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by 0 comments on "Parkinson Historical 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…

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by 0 comments on "Close-to-Close 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…

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by 0 comments on "What is Stock Beta and How to Calculate Stock Beta 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…

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by 0 comments on "Value At Risk – Financial Risk Management 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…

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by 0 comments on "Another Misuse of Financial Derivatives"

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…

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by 1 comment on "Valuing European Options Using Monte Carlo Simulation-Derivative Pricing in Python"

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…

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by 0 comments on "Black-Scholes-Merton Option Pricing Model-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…

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by 0 comments on "Are Collateralized Loan Obligations the New Debt Bombs? Part Two"

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…

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by 0 comments on "Valuing a Convertible Bond-Derivative Pricing in Python"

In a previous post, we presented a theoretical framework for pricing convertible bonds and preferred shares.  We also provided an example of pricing a convertible bond in Excel. In this installment, we present an example of pricing a convertible bond in Python. Recall that a convertible bond (or preferred share) is a hybrid security, part…

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by 0 comments on "How Negative Interest Rates Affect Derivative Pricing Models"

As negative interest rates started popping up around the world, quantitative analysts and traders have been asking a mundane but fundamental question: How to price trillions of dollars of financial instruments when their complex pricing models don’t work with negative numbers? Intuitively, we would say that negative interest rates will affect the prices of interest-rate…

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