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Stationarity and Autocorrelation Functions of VXX-Time Series Analysis in

DerivValuation Posted 9 Apr.
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 the last 5 years. From the Figure, it’s evident that the time series has a strong downward drift. The cause of this downward drift has been discussed to a great extent in the investment c…
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A Volatility Trading System-Time Series Analysis in Python

DerivValuation Posted 2 Apr.
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 to smooth out short-term noises and identify longer-term trends. We apply them to VXX, a volatility ETN. Note that VXX
  • Launched in 2009
…
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Differences Between the VIX Index And At-the-Money Implied

DerivValuation Posted 29 Mar.
When trading options, we often use the VIX index as a measure of volatility to help enter and manage positions. This works most of the time. However, there exist some differences between the VIX index and at-the-money implied volatility (ATM IV). In this post, we are going to show such a difference through an example. Specifically, we study the relationship between the implied volatility and forward realized volatility (RV) [1] of SP500. We utilize data from April 2009 to December 2018.
Recall t[/1]…
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Valuation of European and American Options-Derivative Pricing in Python

DerivValuation Posted 26 Mar.
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 model (BOPM) provides a generalizable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinst…
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Interest Rate Swap-Derivative Pricing in Python

DerivValuation Posted 21 Mar.
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.
USD Swap Curve as at Dec 31, 2018. Source: Bloomberg
Recall that an interest rate swap (IRS) is a financial derivative instrument that involves an exchange of a fixed interest rate for a floating interest rate. More speci…
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Weighted Average Cost of Capital (WACC)-Business Valuation Calculator

DerivValuation Posted 27 Jan.
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 referred to as the firm’s cost of capital. Importantly, it is dictated by the external market and not by management. The WACC represents the minimum return that a company must earn on an existing a…
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Is Asset Dynamics Priced In Correctly by Black-Scholes-Merton?

DerivValuation Posted 31 Dec.
A lot of research has been devoted to answering the question: do options price in the volatility risks correctly? The most noteworthy phenomenon (or bias) is called the volatility risk premium, i.e. options implied volatilities tend to overestimate future realized volatilities. Much less attention is paid, however, to the underlying asset dynamics, i.e. to answering the question: do options price in the asset dynamics correctly?
Note that within the usual BSM framework, the underlying asset is a…
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Valuing a Fixed Rate Bond-Derivative Pricing in Python

DerivValuation Posted 23 Dec.
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 dates before bond maturity. Due to the fixed coupon, the market value of a fixed-rate bond is susceptible to fluctuations in interest rates, and therefore has a significant amount of interest …
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Merton Credit Risk Model, a Case Study

DerivValuation Posted 30 Nov.
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 the Merton model to understand how capable a company is at meeting financial obligations, servicing its debt, and weighing the general possibility that it will go into…
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Interest Rate Swap-Derivative Pricing in Excel

DerivValuation Posted 30 Oct.
An interest rate swap (IRS) is a financial derivative instrument that involves an exchange of a fixed interest rate for a floating interest rate. More specifically,
An interest rate swap’s (IRS’s) effective description is a derivative contract, agreed between two counterparties, which specifies the nature of an exchange of payments benchmarked against an interest rate index. The most common IRS is a fixed for floating swap, whereby one party will make payments to the other based on an initially …
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