In a previous post, we presented theory and a practical example of calculating implied volatility for a given stock option. In this post, we are going to implement a model for forecasting the implied volatility. Specifically, we are going to use the Autoregressive Integrated Moving Average (ARIMA) model to forecast the volatility index VIX.

http://tech.harbourfronts.com/trading/forecasting-implied-volatility-arima-model-volatility-analysis-python/

In a previous post, we presented an example of volatility analysis using Close-to-Close historical volatility. In this post, we are going to use the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to forecast volatility.

http://tech.harbourfronts.com/trading/forecasting-volatility-garch-model-volatility-analysis-python/

There are two types of volatility: historical volatility and implied volatility. In a series of previous posts, we presented methods and provided Python programs for calculating historical volatilities. In this post, we are going to discuss implied volatility and provide a concrete example of implied volatility calculation in Python.

http://tech.harbourfronts.com/trading/implied-volatility-options-volatility-analysis-python/

In a previous post, we presented a method for calculating a stock beta and implemented it in Python. In this follow-up post, we are going to implement the calculation in Excel. We continue to use Facebook as an example.

http://tech.harbourfronts.com/trading/calculate-stock-beta-excel-replicating-yahoo-stock-beta/

We are going to discuss valuation of a callable bond. We chose the Hull-White model to describe the interest rate dynamics. We then use a Python program to build a trinomial tree for the risk-free rates

http://tech.harbourfronts.com/derivatives/valuation-callable-puttable-bonds-derivative-pricing-python/

A warrant is a financial derivative instrument that is similar to a regular stock option except that when it is exercised, the company will issue more stocks and sell them to the warrant holder. The valuation of warrants is similar to the valuation of stock options except that the effect of dilution should be considered.

http://tech.harbourfronts.com/derivatives/valuation-warrants-derivative-pricing-python/

Performance share units are hypothetical share units that are granted to you based mainly on corporate and/or individual performance. Structurally, they are very similar to restricted stock units except these are more focused on your performance. They are designed to mirror share ownership and you will generally be granted additional units having the same value as dividends being paid on the regular shares

http://tech.harbourfronts.com/derivatives/performance-share-units-derivative-valuation-python/

Valuation of Employee Stock Options is different from regular stock options. In this post, we are going to implement the approach proposed by Hull and White. Specifically, we are going to implement the vesting and forfeiture rate features. Other features can also be implemented without difficulty

http://tech.harbourfronts.com/derivatives/employee-stock-options-derivative-pricing-python/

We are going to present a method for valuing American options using Monte Carlo simulation. This method will allow us to implement more complex option payoffs with greater flexibility, even if the payoffs are path-dependent. Specifically, we use the Least-Squares Method of Longstaff and Schwartz in order to take into account the early exercise feature. The stock price is assumed to follow the Geometrical Brownian Motion.

http://tech.harbourfronts.com/derivatives/valuing-american-options-using-monte-carlo-simulation-derivative-pricing-python/

We present an extension of the Garman-Klass volatility estimator that also takes into consideration overnight jumps. Garman-Klass-Yang-Zhang (GKYZ) volatility estimator consists of using the returns of open, high, low, and closing prices in its calculation. It also uses the previous day’s closing price.

http://tech.harbourfronts.com/trading/garman-klass-yang-zhang-historical-volatility-calculation-volatility-analysis-python/