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optstocksensbybjs

Determine American option prices or sensitivities using Bjerksund-Stensland 2002 option pricing model

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Syntax

PriceSens = optstocksensbybjs(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike)
PriceSens = optstocksensbybjs(___，Name,Value)

Description

example

PriceSens= optstocksensbybjs(RateSpec，StockSpec，Settle，Maturity，OptSpec，Strike)computes American option prices or sensitivities using the Bjerksund-Stensland 2002 option pricing model.

Note

optstocksensbybjscomputes prices of American options with continuous dividend yield using the Bjerksund-Stensland option pricing model. All sensitivities are evaluated by computing a discrete approximation of the partial derivative. This means that the option is revalued with a fractional change for each relevant parameter, and the change in the option value divided by the increment, is the approximated sensitivity value.

PriceSens= optstocksensbybjs(___，Name,Value)adds an optional name-value pair argument forOutSpec.

Examples

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Open Live Script

This example shows how to compute American option prices and sensitivities using the Bjerksund-Stensland 2002 option pricing model. Consider four American put options with an exercise price of $100. The options expire on October 1, 2008. Assume the underlying stock pays a continuous dividend yield of 4% and has a volatility of 40% per annum. The annualized continuously compounded risk-free rate is 8% per annum. Using this data, calculate thedelta，gamma，and价格of the American put options, assuming the following current prices of the stock on July 1, 2008: $90, $100, $110 and $120.

Settle ='July-1-2008'; Maturity ='October-1-2008'; Strike = 100; AssetPrice = [90;100;110;120]; Rate = 0.08; Sigma = 0.40; DivYield = 0.04;% define the RateSpec and StockSpecStockSpec = stockspec(Sigma, AssetPrice, {'continuous'}, DivYield); RateSpec = intenvset('ValuationDate'，Settle,'StartDates'，Settle,...'EndDates'，Maturity,'Rates'，Rate,'Compounding'，-1);% define the option typeOptSpec = {'put'}; OutSpec = {'Delta'，'Gamma'，'Price'}; [Delta, Gamma, Price] = optstocksensbybjs(RateSpec, StockSpec, Settle, Maturity,...OptSpec, Strike,'OutSpec'，OutSpec)
Delta =4×1-0.6572 -0.4434 -0.2660 -0.1442
Gamma =4×10.0217 0.0202 0.0150 0.0095
Price =4×112.9467 7.4571 3.9539 1.9495

Input Arguments

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Interest-rate term structure (annualized and continuously compounded), specified by theRateSpecobtained fromintenvset. For information on the interest-rate specification, seeintenvset.

Data Types:struct

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

stockspechandles several types of underlying assets. For example, for physical commodities the price isStockSpec.Asset，the volatility isStockSpec.Sigma，and the convenience yield isStockSpec.DividendAmounts.

Data Types:struct

Settlement or trade date, specified as serial date number or date character vector using aNINST-by-1vector.

Data Types:double|char

Maturity date for option, specified as serial date number or date character vector using aNINST-by-1vector.

Data Types:double|char

Definition of the option as'call'or'put'，specified as aNINST-by-1cell array of character vectors with values'call'or'put'.

Data Types:char|cell

Option strike price value, specified as a nonnegativeNINST-by-1vector.

Data Types:double

Name-Value Arguments

Specify optional pairs of arguments asName1=Value1,...,NameN=ValueN，whereNameis the argument name andValueis 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 encloseNamein quotes.

Example:[Delta,Gamma,Price] = optstocksensbybjs(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,'OutSpec',OutSpec)

Define outputs, specified as the comma-separated pair consisting of'OutSpec'and aNOUT- by-1or1-by-NOUTcell array of character vectors with possible values of'Price'，'Delta'，'Gamma'，'Vega'，'Lambda'，'Rho'，'Theta'，and'All'.

OutSpec = {'All'}specifies that the output should beDelta，Gamma，Vega，Lambda，Rho，Theta，andPrice，in that order. This is the same as specifyingOutSpecto include each sensitivity:

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

Data Types:char|cell

Output Arguments

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Expected future prices or sensitivities values, returned as aNINST-by-1vector.

Data Types:double

More About

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Vanilla Option

Avanilla optionis a category of options that includes only the most standard components.

有一个过期日期和straig香草选择htforward strike price. American-style options and European-style options are both categorized as vanilla options.

The payoff for a vanilla option is as follows:

  • For a call: max ( S t − K ， 0 )

  • For a put: max ( K − S t ， 0 )

where:

Stis the price of the underlying asset at timet.

Kis the strike price.

For more information, seeVanilla Option.

References

[1] Bjerksund, P. and G. Stensland. “Closed-Form Approximation of American Options.”Scandinavian Journal of Management.Vol. 9, 1993, Suppl., pp. S88–S99.

[2] Bjerksund, P. and G. Stensland.“Closed Form Valuation of American Options.”Discussion paper, 2002.

Version History

Introduced in R2008b

See Also

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