Credit spreads

Key words: CDS, credit curves, reduced-form models, credit triangle, hazard rates and unconditional default probability density There are two important curves when dealing with interest rate derivatives. These are spot (discount) and forward curves. In order to deal with credit derivatives, such as CDS, we need both interest rate and credit curves. Credit curves help…

Siegel’s paradox

Key words: Jensen’s inequality, Expectation of forward rates, Siegel(1972) An important conceptual problem is the Siegel Paradox. It states that if the equality between the forward exchange rate and the expected spot rate holds in the domestic currency then it can’t be simultaneously true in the foreign currency. This simply violates Jensen’s inequality. Mathematicians say…

Jensen’s Inequality

Key words: Convexity adjustment, Convex function, Non-linearity in derivatives, time value of an option Inequality generalizes the statement that a secant line of a convex/concave function is above/below the graph. This was proved by Danish mathematician in 1906. Concept of convexity and Jensen’s inequality are intricately linked. Generally convexity can be used to interpret derivative…

Corporate FX strategies, part 2

Key words: Risk reversal, Collar, Range forward, Seagull, Participating forward In the previous article, a large EU company exported to the USA and got payment in US dollars. If the company expects a stronger EUR/USD in the future which strategy to use in order to eliminate FX exposure? One simple possibility is to buy a…

Corporate FX strategies, part 1

Key words: Synthetic forwards, First and second generation options, Third generation options, Zero-cost strategies, Low premium strategies, Boston options, Range forwards, Profit sharing forwards Foreign exchange (FX) risk is invariably associated with import and export transactions when future payments are denominated in a foreign currency. Pricing in the currency of the target market require special…

Delta

Key words: Option Sensitivities, Spot delta, Slope of the tangent line, Option hedge ratio, Probability of the option expiring, Up-and-In barrier call option 1. Delta or sometimes called spot delta is the first derivative of option market value (MV) with respect to spot price. If P is an option price and S is a spot…

CCIRS: FX Delta calculation

Key words: Cross-currency interest rate swaps, CCIRS, Interest rate swap, IRS, Interest rate risk, Currency risk Swap is a financial contract in which two parties agree to exchange “something” for “something” within an agreed time period, parties swapping things between each other. Often, there are cash flows, so called periodic payments swapped at a reasonable…

FX Market: spot, forwards and swaps

Key words: FX Quotation, FX spot, Pips, FX figure, Base currency, Quote currency, FX Forward rate, Swap points, NDF, Swap funding, Residual FX swap risk In the article “FX Quotation” I wrote about quotation styles and how currencies are denoted with a letter code like CCY1 and CCY2. The quoting conventions associated with FX market…

Interest rate sensitivity

Key words: DV01, Dollar Duration, PV01/PVBP, Delta, Effective DV01, Macaulay Duration, Modified Duration, Interest rate swaps sensitivities The concept of interest rate risk is often confused by a lot of terminology but actually is one of the easiest and straight forward approaches: how price changes as yields change, i.e. what is the sensitivity? There are…

Interest rate swaps valuation with Quantlib

Key words: Interest Rate Swap, IRS, Quantlib, Plain Vanilla IRS, IMM dates, Swap valuation, Fixed leg, Floating Leg, Curve constraction, Swaps NPV The interest rate swap (IRS) market is the largest derivative market. The size and continued growth of this market is really impressive: the article shows statistic across all OTC derivatives where IRS outstanding…