Tmp/MertonJumpReturn.R

In AnthonyTedde/StockPriceSimulator: Stock Price Simulator

initial_stock_price = 50
time_to_maturity = .25
seed = i
scale = 365 # Daily measurement
sigma = .2
alpha = 0.03
lambda =  1
jumps_intensity_parameters = list(mean = 0.5,
                                  sd = 0.1)

    set.seed(seed)
    ## Simply the parameters
    mu <- jumps_intensity_parameters$mean
    delta <- jumps_intensity_parameters$sd
    lognormal_mean <- exp(mu  + 1/2 * delta ^2)
    lognormal_sd <- exp(2 * mu + delta ^2) * (exp(delta ^2) - 1)
    k <- lognormal_mean - 1

    ##
    ## Generate the Compounded poisson process along with the jump intensity
    ##

    ## The first step is to define the occurences of the jumps.
    ## rpois function is used to model a poison random distribution with paramter lambda * scale ^-1
    n <- rpois(time_to_maturity * scale, lambda * scale ^ -1)
    N <- c(0, cumsum(n))

    ## Next step is to define the size of each jump depending on the according distribution
    ## y ~ iid normal(mu, delta)
    jump_intensity <- do.call(what = rlnorm, args = c(n = tail(N, 1),
                                                      jumps_intensity_parameters))
    cumulative_jump_intensity <- purrr::map_dbl(N, ~ sum(log(jump_intensity[0:.x])))

    ##################################
    ## Generate the Brownian Motion ##
    ##################################

    bm <- RandomWalk::sbmotion(time_to_maturity = time_to_maturity,
                               scale = scale,
                               seed = seed)
    W <- bm$brownian_motion_path
    t <- bm$time_periods

    ######################################################
    ## Generate the non-random part of the Levy process ##
    ######################################################

    l <- (alpha - sigma ^2 / 2 - lambda * k) * t

    #########################################
    ## Construct the whole Levy process, L ##
    #########################################

    L <- l + sigma * W + cumulative_jump_intensity

    ###############################################
    ## Construct the Stock Price Jumping Process ##
    ###############################################

    data.frame(stock_price_path = initial_stock_price * exp(L),
               time = t,
               grp = as.factor(N))