Rho'}) OutSpec = {'All'} specifies that the output should be Delta, Gamma, Vega, Lambda, Rho, Theta, and Price, in that order. This is the same as specifying OutSpec as OutSpec = {'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', 'Price'};. Default is OutSpec = {'Price'}.

Description

PriceSens = supersharesensbybls(RateSpec, StockSpec, Settle, Maturity, StrikeLow, StrikeHigh) computes supershare option prices using the Black-Scholes option pricing model.

PriceSens = supersharesensbybls(RateSpec, StockSpec, Settle, Maturity, StrikeLow, StrikeHigh, OutSpec) includes an OutSpec argument defined as parameter/value pairs, and computes supershare option prices and sensitivities using the Black-Scholes option pricing model.

PriceSens is a NINST-by-1 vector of expected option prices and sensitivities.

Examples

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.

Create the RateSpec:

Settle = 'Nov-1-2008';
Maturity = 'Feb-1-2009';
Rates = 0.045;
Basis = 1;
Compounding = -1;
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

See Also

supersharebybls

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