In the article Cholesky decomposition is shown how to deal with correlation between two or more underlyings to get correlated random variables. The decomposition is used in Monte Carlo process which also requires valuation algorithm with the mathematical construction of the geometric Brownian motion. Brownian motion is a stochastic process and shows the same behaviour…

##### Cholesky decomposition

Valuation of investment portfolios, structured products and different strategies that consist of several underlying assets may require advanced methodology and algorithms. Monte Carlo technique that includes valuation algorithm is often used in such cases, especially if there is no closed form solution for option pricing. Standard inputs parameters to Monte Carlo process are: 1. Correlation/covariance…

##### 3. RVA of credit instruments: pricing bonds from CDS quotes

Bringing all previous ideas and concepts together we approach an arguable subject of bond trading based on several criteria: 1) derivation of hypothetical bond prices and 2) the spreads and basis comparison. Survival probability curve can be used to perform respective adjustments to the bond cash flows. We employ the following formula: Hypothetical price =…

##### Spread: Brent and WTI

After hitting $24.79 on December 13, 2012, the WTI-Brent price differential tightened to $8.35 on April 2013. Many traders bet the spread would narrow in 2011/2012. Movement in the spread has been volatile since 2010 when the price started to increase and topped at $29.59 on september 2011. Now, the spread is less volatile, so…

##### ETN or ETF?

Exchange traded notes (ETN) are structured investments linked to market instruments such as market Indices, Commodity, Currency, Emerging Markets, Fixed Income, Leveraged products and Strategies. Introduced on June 12, 2006 by Barclays Bank, the first ETNs named iPath, was issued as unsecured debt which means such notes don’t own anything while ETFs represent a stake…

##### Global Industry Classification Standard (GICS)

Global Industry Classification Standard (GICS) was developed by Morgan Stanley Capital International (MSCI) and S&P to enhance research and investment process and to classify a company according to its principal business activity. GICS consists of 10 sectors, 24 industry groups. There are also industries and sub-industries introduced in GICS methodology to fine tune all business…

##### Instantaneous Forward Rates

Note: Instantaneous forward rate calculations can be downloaded here. The main focus of this article is to clarify the difference between spot, forward and instantaneous forward rates, define the meaning of the latter and outline its application. The main feature of interest rates as a class is that they do not represent any specific financial…

##### 2. RVA of credit instruments: yield curve construction

Note: We enclose a spreadsheet on Nelson-Siegel and Svensson curve fitting to this part of the topic. Constructing a yield curve is a 2 step process. The first step in most cases is fairly easy and straightforward as it deals with selecting the appropriate bonds. For example, if we are looking at a highly developed…

##### I.RVA of credit instruments: Introduction

Relative value analysis (RVA) is an important subject for the debt market, as it allows comparing different FI and MM instruments (bonds, CDS, swaps, etc.) with one another and making respective trading decisions. In this series of articles you will find the description of its purpose and application. Why is this value analysis called “relative”?…