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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

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…

Read More Valuing a Convertible Bond-Derivative Pricing in Python

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…

Read More How Negative Interest Rates Affect Derivative Pricing Models

Investors in South Korea have lost money in a complex derivative linked to constant maturity swap.  In search for higher yields, they are also putting money into another complex financial instrument, convertible bonds. Bloomberg recently reported, Sales of convertibles, which pay low coupons and let investors convert into stock if the issuer’s shares rise enough,…

Read More Are Convertible Bonds Really Attractive?

Yonhap recently reported that South Korea’s investors appear to have lost money by investing in complex derivative products. The Financial Supervisory Service (FSS) said 3,654 individual investors and 188 businesses were found to have bought 822.4 billion won (US$677.8 million) worth of so-called “derivatives-linked fund” options sold by banks as of Aug. 7. Such derivative…

Read More Complex Derivative Linked to Constant Maturity Swap