EuropeanBinomCall#

Purpose#

Prices European call options using binomial method.

Format#

c = EuropeanBinomCall(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) – number of time segments. A higher number of time segments will increase accuracy at the expense of increased computation time.

Returns:

c (Mx1 vector) – call premiums.

Examples#

// Specify current price
S0 = 718.46;

// Specify strike prices
K = { 720, 725, 730 };

// Specify risk free rate
r = .0498;

// Specify volatility
sigma = .2493;

// Specify start and end dates
t_start = dtday(2001, 1, 30);
t_end = dtday(2001, 2, 16);

// Find annualize elapsed trading days
tau = elapsedTradingDays(t_start, t_end) /
    annualTradingDays(2012);

// Compute call premiums
c = EuropeanBinomCall(S0, K, r, 0, tau, sigma, 60);
print c;

produces:

17.1325
14.8599
12.6383

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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