AmericanBinomCall#

Purpose#

Prices American call options using the binomial method.

Format#

c = AmericanBinomCall(S0, K, r, div, tau, sigma, N)#
Parameters:

  • S0 (Scalar) – Current price.

  • K (Mx1 vector) – Strike prices.

  • r (Scalar) – Risk free rate.

  • div (Scalar) – Continuous dividend yield.

  • tau (Scalar) – Elapsed time to exercise in annualized days of trading.

  • sigma (Scalar) – Volatility.

  • N (Scalar) – The number of time segments. A higher number of segments will increase accuracy at the cost of computation time.

Returns:

c (Mx1 vector) – Call premiums.

Examples#

S0 = 718.46;
K = { 720, 725, 730 };
r = .0498;
sigma = .2493;

t0 = dtday(2001, 1, 30);
t1 = dtday(2001, 2, 16);
tau = elapsedTradingDays(t0, t1) /
    annualTradingDays(2001);

c = AmericanBinomCall(S0, K, r, 0, tau, sigma, 60);
print c;

produces the output:

17.246407
14.973715
12.745272

Remarks#

The binomial method of Cox, Ross, and Rubinstein (“Option pricing: a simplified approach,” Journal of Financial Economics, 7:229:264) as described in Options, Futures, and other Derivatives by John C. Hull is the basis of this procedure.

Source#

finprocs.src

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