Key words: Capital Protection notes, Exchangeable notes, Cap, Range notes, Absolute Return notes. This is a second article about structured notes. As been stated previously in the article “A Simple Guide to Structured Products”, there are four major classes of SPs. One of them is Capital Protection Notes. According to the picture below, there are…

##### Finite-difference methods for options pricing

Key words: finite difference, greeks, black scholes, option, pricing, simulation, volatility, quantitative finance, financial engineering, analysis, derivatives, delta, theta, central difference method When it comes to simulations, one of the first steps is to choose a method that would actually run through the hypothetical time steps or simply perform certain calculations and bring us to…

##### A Simple Guide to Structured Products

Key words: Capital Protection, Participation, Yield enhancement, Leverage It has been said a lot about structured products(SPs) since the last credit crunch in 2008. Many articles claimed SPs to be very risky investments with unpredictable outcomes. As for me, I have doubts about such rumors. Firts of all, SPs can be characterized by its Functionality(payoff),…

##### OIS – untold story

Key words: OIS and LIBOR rates I was very impressed by reading an article in the Internet about OIS and LIBOR rates that are used to value swap trades. Clearly stated, simple Interest Rate Swaps can be valued using different approaches to interest rates. Commonly used Libor is the market indicator but it seems like…

##### Portfolio simulation

This is an article that will sum up all previous results made in: 1. Cholesky decomposition 2. Stock price simulation 3. Ito’s lemma and stock price By applying Cholesky decomposition to the portfolio of 4 stocks(A,B,C and D), usnig Monte-Carlo simulation and taking into account Geometric Brownian Motion(GBM) we simulate our portfolio to see possible…

##### Ito’s lemma and stock price

Previously, Stock price simulation , we saw that stock prices can be described by geometric brownian motion (GBM). In order to solve a partial differential equation GBM, we need to appreciate Ito’s lemma. Let us consider G is a function of two variables, x and t. The change in G for a small changes in…

##### Stock price simulation

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…