| Library: | finance |
| See also: | HestonVanilla ImplVolaFX |
| Quantlet: | HestonVanillaSmile | |
| Description: | determines the volatility smile implied by the Heston model. |
| Usage: | smile = HestonVanillaSmile(phi,spot,strikes,v0,vv,rd,rf,tau,kappa,theta,lambda,rho,GL) | |
| Input: | ||
| phi | scalar, phi = 1 - call option, phi = -1 - put option | |
| spot | scalar, spot price | |
| strikes | n x 1 vector, strikes | |
| v0 | scalar, initial volatility | |
| vv | scalar, vol of vol | |
| rd | scalar, domestic interest rate | |
| rf | scalar, foreign interest rate | |
| tau | scalar, maturity (in years) | |
| kappa | scalar, mean reversion | |
| theta | scalar, long-run mean | |
| lambda | scalar, market price of risk | |
| rho | scalar, correlation | |
| GL | vector, Gauss-Legendre quadrature (e.g. as obtained using GaussLegendre) | |
| Output: | ||
| smile | vector (n x 1), volatility smile | |
library("finance")
delta = #(.1,.2,.3,.4,.5,.6,.7,.8,.9)
marketvols = #(0.1135, 0.109, 0.10425, 0.1025, 0.102, 0.103, 0.10575, 0.1105, 0.1165)
spot = 1.215 ; spot on July 1, 2004
rd = 0.02165
rf = 0.01845
tau = 0.5
phi = 1 ; call option
strikes = GarmanKohlhagen(spot,delta,marketvols,rd,rf,tau,phi,20)
GL = GaussLegendre(0,100,100,1e-14)
v0 = 0.01
vv = 0.25
kappa = 1.5
theta = 0.015
rho = 0.05
lambda = 0
smile=HestonVanillaSmile(phi,spot,strikes,v0,vv,rd,rf,tau,kappa,theta,lambda,rho,GL)
smile
Contents of smile [1,] 0.11361 [2,] 0.10754 [3,] 0.10404 [4,] 0.10209 [5,] 0.10114 [6,] 0.10111 [7,] 0.10214 [8,] 0.10475 [9,] 0.1104