American standard options are valuated using the binomial procedure.

The price calculator for American standard options has the following parameters:

• Term: Remaining option term in days
• Domrate: Interest rate_1 in percent
• Forrate: Interest rate_2 in percent
• Spot: Spot amount
• Strike: Strike amount
• Steps: Number of steps in binomial tree
• Cat UL: Category of the underlying
• Vola: Volatility
• Put/call: Indicator whether call or put option

If the expiration date of the option is reached, the internal value of the option (difference between spot and strike) is used.

For a positive value for an option, the option price is calculated as follows:

Starting from the root node and working backwards, the exercise value and the holding value of each option is calculated for each node. The greater of the two prices is the option price for each node. The node value is the sum of the previous node values weighted with the probability of occurrence.

lograte = log( 1 + domestic_rate / 100).

logforeign = log( 1 + foreign_rate / 100).

d_time = days / 365 / steps. " time in years per step

disc = 1 / exp( lograte * d_time).

up = exp( vola * sqrt( d_time) / 100).

uplog = log( up).

down = 1 / up

ha = exp( ( lograte - logforeign) * d_time).

prob = ( ha - down) / ( up - down).

Holding value_ij = (Price of largest predecessor * probability of upward movement + price of smaller predecessor * probability of downward movement) * discounting factor for a unit of time

exercise value_ij = price of underlying at time period i - Strike

P_ij = Max(exercise value _ij | holding value _ij)

P₀₁ = price of the option

The price of an American option is calculated as the average value of the price with the prespecified number of time units and the price for one unit more. It has been determined that the price for an even number of time units and the price for an uneven number of time units converge on the correct price from above and below (respectively).