# ARTICLES

## 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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## 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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## 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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## 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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## 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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## Are Convertible Bonds Really Attractive?

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,…

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## Complex Derivative Linked to Constant Maturity Swap

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…

## Stationarity and Autocorrelation Functions of VXX-Time Series Analysis in Python

In the previous post, we presented a system for trading VXX, a volatility Exchange Traded Note. The trading system was built based on simple moving averages.  In this post, we are going to examine the time series properties of VXX in more details. The figure below shows the VXX and its 200-day moving average for…

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## A Volatility Trading System-Time Series Analysis in Python

Time series analysis is an important subject in finance. In this post, we are going to apply a time series technique to a financial time series and develop an investment strategy.  Specifically, we are going to use moving averages to trade volatility Exchange Traded Notes (ETN). Moving averages are used on financial time series data…

## Valuation of European and American Options-Derivative Pricing in Python

In previous posts, we provided examples of pricing European and American options in Excel. For pricing the European option, we utilized the Black-Scholes formula, and for pricing the American option we utilized the binomial approach. In this post, we are going to implement these methods in Python. Recall that, In finance, the binomial options pricing…

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