optstockbybjs

Price American options using Bjerksund-Stensland 2002 option pricing model

Syntax

Price = optstockbybjs(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike)

Description

Price = optstockbybjs(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike) computes American option prices with continuous dividend yield using the Bjerksund-Stensland 2002 option pricing model.

Note

Alternatively, you can use the Vanilla object to price vanilla options. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

Examples

Compute the American Option Prices With Continuous Dividend Yield Using the Bjerksund-Stensland 2002 Option Pricing Model

This example shows how to compute the American option prices with continuous dividend yield using the Bjerksund-Stensland 2002 option pricing model. Consider two American stock options (a call and a put) with an exercise price of $100. The options expire on April 1, 2008. Assume the underlying stock pays a continuous dividend yield of 4% as of January 1, 2008. The stock has a volatility of 20% per annum and the annualized continuously compounded risk-free rate is 8% per annum. Using this data, calculate the price of the American call and put, assuming the following current prices of the stock: $90 (for the call) and $120 (for the put).

Settle = datetime(2008,1,1);
Maturity = datetime(2008,4,1);
Strike = 100;
AssetPrice = [90;120];
DivYield = 0.04;
Rate = 0.08;
Sigma = 0.20;

% define the RateSpec and StockSpec
StockSpec = stockspec(Sigma, AssetPrice, {'continuous'}, DivYield);

RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,...
'EndDates', Maturity, 'Rates', Rate, 'Compounding', -1);

% define the option type
OptSpec = {'call'; 'put'};

Price = optstockbybjs(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike)

Price = 2×1

    0.8420
    0.1108

The first element of the Price vector represents the price of the call ($0.84); the second element represents the price of the put option ($0.11).

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, specified as a NINST-by-1 vector using a datetime array, string array, or date character vectors.

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

Maturity — Maturity date for option

datetime array | string array | date character vector

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

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

OptSpec — Definition of option

cell array of character vectors with values 'call' or 'put'

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

Data Types: char | cell

Strike — Option strike price value

nonnegative vector

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

Data Types: double

Output Arguments

Price — Expected option prices

vector

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

Data Types: double

More About

Vanilla Option

A vanilla option is a category of options that includes only the most standard components.

A vanilla option has an expiration date and straightforward 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: $$\max (St-K,0)$$

• For a put: $$\max (K-St,0)$$

where:

St is the price of the underlying asset at time t.

K is the strike price.

For more information, see Vanilla 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

R2022b: Serial date numbers not recommended

Although optstockbybjs 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.