EuropeanBinomCall_ImpVol#

Purpose#

Computes implied volatilities for European call options using binomial method.

Format#

sigma = EuropeanBinomCall_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#

// Call  premiums
c = { 13.70, 11.90, 9.10 };

// Specify current price
S0 = 718.46;

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

// Specify risk free rate
r = .0368;

// Specify dividend
div = 0;

// Specify start and end dates
t_start = dtday(2012, 1, 30);
t_end = dtday(2012, 2, 16);

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

// Compute implied volatility
sigma = EuropeanBinomCall_ImpVol(c, S0, K, r, div, tau, 30);
print sigma;

produces:

2027
2081
1989

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