Risk-neutralize simulations

Contents:

• 0 - Install ahead

• 1 - Get and transform data

• 2 - Risk-neutralize simulations

• 3 - Visualization

0 - Install ahead

ahead is released under the BSD Clear license. Here’s how to install the R version of the package:

• 1st method: from R-universe

  In R console:

  options(repos = c(
      techtonique = 'https://techtonique.r-universe.dev',
      CRAN = 'https://cloud.r-project.org'))
  
  install.packages("ahead")

• 2nd method: from Github

  In R console:

  devtools::install_github("Techtonique/ahead")

  Or

  remotes::install_github("Techtonique/ahead")

Using ahead:

library(ahead)
library(fpp)

1 - Get and transform data

data(EuStockMarkets)

EuStocks <- ts(EuStockMarkets[1:100, ], 
               start = start(EuStockMarkets),
               frequency = frequency(EuStockMarkets))

EuStocksLogReturns <- ahead::getreturns(EuStocks, type = "log")

print(head(EuStocksLogReturns))

##               DAX          SMI          CAC         FTSE
## [1,] -0.009326550  0.006178360 -0.012658756  0.006770286
## [2,] -0.004422175 -0.005880448 -0.018740638 -0.004889587
## [3,]  0.009003794  0.003271184 -0.005779182  0.009027020
## [4,] -0.001778217  0.001483372  0.008743353  0.005771847
## [5,] -0.004676712 -0.008933417 -0.005120160 -0.007230164
## [6,]  0.012427042  0.006737244  0.011714353  0.008517217

2 - Risk-neutralize simulations

2 - 1 Yield to maturities (fake risk-free rates)

ym <- c(0.03013425, 0.03026776, 0.03040053, 0.03053258, 0.03066390, 0.03079450, 0.03092437)

freq <- frequency(EuStocksLogReturns)
(start_preds <- tsp(EuStocksLogReturns)[2] + 1 / freq)

## [1] 1991.881

(ym <- stats::ts(ym,
                 start = start_preds,
                 frequency = frequency(EuStocksLogReturns)))

## Time Series:
## Start = c(1991, 230) 
## End = c(1991, 236) 
## Frequency = 260 
## [1] 0.03013425 0.03026776 0.03040053 0.03053258 0.03066390 0.03079450 0.03092437

2 - 2 Risk-neutralized simulations

obj <- ahead::ridge2f(EuStocksLogReturns, h = 7L,
                      type_pi = 'bootstrap',
                      B = 10L, ym = ym)

## 
  |                                                                            
  |                                                                      |   0%
  |                                                                            
  |=======                                                               |  10%
  |                                                                            
  |==============                                                        |  20%
  |                                                                            
  |=====================                                                 |  30%
  |                                                                            
  |============================                                          |  40%
  |                                                                            
  |===================================                                   |  50%
  |                                                                            
  |==========================================                            |  60%
  |                                                                            
  |=================================================                     |  70%
  |                                                                            
  |========================================================              |  80%
  |                                                                            
  |===============================================================       |  90%
  |                                                                            
  |======================================================================| 100%

rowMeans(obj$neutralized_sims$CAC)

## [1] 0.03013425 0.03026776 0.03040053 0.03053258 0.03066390 0.03079450 0.03092437

print(ym)

## Time Series:
## Start = c(1991, 230) 
## End = c(1991, 236) 
## Frequency = 260 
## [1] 0.03013425 0.03026776 0.03040053 0.03053258 0.03066390 0.03079450 0.03092437

rowMeans(obj$neutralized_sims$DAX)

## [1] 0.03013425 0.03026776 0.03040053 0.03053258 0.03066390 0.03079450 0.03092437

print(ym)

## Time Series:
## Start = c(1991, 230) 
## End = c(1991, 236) 
## Frequency = 260 
## [1] 0.03013425 0.03026776 0.03040053 0.03053258 0.03066390 0.03079450 0.03092437

3 - Visualization

#par(mfrow = c(2, 2))

matplot(EuStocksLogReturns, type = 'l', 
     main = "Historical log-Returns", xlab = "time")

plot(ym, main = "fake spot curve", 
     xlab = "time to maturity",
     ylab = "yield", 
     ylim = c(0.02, 0.04))

matplot(obj$neutralized_sims$DAX, type = 'l', 
     main = "simulations of \n predicted DAX log-returns ('risk-neutral')", 
     ylim = c(0.02, 0.04), 
     ylab = "log-returns")

ci <- apply(obj$neutralized_sims$DAX, 1, function(x) t.test(x)$conf.int)
plot(rowMeans(obj$neutralized_sims$DAX), type = 'l', main = "average predicted \n DAX log-returns ('risk-neutral')", col = "blue", 
     ylim = c(0.02, 0.04), 
     ylab = "log-returns")
lines(ci[1, ], col = "red")
lines(ci[2, ], col = "red")