| Library: | finance |
| See also: | optstart influence |
| Quantlet: | greeks | |
| Description: | calculates or displays the different sensitivities (the so called greeks) which are used for trading with options. |
| Usage: | dat=greeks() or dat=greeks(S,K,r,sigma,tau,carry,opt,pder{,v1,ub1{,v2,ub2}}) | |
| Input: | ||
| S | price of the underlying asset, see the notes for further information about the dimension of all parameters | |
| K | exercise price | |
| r | domestic interest rate in the interval: [0%, 100%] | |
| sigma | volatility per year which can be found in the following interval (0%,100%) | |
| tau | time to expiration (in years) | |
| carry | cost of carry in percent of the value of the underlying object (0%, 100%) | |
| opt | type of the option, if opt = 1, a call is assumed, opt = 0, a put is considered | |
| pder | scalar, determines which partial derivative should be computed: 1 for delta, 2 for gamma, 3 for eta, 4 for delta-k, 5 for vega, 6 for theta, 7 for rho, 8 for rho-b | |
| v1 | scalar, explanatory variable for the a 2- or 3-dimensional plot: 1 for S, 2 for K , 3 for r, 4 for sigma, 5 for tau, 6 for carry. If not specified, no plot will be displayed. | |
| ub1 | upper bound for the chosen explanatory variable v1. The lower bound represents the already specified value (S,K,r,sigma,tau or carry). | |
| v2 | scalar, second explanatory variable for the 3-dimensional plot. | |
| ub2 | upper bound for the second explanatory variable v2. | |
| Output: | ||
| dat | the computed values of greeks at the specified points | |
2) The greeks are in particular: "delta" (partial derivative (p.d.) of the BS option pricing formula with respect to (w.r.t.) the price of the underlying asset S), "gamma" (2 x p.d. w.r.t. S), "eta" (delta x S / option price), "delta-K" (p.d. w.r.t. exercise price K), "vega" (p.d. w.r.t. the volatility of the asset), "theta" (p.d. w.r.t. time to expiration), "rho" (p.d. w.r.t. domestic interest rate) and "rho-b" (p.d. w.r.t. costs of carry).
3) The interest rate and the cost of carry are used as continuous rates (log(0.01*r + 1) resp. log(0.01*carry + 1)) in the algorithm.
4) If the plot should be depicted (at least v1 is specified), all obligatory input parameters (i.e., S, K, r, sigma, tau, carry, opt and pder) must be scalars. If the parameters v2 and ub2 are specified, a three-dimensional plot will be shown. The given greeks are computed (and depicted afterwards) in the interval (upper bound - lower bound), which is divided into 30 equally spaced parts. The output "dat" has two or three columns - the first column contains the values of the first specified variable v1, the second column the values of the second variable v2 (if specified) and the last column consists of the computed values of the given greek in these specified points.
5) If only a text output is desired (v1 is not specified), the obligatory inputs can be generally n x 1 vectors. Scalars will be expanded automatically into vectors of the length n. The output is a (n x 9) matrix. The first 8 columns correspond to 8 input variables and the last column contains the computed greeks.
library("finance")
dat = greeks()
Opens several interactive menus where you are asked to specify the option features and your variables of interest. According to your choice a two or three dimensional graph displays the sensitivities.
library("finance")
S = 230 ; spot price
K = 210 ; strike price
r = 5 ; interest rate
sigma = 25 ; volatility
tau = 0.5 ; time to expiration
carry = 5 ; cost of carry
opt = 0 ; put
pder = 3 ; eta
v1 = 4 ; volatility
ub1 = 40
v2 = 3 ; interest rate
ub2 = 10
g2=greeks(S,K,r,sigma,tau,carry,opt,pder,v1,ub1,v2,ub2)
g2[1:10,] ; the first ten values of eta can be found
; in the last column
Contents of _tmp [ 1,] 0.25 0.04879 -14.699 [ 2,] 0.255 0.04879 -14.273 [ 3,] 0.26 0.04879 -13.872 [ 4,] 0.265 0.04879 -13.495 [ 5,] 0.27 0.04879 -13.14 [ 6,] 0.275 0.04879 -12.804 [ 7,] 0.28 0.04879 -12.487 [ 8,] 0.285 0.04879 -12.186 [ 9,] 0.29 0.04879 -11.9 [10,] 0.295 0.04879 -11.629 The first column contains different values of volatility, the second column consists of one value only, which corresponds to the continuous interest rate of 5% (other values of the interest rate are in the following rows). The third column contains the corresponding values of eta at the specified points. A three-dimensional plot, the eta-surface of the specified European put option, is depicted as well.
library("finance")
S = aseq(150,16,10)
K = aseq(150,16,15)
r = 10
sigma = aseq(5, 16,2)
tau = 5:20
carry = 5:20
opt =(matrix(8)|0*matrix(8))
pder =(1:8|1:8)
greeks(S,K,r,sigma,tau,carry,opt,pder)
Contents of dat [ 1,] 150 150 10 5 5 5 1 1 0.77547 [ 2,] 160 165 10 7 6 6 1 2 0.0068436 [ 3,] 170 180 10 9 7 7 1 3 2.3355 [ 4,] 180 195 10 11 8 8 1 4 -0.18682 [ 5,] 190 210 10 13 9 9 1 5 203.47 [ 6,] 200 225 10 15 10 10 1 6 3.0756 [ 7,] 210 240 10 17 11 11 1 7 96.214 [ 8,] 220 255 10 19 12 12 1 8 619.08 [ 9,] 230 270 10 21 13 13 0 1 -1.2112 [10,] 240 285 10 23 14 14 0 2 0.0015297 [11,] 250 300 10 25 15 15 0 3 1.1903 [12,] 260 315 10 27 16 16 0 4 0.21657 [13,] 270 330 10 29 17 17 0 5 328.81 [14,] 280 345 10 31 18 18 0 6 -69.859 [15,] 290 360 10 33 19 19 0 7 -1117.9 [16,] 300 375 10 35 20 20 0 8 -33480