parsiad / AmericanBinary

Code for pricing American binary (a.k.a. digital) calls and puts

AmericanBinary

AmericanBinary computes the value of American binary (a.k.a. digital) calls and puts.

AmericanBinary is written by Parsiad Azimzadeh and released under a BSD 2-clause license.

Methodology

We assume that the asset follows a geometric Brownian motion:

dS = (Rate - Yield) dt + Volatility dW

An American binary call is an option which can be exercised at any time, having an exercise value 1 if S > Strike and exercise value 0 otherwise. An American binary put is defined similarly.

The derivation of the closed-form expression for the value of the American binary call and put are here.

Usage

[Call, Put] = AmericanBinary(Price, Strike, Rate, Time, Volatility, Yield)

• Price: The initial value of the asset S
• Strike: The strike price
• Rate: The risk-free interest rate
• Time: The expiry time (use Inf for a perpetual option)
• Volatility: The volatility of the asset S
• Yield: The dividend rate of the asset S
• Call: The value of the call
• Put: The value of the put

The function, similar to blsprice, accepts vector/matrix arguments.

Example

Strike     = 100.;
Price      = 0 : 1 : Strike * 2;
Rate       = 0.04;
Time       = 1.;
Volatility = 0.2;
Yield      = 0.01;

[Call, Put] = AmericanBinary(Price, Strike, Rate, Time, Volatility, Yield);

plot(Price, Put, 'linewidth', 2);
xlabel('Asset price');
ylabel('Option value');
title('American binary put');