Key words: Monte-Carlo, C#, call option by simulation, Box-Muller function This article describes a simple crude pricing of call option using Monte-carlo simulation. Taking into account GBM described in the article Stock price simulation, we now develope a code in C# that takes all inputs similar to Black-Scholes inputs and loop over all the path…

##### Yield Enhancement Notes

Key words: Structured products, Capital protection, Autocallable Notes, Reverse Convertible, Discount Certificates. Yield Enhancement Notes generally provide a fixed coupon that is very similar to a form of income product, like simple bonds. In the same manner like bonds, these Notes pay coupon no matter how the market develops, whether the market is down or…

##### Understanding CVA (part 2)

Key words: CVA, credit valuation adjustment, credit value adjustment, DVA, debt valuation adjustment, debt value adjustment, option, hedging, greeks, gamma, cross-gamma, hedge, credit risk, SPV01, DV01, sensitivities, exposure, EAD, billion trader, ENE, EPE, FVA, Basel III Note: you can download this article in PDF here. The previous article on credit valuation adjustment and counterparty credit…

##### Understanding CVA (part 1)

Key words: CVA, credit valuation adjustment, credit value adjustment, DVA, debt valuation adjustment, debt value adjustment After the credit crunch of 2008 a significant amount of global attention was focused on the methodology of estimating counterparty credit risk (CCR) and utilizing it to adjust the P&L in order to reflect this risk. Today CVA is…

##### Capital Protection Notes

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…