AmericanBSCall_ImpVol

Purpose

Computes implied volatilities for American call options using the Black, Scholes, and Merton method.

Format

sigma = AmericanBSCall_ImpVol(c, S0, K, r, div, tau)

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.

Returns:

sigma (Mx1 vector) – volatility.

Examples

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

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

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

produces:

0.19724517
0.20503722
0.19375031

Source

finprocs.src