- Overview of Derivatives with R Tutorial
- How to Create Futures Continuous Series
- Exploring Crude Oil (CL) Future Data from Quandl in R
- R Visualization of Statistical Properties of Future Prices
- Comparing Futures vs Spot Prices for WTI Crude Oil
- Different Parties in the Futures Market
- Creating Term Structure of Futures Contracts Using R
- Contango and Backwardation
- Exploring Open Interest for Futures Contracts with R
- Review of Options Contracts
- Black Scholes Options Pricing Model in R
- Binomial Option Pricing Model in R
- Understanding Options Greeks
- Options Strategy: Create Bull Call Spread with R Language
- Options Strategy: Create Long Straddle with R Language

# R Visualization of Statistical Properties of Future Prices

Future contracts have some particular properties that make them a special assets class. In this article, we will learn about these statistical properties by visualizing them in R.

### Futures Prices have High Volatility and Distribution with Leptokurtic Shape

First of all future contracts are well known for their higher volatility. The price distribution of future prices widely differs from a normal distribution, as it has a considerable number of extreme points that moves the prices beyond the limits of a normal distribution.

The distribution of future prices has a leptokurtic shape because there are too many observations beyond the limits given by the normal distribution. This distribution is characterized by fat tails and high peaks.

### Plot Quantiles and Histogram of Returns

As an exploratory task, we will use the futures prices of WTI Crude Oil and plot the quantiles and the histogram of the returns of the ** Last** field column on the CME_CL_Data_ dataframe. We downloaded this data in the previous article.

```
# Compare returns quantiles to quantiles of a normal distribution using the qqnorm and qqline commands that plot the quantiles of the series and a quantiles of a normal distribution as a theoretical line
par(mfrow=c(2, 1))
# Define the returns vector with the values of the returns column from CME_CL_DATA_
returns <- CME_CL_Data_$returns
qqnorm(returns, main="CL Returns")
qqline(returns, col="red")
# Generate a histogram with the returns
ret_hist <- hist(returns, breaks=50,col='red')
```

**CL returns Quantiles and Histogram**

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