chooserbybls

Price European simple chooser options using Black-Scholes model

Syntax

Price = chooserbybls(RateSpec,StockSpec,Settle,Maturity,Strike,ChooseDate)

Description

Price = chooserbybls(RateSpec,StockSpec,Settle,Maturity,Strike,ChooseDate) computes the price for European simple chooser options using the Black-Scholes model.

Examples

Price European Simple Chooser Options Using the Black-Scholes Model

Consider a European chooser option with an exercise price of $60 on June 1, 2007. The option expires on December 2, 2007. Assume the underlying stock provides a continuous dividend yield of 5% per annum, is trading at $50, and has a volatility of 20% per annum. The annualized continuously compounded risk-free rate is 10% per annum. Assume that the choice must be made on August 31, 2007. Using this data:

AssetPrice = 50;
Strike = 60;
Settlement = 'Jun-1-2007';
Maturity = 'Dec-2-2007'; 
ChooseDate = 'Aug-31-2007';
RiskFreeRate = 0.1;
Sigma = 0.20;
Yield = 0.05

Yield = 0.0500

Define the RateSpec and StockSpec.

RateSpec = intenvset('Compounding', -1, 'Rates', RiskFreeRate, 'StartDates',...
Settlement, 'EndDates', Maturity);
StockSpec = stockspec(Sigma, AssetPrice,'continuous',Yield);

Price the chooser option.

Price  = chooserbybls(RateSpec, StockSpec, Settlement, Maturity,...
Strike, ChooseDate)

Price = 8.9308

Input Arguments

RateSpec — Annualized zero rate term structure

structure

Annualized zero rate term structure, 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 underlying asset, specified using StockSpec obtained from stockspec. For information on the stock specification, see stockspec.

stockspec can handle other types of underlying assets. For example, stocks, stock indices, and commodities. If dividends are not specified in StockSpec, dividends are assumed to be 0.

Note

Only dividends of type continuous can be considered for choosers.

Data Types: struct

Settle — Settlement or trade dates

serial date numbers | cell array of character vectors

Settlement or trade dates, specified using an NINST-by-1 vector of serial date numbers or a cell array of date character vectors. Settle must be earlier than Maturity.

Data Types: double | char | cell

Maturity — Maturity date

serial date numbers | cell array of character vectors

Maturity date, specified as an NINST-by-1 vector using serial date numbers or a cell array of date character vectors.

Data Types: double | char | cell

Strike — Option strike price value

nonnegative integer

Option strike price value, specified with a NINST-by-1 vector of nonnegative integers.

Data Types: double

ChooseDate — Chooser dates

serial date numbers | cell array of character vectors

Choose dates, specified with a NINST-by-1 vector of serial date numbers or cell array of date character vectors.

Data Types: double | char | cell

Output Arguments

Price — Expected prices

vector

Expected prices, returned as an NINST-by-1 vector.

References

[1] Rubinstein, Mark. "Options for the Undecided." Risk. Vol 4, 1991.