Compute American call and put option prices using a binomial tree.
- Variable: Price The current price of the underlying asset.
- Variable: Strike The strike price the option is written on.
- Variable: Rate The risk-free interest rate.
- Variable: Time The time-to-expiry.
- Variable: Increment Time increment. Increment is rounded to
ensure that Time/Increment is an integer.
- Variable: Volatility The volatility of the underlying asset.
- Variable: OptType Option type. 1 = call option, 0 = put option.
- Variable: DividendRate (Optional, default = 0) Annualized, continuously
compounded rate of dividends of the underlying asset.
- Variable: Dividend (Optional, default = 0) The dividend payment at an
ex-dividend date as specified by ExDiv.
- Variable: ExDiv (Optional, default = 0) A vector used to determine the
ex-dividend dates. For each j, ExDiv(j) * Increment is the
corresponding dividend date.
Computes the American call and put option prices using the
Cox-Ross-Rubinstein binomial tree.
Discrete dividends (i.e. Dividend and ExDiv) have not yet been
implemented.
Binomial trees are a particular explicit finite difference method for solving
the Black-Scholes equation (see
M. Rubinstein. On the relation between binomial and trinomial option
pricing models. Journal of Derivatives, 8(2):47-50, 2000),
and exhibit linear convergence along with the usual strict stability
requirements of an explicit method.
The serious practitioner should consider using a more
sophisticated method, and use binomial trees only for explanatory or
heuristic purposes.
See also: blkprice, blsprice.