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In the previous post, we introduced the Garman-Klass volatility estimator that takes into account the high, low, open, and closing prices of a stock. In this installment, 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,…

Read More Garman-Klass-Yang-Zhang Historical Volatility Calculation – Volatility Analysis in Python

In the previous post, we introduced the Parkinson volatility estimator that takes into account the high and low prices of a stock. In this follow-up post, we present the Garman-Klass volatility estimator that uses not only the high and low but also the opening and closing prices. Garman-Klass (GK) volatility estimator consists of using the…

Read More Garman-Klass Volatility Calculation – Volatility Analysis in Python

In the previous post, we discussed the close-to-close historical volatility. Recall that the close-to-close historical volatility (CCHV) is calculated as follows, where xi are the logarithmic returns calculated based on closing prices, and N is the sample size. A disadvantage of using the CCHV is that it does not take into account the information about…

Read More Parkinson Historical Volatility Calculation – Volatility Analysis in Python

In a previous post, we touched upon a stock’s volatility through its beta. In this post, we are going to discuss historical volatilities of a stock in more details. Also referred to as statistical volatility, historical volatility gauges the fluctuations of underlying securities by measuring price changes over predetermined periods of time. It is the…

Read More Close-to-Close Historical Volatility Calculation – Volatility Analysis in Python

In finance, beta measures a stock’s volatility with respect to the overall market. It is used in many areas of financial analysis and investment, for example in the calculation of the Weighted Average Cost of Capital, in the Capital Asset Pricing Model and market-neutral trading. Beta of an investment is a measure of the risk…

Read More What is Stock Beta and How to Calculate Stock Beta in Python

Value at Risk (VaR) is a tool for measuring a portfolio’s risk. Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. … For…

Read More Value At Risk – Financial Risk Management in Python

Just like any financial derivatives that were initially designed for risk management purposes, interest rate swaps are an effective tool for managing and transferring interest rate risks as long as those risks are well understood.  But as banks and financial institutions are constantly trying to invent new financial products to sell to their consumers, sometimes…

Read More Another Misuse of Financial Derivatives

In a previous post, we presented a methodology for pricing European options using a closed-form formula. In this installment, we price these options using a numerical method. Specifically, we will use Monte Carlo simulation. Recall that, A call option gives the buyer the right, but not the obligation to buy an agreed quantity of the…

Read More Valuing European Options Using Monte Carlo Simulation-Derivative Pricing in Python

The Black-Scholes-Merton model is one of the earliest option pricing models that was developed in the late 1960s and published in 1973 [1,2]. The most important concept behind the model is the dynamic hedging of an option portfolio in order to eliminate the market risk. First, a delta-neutral portfolio is constructed, and then it is…

Read More Black-Scholes-Merton Option Pricing Model-Derivative Pricing in Python

In a previous post, we discussed the risks of Collateralized Loan Obligations, a type of complex credit derivatives.  Since then, the trend in securitizing loans is still upward. Nowadays, not only performing loans but also non-performing loans are being securitized and sold to investors. A non-performing loan is a loan that is in default or…

Read More Are Collateralized Loan Obligations the New Debt Bombs? Part Two