---
title: "More flexibility for simulations"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{More flexibility for simulations}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---


```{r}
library(esgtoolkit)
```

```{r 1-shocks, fig.width=7.2}
# Spot variance
V0 <- 0.1372

# mean-reversion speed
kappa <- 9.5110/100

# long-term variance
theta <- 0.0285

# volatility of volatility
volvol <- 0.8010/100

# Correlation between stoch. vol and prices
rho <- -0.5483

# Intensity of the Poisson process
lambda <- 0.3635

# mean and vol of the merton jumps diffusion
mu_J <- -0.2459
sigma_J <- 0.2547/100
m <- exp(mu_J + 0.5*(sigma_J^2)) - 1

# Initial stock price
S0 <- 4468.17

# Initial short rate
r0 <- 0.0357

# ============================================================================
# SIMULATION SETUP
# ============================================================================

n <- 300
horizon <- 1
freq <- "weekly"

start_ <- start(EuStockMarkets)
end_ <- end(EuStockMarkets)
print(end_ - start_)
freq_ <- frequency(EuStockMarkets)

# Simulation of shocks, with antithetic variates
shocks <- esgtoolkit::simshocks(n = n,
                                horizon = 8L,
                    method = "anti",
                    family = 1, par = rho, 
                    start = start_, frequency=freq_)

print(start_)
print(freq_)
print(end_)
print(start(shocks[[1]]))
print(frequency(shocks[[1]]))
print(end(shocks[[1]]))
```

# ============================================================================
# VOLATILITY SIMULATION (CIR PROCESS)
# ============================================================================

```{r 2-vol, fig.width=7.2}
# Vol simulation
sim_vol <- esgtoolkit::simdiff(n = n, 
                   model = "CIR", x0 = V0,
                   theta1 = kappa*theta, theta2 = kappa,
                   theta3 = volvol,
                   eps = shocks[[1]], 
                   start = start_,
                   frequency=freq_,
                   horizon = 8L)
print(start(sim_vol))
print(frequency(sim_vol))
print(end(sim_vol))
```

# ============================================================================
# ASSET PRICE SIMULATION (GBM WITH JUMPS)
# ============================================================================

```{r 3-price, fig.width=7.2}
# prices simulation
sim_price <- esgtoolkit::simdiff(n = n, start = start_, 
                                 end = end_,
                                 frequency=freq_,
                     horizon = 8L,
                     model = "GBM", x0 = S0,
                     theta1 = r0 - lambda*m, theta2 = sim_vol,
                     lambda = lambda, mu_z = mu_J,
                     sigma_z = sigma_J,
                     eps = shocks[[2]])
print(start(sim_price))
print(frequency(sim_price))
print(end(sim_price))
print(dim(sim_price))
```


```{r 4-plot, fig.width=7.2}
# Plot the simulated price paths
esgtoolkit::esgplotbands(sim_price)
```