AmericanBinomCall_Greeks ============================================== Purpose ---------------- Computes Delta, Gamma, Theta, Vega, and Rho for American call options using the binomial method. Format ---------------- .. function:: { d, g, t, v, rh } = AmericanBinomCall_Greeks(S0, K, r, div, tau, sigma, N) :param S0: current price. :type S0: scalar :param K: strike prices. :type K: Mx1 vector :param r: risk free rate. :type r: scalar :param div: continuous dividend yield. :type div: scalar :param tau: elapsed time to exercise in annualized days of trading. :type tau: scalar :param sigma: volatility. :type sigma: scalar :param N: number of time segments. A higher number of time segments will increase accuracy at the expense of increased computation time. :type N: scalar :return d: delta. :rtype d: Mx1 vector :return g: gamma. :rtype g: Mx1 vector :return t: theta. :rtype t: Mx1 vector :return v: vega. :rtype v: Mx1 vector :return rh: rho. :rtype rh: Mx1 vector Global Input ------------ .. data:: \_fin_thetaType *scalar*, if 1, one day look ahead, else, infinitesmal. Default = 0. .. data:: \_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. Source -------------- finprocs.src .. seealso:: Functions :func:`AmericanBinomCall_ImpVol`, :func:`AmericanBinomCall`, :func:`AmericanBinomPut_Greeks`, :func:`AmericanBSCall_Greeks`