AmericanBinomCall_ImpVol#

Purpose#

Computes implied volatilities for American call options using the binomial method.

Format#

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

  • c (Mx1 vector) – call premiums

  • 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.

  • N (scalar) – number of time segments. A higher number of time segments will increase accuracy at the expense of increased computation time.

Returns:

sigma (Mx1 vector) – volatility.

Examples#

c = { 13.70, 11.90, 9.10 };
S0 = 718.46;
K = { 720, 725, 730 };
r = .0498;
div = 0;

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

sigma = AmericanBinomCall_ImpVol(c, S0, K, r, 0, tau, 30);
print sigma;

produces:

0.19746150
0.20337431
0.19472673

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.

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