##### Random walk and the arc-sine laws

Key words: The first arc-sine law, the second arc-sine law, coin tossing, random walks Brownian motion can be treated as a limit of random walks. Random walk can be simulated by tossing a fair coin. Suppose that there is an ideal coin tossing game in which each player wins or loses a constant amount with…

##### CVA/DVA calculation

Key words: Asset and Liability CVA, PD, LGD, EAD, DVA, EPE, ENE CVA is the value of the expected losses from counterparty defaulting and can be formulated as well as: СVA = Present Value of (PD * EAD * LGD) CVA – adjustment to the price of derivative to account for counterparty credit risk. It…

##### Probabilities of Default

Key words: CDS spreads, Cumulative, Conditional (probability intensities) and Unconditional probability of default, Survival probability Probability of default is a financial term describing the likelihood of a default over a particular time horizon. Measurement of the probability of default for a credit exposure over a given horizon is often the first step in credit risk…

##### Measures of Variability

Key words: The Range, Mean Deviations, Variance, Standard and Median Deviations Let’s say you earned \$1 one week, \$10 the following week and \$100 the third week. As it follows from the previous article, Measures of Central Tendency, the mean μ for this distribution is \$37 per week. The mean reveals the center of the…

##### Measures of Central Tendency

Key words: Mode, Median, Mean The term “central tendency” determines a single value that best represents a distribution of data. A single value is needed to distinguish among multiple values when describing data. The mode, median and mean are the most common measures of central tendency. The mode, median and mean are all valid measures…

Key words: Convexity Bias, convexity adjustment, FRA, EuroDollars, Interest Rates As it was written in the previous article “Futures and forward convexity adjustment”, there is a systematic advantage to being short EuroDollar futures relative to FRAs. This advantage is characterized as a convexity bias and appropriate methods exist to adjust Eurodollar futures prices to eliminate…

##### FRA

Key words: Forward rate agreement (FRA), FRAs quoting terminology, “borrowing” funds, FRA mechanics FRA (forward rate agreement) is an OTC (over-the-counter) contract that guarantees a borrowing or lending rate for a future period based on a given notional principal amount. Usually, the reference rate used in the FRA is the same as the actual borrowing…

##### Eurodollar futures

Key words: Interest rate futures, LIBOR (the London Interbank Offer Rate), 3-month Eurodollar time deposit There are four money markets in the world having interbank offered rate fixings in USD. The USD LIBOR in London is the most recognised and predominant one. LIBOR rates are calculated for 7 maturities, including 1 day, 1 week, 1…

##### CDS valuation

Key words: Duffie, Hull-White no-arbitrage models, Hazard rates, Recovery rate, Unconditional cumulative default probability, Cumulative probability, Conditional probability Generally, there are two models to value CDS. Probability model is based on hazard rates and no-arbitrage model assumes that there is no risk free arbitrage. The latter model was developed by both Duffie and Hull –…

##### CDS

Key words: Credit events, Reference entity, Valuation of CDS, CDS spread Credit default swaps (CDS) are the most basic credit derivatives instruments. A credit default swap is a privately negotiated bilateral contract designed to transfer the credit exposure between two parties. Therefore CDS provides insurance on a notional amount against the risk of a default…