# AmericanBinomPut_Greeks#

## Purpose#

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

## Format#

{ d, g, t, v, rh } = AmericanBinomPut_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;
div = 0;
sigma = .25;
tau = .33;

print AmericanBinomPut_Greeks(S0, K, r, 0, tau, sigma, 60);
```

produces

``` -0.37483952
0.0031359210
0.99863719
65.800721
-31.075062
```

## 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