---
title: "Read Me"
output:
html_document: default
html_notebook: default
pdf_document: default
---
```{r include=FALSE, cache = FALSE}
library(dplyr)
library(ggplot2)
source('svi_h.R')
```
Quasi-explicit calibration of the modified SVI model. The optimization method follows Martini & Marco (2009), with some modificiation.
The modified SVI function is:
$$ v(x) = [a + b(\rho(x-m)+\sqrt{(x-m)^2 + \sigma^2})]^H
$$
Given that the function has 6 parameters, and many local minimums, two-step quasi-explicit calibration method has some advantages to find global optimal parameters.
Read a sample chain (iv.csv, $\tau = 0.12$ ), and fit with the two-step optimization.
```{r}
# read one sample ivs at tau = 0.12
tau = 0.12
c <- read.csv('iv.csv')
# measure estimation time
ptm <- proc.time()
param <- fit_ga_svi(c$k,c$iv,tau)
#show how long it takes for estimate the parameters
print(proc.time()-ptm)
ptm <- proc.time()
param <- fit_svih(c$k,c$iv,tau, 0.95)
#show how long it takes for estimate the parameters
print(proc.time()-ptm)
print(param)
```
```{r}
# SVI parameterized IV estimation
c$svi <- svi_fun(c$k,as.numeric(param[1,2:7]))/sqrt(tau)
# plot fitting results
ggplot(c, aes(x = k, y = iv)) + geom_point() +
geom_line(aes(y = svi), color = 'red')
```
```{r}
c$err = c$iv - c$svi
ggplot(c, aes(x = k, y = err)) + geom_point()
print(sd(c$err))
```
Using `par_fit_svi` function, one can fit the whole surface with paralell computation. An example is shown below:
```{r}
# read a chain
library(parallel)
c2 <- read.csv('chain.csv')
# suppose now H = 0.65. This can be done by using genetic algo
ptm <- proc.time()
para <- par_fit_svi(c2, 0.65)
print(proc.time()-ptm)
print(para)
```