EuropeanBinomCall_Greeks#

Purpose#

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

Format#

{ d, g, t, v, rh } = EuropeanBinomCall_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#

// Specify current price
S0 = 305;

// Specify strike prices
K = 300;

// Specify risk free rate
r = .08;

// Specify volatility
sigma = .25;

// Specify elapsed time to exercise
tau = .33;

// Specify continuous dividend yield
div = 0;

print EuropeanBinomcall_Greeks(S0, K, r, div, tau, sigma, 30);

produces:

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