American Standard Options (OTC)
Use
American standard options are valued according to the binomial process.
Integration / Calculation Basis
The price calculator for American standard options uses the following parameters:
Term: |
Remainder of the option term in days |
Dom-rate: |
Interest rate 1 as a percentage |
For-rate: |
Interest rate 2 as a percentage |
Spot: |
Spot |
Strike: |
Strike |
Steps: |
Number of steps in the binomial tree |
Type UL: |
Type of underlying |
Vola: |
Volatility |
Put/Call: |
Put/call option indicator |
Scope of Functions / Valuation
If the expiration date of the option is reached, the inner value of the option is displayed (the difference between the spot and strike).
If the option term has not expired, the price is calculated as follows:
Starting from the bottom node, the exercise value and the holding value of the option are calculated backwards, for each node. The larger of the two is the option price at each node. A node value results from the total of the previous node values, weighted according to the likelihood of its 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 valueij =
(Price of the larger predecessor * Probability of upward movement+
Price of the smaller predecessor * Probability of a downward movement ) * Discount factor for one time step
= (Pi+1,j * prob + P i+1,j+1 * ( 1 - prob ) ) * disc
Exercise valueij =
Underlying price at time point i - Strike
= spot * exp( uplog * ( 2 * i - j ) ) - strike
Pij = Max(Exercise value ij | Holding value ij )
P01 = Price of the option
The price of an American option is calculated as the mean from the price of the given number of time steps and the price of one more time step, since the price for an even number of time steps converges towards the right price from above and that for an odd number of time steps with an increasing number of steps converges from below.