esgmartingaletest: Test for martingale property and market consistency

In Techtonique/ESGtoolkit: Toolkit for Monte Carlo Simulations

Test for martingale property and market consistency

Description

Performs statistical tests to verify if a time series follows a martingale property and maintains market consistency. Three different testing methods are available.

Usage

esgmartingaletest(
  r,
  X,
  p0,
  alpha = 0.05,
  method = c("onevsone", "trend", "ratio")
)

Arguments

r	Risk-free rate (scalar or time series)
X	Time series of asset prices or values
p0	Initial price(s) for comparison
alpha	Significance level for hypothesis tests (default: 0.05)
method	Testing method: "onevsone": One-to-one comparison test "trend": Trend analysis test "ratio": Ratio-based test

Details

The function implements three different approaches to test for martingale properties:

• "onevsone": Compares each observation against its expected value

• "trend": Analyzes trends in the martingale differences

• "ratio": Tests the ratio between discounted values and initial prices

The test results help determine if the time series maintains the martingale property and market consistency under the risk-neutral measure.

Value

A list containing test results, which may include:

• t-statistic and p-value for ratio test

• trend analysis results

• mean and standard deviation of martingale differences

Examples

# Generate sample data
r <- 0.05
X <- ts(matrix(rnorm(1000), 100, 10), start = 0, deltat = 0.1)
p0 <- 100

# Perform martingale test using ratio method
result <- esgmartingaletest(r, X, p0, method = "ratio")

# Perform trend analysis
trend_result <- esgmartingaletest(r, X, p0, method = "trend")

Techtonique/ESGtoolkit documentation built on June 11, 2025, 6:24 p.m.