Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

 Quantlet: HestonVanillaFitSmile Description: fits the Heston model to the FX market implied volatility smile.

Reference(s):
[1] R. Weron, U. Wystup (2005) Heston's model and the smile, in "Statistical Tools for Finance and Insurance", eds. P. Cizek, W. Härdle, R. Weron, Springer.

 Usage: {v0,vv,kappa,theta,rho,IV,SSE} = HestonVanillaFitSmile(delta,marketvols,spot,rd,rf,tau,phi) Input: delta n x 1 vector, delta pillars marketvols n x 1 vector, market implied volatilities spot scalar, spot price rd scalar, domestic interest rate rf scalar, foreign interest rate tau scalar, maturity (in years) phi scalar, phi = 1 - call option, phi = -1 - put option Output: v0 scalar, initial volatility vv scalar, vol of vol kappa scalar, mean reversion theta scalar, long-run mean rho scalar, correlation IV n x 1 vector, implied volatilities assuming the Garman-Kohlhagen model SSE scalar, sum of squared errors

Example:
```library("finance")
;Marketvols July 1, 2004
delta         = #(0.1,     0.25,    0.5,    0.75,    0.9)
Marketvols  = #(0.106,   0.1015,  0.1005, 0.1025,  0.107)
;interest rates July 1, 2004
Rd  = 0.02055
Rf  = 0.01305
Tau = 7/365
Spot = 1.215 ; spot on July 1, 2004
Phi = 1      ; call option
fit = HestonVanillaFitSmile(delta,Marketvols,Spot,Rd,Rf,Tau,Phi)
fit

```
Result:
```Contents of fit.v0
[1,]   0.0101
Contents of fit.vv
[1,]  0.0087383
Contents of fit.kappa
[1,]      1.5
Contents of fit.theta
[1,]  0.14094
Contents of fit.rho
[1,] -0.025377
Contents of fit.IV
[1,]  0.11621
[2,]  0.098227
[3,]  0.095177
[4,]  0.098164
[5,]  0.11617
Contents of fit.SSE
[1,]  0.00024612
```

Author: R. Weron, 20040403 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006