AmericanBinomCall_Greeks#

Purpose#

Computes Delta, Gamma, Theta, Vega, and Rho for American call options using the binomial method.

Format#

{ d, g, t, v, rh } = AmericanBinomCall_Greeks(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:
• d (Mx1 vector) – delta.

• g (Mx1 vector) – gamma.

• t (Mx1 vector) – theta.

• v (Mx1 vector) – vega.

• rh (Mx1 vector) – rho.

Global Input#

_fin_thetaType#

scalar, if 1, one day look ahead, else, infinitesmal. Default = 0.

_fin_epsilon#

scalar, finite difference stepsize. Default = 1e-8.

Examples#

S0 = 305;
K = 300;
r = .08;
sigma = .25;
tau = .33;
div = 0;

{ d, g, t, v, rh } = AmericanBinomCall_Greeks(S0, K, r, 0, tau, sigma, 30);

print d;g;t;v;rh;

produces:

0.66998622
-7.6381912e-16
-14.399673
65.170395
56.676624

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.

finprocs.src