Issue #17, increase test coverage

tests/testthat/test-BS_Malliavin_Asian_Greeks.R

@@ -1,15 +1,17 @@
 test_that("BS_Malliavin_Asian_Greeks is correct", {
 
-  # We check the Greeks by also computing the derivative with finite difference
-  # and comparing the results
-
-  number_of_runs <- 2
-
   definition_of_greeks <-
     data.frame(greek = "delta", start = "fair_value", param = "initial_price") %>%
     add_row(greek = "rho", start = "fair_value", param = "r") %>%
     add_row(greek = "vega", start = "fair_value", param = "volatility")
 
+  # We check the Greeks by also computing the derivative with finite difference
+  # and comparing the results
+
+  # We start with checking delta
+
+  number_of_runs <- 10
+
   error <- numeric(number_of_runs)
 
   set.seed(42)
@@ -20,12 +22,79 @@ test_that("BS_Malliavin_Asian_Greeks is correct", {
     initial_price <- runif(1, 90, 110)
     exercise_price <- runif(1, 90, 110)
     r <- runif(1, -0.01, 0.1)
-    time_to_maturity <- runif(1, 0.2, 6)
+    time_to_maturity <- runif(1, 0.2, 2)
     dividend_yield <- runif(1, 0, 0.1)
     volatility <- runif(1, 0.01, 1)
     model <- "Black_Scholes"
-    payoff <- rep(c("call", "put"), 3)[i]
-    greek <- rep(c("delta"), 2)[i]
+    payoff <- rep(c("call", "put"), number_of_runs)[i]
+    greek <- "delta"
+    param <- "initial_price"
+    start <- "fair_value"
+
+    Vals <-
+      BS_Malliavin_Asian_Greeks(
+        initial_price = initial_price,
+        exercise_price = exercise_price,
+        r = r,
+        time_to_maturity = time_to_maturity,
+        volatility = volatility,
+        dividend_yield = dividend_yield,
+        payoff = payoff,
+        greek = greek
+      )
+
+    F <- function(epsilon) {
+      assign(param,
+             c(get(param) + 2*epsilon, get(param) + epsilon,
+               get(param) - 2*epsilon, get(param) - epsilon))
+      BS_Malliavin_Asian_Greeks(
+        initial_price = initial_price,
+        exercise_price = exercise_price,
+        r = r,
+        time_to_maturity = time_to_maturity,
+        volatility = volatility,
+        dividend_yield = dividend_yield,
+        payoff = payoff,
+        greek = start
+      )
+    }
+
+    epsilon <- initial_price * 0.1
+
+    F_eps <- F(epsilon)
+
+    # We compute the derivative by Richardsons' extrapolation
+
+    Vals_fd <- (-F_eps[1] + 8*F_eps[2] - 8*F_eps[3] + F_eps[4]) / (12 * epsilon)
+
+    error[i] <-
+      min(abs(Vals - Vals_fd)/(abs(Vals + epsilon)),
+          abs(Vals - Vals_fd))
+
+  }
+
+  expect(max(error) < 0.1, "BS_Malliavin_Asian_Greeks: Delta error too high")
+
+  # Now, we check rho and vega
+
+  number_of_runs <- 4
+
+  set.seed(42)
+
+  error <- numeric(number_of_runs)
+
+  for(i in 1:number_of_runs) {
+
+    # the parameters are chosen at random
+    initial_price <- runif(1, 90, 110)
+    exercise_price <- runif(1, 90, 110)
+    r <- runif(1, 0.01, 0.1)
+    time_to_maturity <- runif(1, 0.2, 2)
+    dividend_yield <- 0
+    volatility <- runif(1, 0.01, 1)
+    model <- "Black_Scholes"
+    payoff <- rep(c("call", "put"), number_of_runs)[i]
+    greek <- c("rho", "rho", "vega", "vega")[i]
     param <-
       definition_of_greeks[definition_of_greeks$greek == greek, "param"] %>%
       as.character()
@@ -47,11 +116,6 @@ test_that("BS_Malliavin_Asian_Greeks is correct", {
         steps = 12
       )
 
-    ## theta is minus the derivative of fair_value w.r.t. time_to_maturity
-    if (greek == "theta") {
-      Vals = -Vals
-    }
-
     F <- function(epsilon) {
       assign(param, get(param) + epsilon)
       BS_Malliavin_Asian_Greeks(
@@ -72,13 +136,13 @@ test_that("BS_Malliavin_Asian_Greeks is correct", {
 
     Vals_fd <- (F(epsilon) - F(-epsilon)) / (2 * epsilon)
 
-
     error[i] <-
       min(abs(Vals - Vals_fd)/(abs(Vals + epsilon)),
           abs(Vals - Vals_fd))
 
   }
 
-  expect(max(error) < 0.1)
+  expect(max(error) < 0.01,
+         paste0("BS_Malliavin_Asian_Greeks: ", greek, " error too high"))
 
 })