The main flaw of the Black Scholes model is that it assumes that the volatility of options contracts is constant for different strike prices. This assumption is not reflected in the real world where different strikes prices have different Implied Volatility values showing that investors and traders assign higher premiums for options that allow them […]

## Black Scholes Options Pricing Model in R

The Black Scholes model estimates the value of a European call or put option by using the following parameters: S = Stock Price K = Strike Price at Expiration r = Risk-free Interest Rate T = Time to Expiration sig = Volatility of the Underlying asset Using R, we can write a function to compute […]

## Review of Options Contracts

Options are financial instruments that give the holders certain rights that they can exercise at the time of expiration. A call option gives its owner the right to purchase an underlying asset at a specified price and at a specific time. A put option gives its owner the right to sell the underlying asset at […]

## Exploring Open Interest for Futures Contracts with R

In this article we will explore in greater depth the Open Interest variable of the futures contracts price data and see in which months of the year this variable tends to increase for a particular contract. For this purpose, we have gathered contracts futures data from CSI 500 Shanghai Index. Our task will be to […]

## Contango and Backwardation

The concepts of Contango and Backwardation are related with the term structure of the futures contracts. During the life of a contract, the difference between the futures price and the expected future price is called basis. At the end of the contract’s life, the futures price converges to the expected future spot price. Each month, […]

## Creating Term Structure of Futures Contracts Using R

The terms structure of the futures contracts for a specific asset is generated by the contracts prices at different expiration times. The contracts have different prices on each expiration date and there is an underlying relationship between them that is reflected with different shapes. The most common shapes are called normal or inverted forms. These […]

## Different Parties in the Futures Market

The future market is composed of different types of agents that go to the futures market for a specific purpose. These agents raise the trading volume and open interest during the contract life. Overall the futures market is composed of speculators and hedgers. Speculators The speculators can be classified into market makers, day traders and […]

## Comparing Futures vs Spot Prices for WTI Crude Oil

In this post, we will be comparing the Futures vs Spot Prices for WTI Crude Oil, i.e., the WTI Futures series with the WTI Spot series. The futures prices generally show high volatility and they are more volatile than the underlying spot price. For this purpose, it would be interesting to compare future and spot […]

## 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 […]

## Exploring Crude Oil (CL) Future Data from Quandl in R

It would be useful to download a dataset of historical future contract prices and explore it using R programming language. For this purpose we will load the futures historical data of Crude Oil (CME_CL1) from the CHRIS database of Quandl. The nomenclature to download futures data from Quandl is the following: CHRIS/{EXCHANGE}_{CODE}{NUMBER} CHRIS refers to […]