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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

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…

Read More Stationarity and Autocorrelation Functions of VXX-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…

Read More A Volatility Trading System-Time Series Analysis 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…

Read More Valuation of European and American Options-Derivative Pricing in Python

In a previous post, we presented an example of Interest Rate Swap Pricing in Excel. In this post, we are going to provide an example of interest rate swap pricing in Python. We are going to use the USD Libor swap curve as at December 31 2018. Picture below shows the swap curve. Recall that…

Read More Interest Rate Swap-Derivative Pricing in Python

In this post, we are going to walk you through an example of calculating the weighted average cost of capital (WACC) using Excel. The weighted average cost of capital (WACC) is the rate that a company is expected to pay on average to all its security holders to finance its assets. The WACC is commonly…

Read More Weighted Average Cost of Capital (WACC)-Business Valuation Calculator in Excel

Debt instruments are an important part of the capital market.  In this post, we are going to provide an example of pricing a fixed-rate bond. A fixed rate bond is a long term debt paper that carries a predetermined interest rate. The interest rate is known as coupon rate and interest is payable at specified…

Read More Valuing a Fixed Rate Bond-Derivative Pricing in Python

In a previous post entitled Credit Risk Management Using Merton Model we provided a brief theoretical description of the Merton structural credit risk model. Note that, The Merton model is an analysis model – named after economist Robert C. Merton – used to assess the credit risk of a company’s debt. Analysts and investors utilize…

Read More Merton Credit Risk Model, a Case Study