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Blog-style articles that help you understand derivatives better by pricing them in Excel.
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Fully Functional Excel Spreadsheet for SOFR Swaption Trading with Lognormal, Normal and Shifted Lognormal SABR Vol Calibration

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Setting up an interest rate swaption trading desk is a complex endeavour. First, the type of the underlying interest rate should be defined, and it can be either a still existing ibor rate such as EURIBOR or JPY TIBOR or – in the case of LIBOR that has been discontinued as of June 30, 2023 - an equivalent ARR (Alternative Reference Rate) such as a ...
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Pricing Currency Swaps with different Collateral Currencies in Excel. The GBP SONIA vs USD SOFR case

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For a review of cross currency swaps and how to build an implied discounting yield curve of the foreign currency from given market basis spreads, read my post Currency Swaps and Basis Curves in Excel, where both the market swaps and the to-be-priced bespoke swap involve the exchange between 3-month USD LIBOR and 3-month EUR LIBOR collateralized thr...
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Yield Curve Building in Excel with Central Bank Meeting Dates and STIR OIS Trading Arbitrage Opportunities: The GBP Sonia case

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One of the central banks' duties is to ensure the cost of money (aka interest rates) is optimal for the economy. If a) the economy is overheated and needs to slow down to avoid a future burst or b) inflation rates are too high due to increased consumer demand, higher interest rates will a₁) have a cooling effect on the economy by raising the c...
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Using the Bootstrapped Market SOFR Caplet Normal Vol Surface to Price in Excel Interest Rate Caps/Floors on Backward/Forward Looking SOFR Term Rates

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In my earlier posts titled Overnight Index Swap (OIS): Pricing and Understanding using Excel and Overnight Index Swap (OIS): Observation Lags, Lookbacks, Rate Cutoffs and step-by-step Pricing in Excel I provided a detailed description of overnight index swaps known as OIS, of which the floating leg index in each payment period was defined...
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Pricing FX Options in Excel using Risk Reversal and Butterfly Market Quotes. The USD / Indian Rupee Case

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Back in 2017 I had shown in a 13-min video titled Option pricing in Excel with Implied Volatility Surface using QuantLib how an option on the EURO STOXX 50 index can be priced using not a single vol quote, but rather a table of market volatilities spanning several option expiries and strikes.On this post I will turn my attention to the pricing of v...
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Sonia OIS Relative Carry and Roll-Down in Excel. Has Bloomberg got it Wrong?

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I have discussed the generic concepts of Carry and Roll-Down in relation to the expected cash flows of any financial instrument in my post titled Carry and Roll-Down of USD Interest Rate Swaps in Excel with Bloomberg Comparison. The emphasis there was placed on their absolute (dollar) definition and a USD Libor interest rate swap was used as exampl...
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Bootstrapping in Excel a Yield Curve to perfectly fit Bloomberg Price/Yield Quotes of US Treasury Bills, Notes and Bonds

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I have already described the bootstrapping method for building a yield curve from various instrument types in the yield curve articles category. In particular, my post on Yield Curve Building in Excel using Bond Prices (QuantLibXL vs Deriscope) demonstrates how this is done in practice using a simplified theoretical setup consisting of three m...
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Overnight Index Swap (OIS): Observation Lags, Lookbacks, Rate Cutoffs and step-by-step Prising in Excel

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I have covered in quite exhausting detail the mathematical description of an Overnight Index Swap (OIS) in my earlier post about Pricing and Understanding OIS using Excel.Since then, OIS have increased in significance due to the cessation of Libor that affected primarily the USD and GBP currencies to the effect that today hardly anyone still trades...
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Libor Transition Impact on Portfolio Pricing: A Comparative Study with and without the published Bloomberg Spread Adjustments

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Everybody these days seems to ask the same question: On D-Day when LIBOR will cease to exist and pricing will rely solely on risk-free reference rates like SOFR or SONIA and the Spread Adjustments published by Bloomberg, what will the impact on portfolio pricing be?The mechanics of pricing a single USD interest rate swap with and without the ISDA-B...
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Pricing and Risk Management in Excel of Inhomogeneous Trading Book containing Different Types of USD Interest Rate Swaps

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In an earlier post with the title Trading Blotter and Book Risk Management of USD Interest Rate Swaps in Excel: Example of a Book with 10,000 Trades, I explained how to calculate the price and risk of a fictitious portfolio of up to 10,000 vanilla fixed-to-floating USD interest rate swaps that all involved the 3-month USD LIBOR index. Apart from th...
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Libor Cessation: Price and Risk of existing Vanilla Interest Rate Swaps by applying the ISDA Fallback Protocol

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Today, the sum of the notional amounts of all financial products referencing the USD LIBOR is estimated to $400 trillion. These are diverse products ranging from derivatives such as interest rate swaps to consumer products such as student loans and home mortgages. About $170 trillion are in outstanding swaps, of which one third have maturities beyo...
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Turn-of-the-Month Effect in SOFR Curve built out of 1- & 3- Month Futures

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In my previous article about building a SOFR yield curve in Excel using QuantLib and Deriscope I was confronted with an unexpected result concerning the short term – less than two years – section of the curve that exhibited a strong oscillatory behavior.In this post I will show how to smooth out this front section of the curve and investigate ...
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How to build a SOFR Yield Curve in Excel using QuantLib and Deriscope

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The markets expect that Libor will be gradually phased out as more investors and lenders prefer financial products tied to the Secured Overnight Financing Rate (SOFR) rather than the USD London Inter-bank Offered Rate (LIBOR).The main reason for this ongoing exodus is the expected cessation of the daily announcements of the interbank lending rates ...
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PnL Explained in Excel when trading USD Interest Rate Swaps

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 In one of my earlier posts I have shown how to use Deriscope to calculate the Carry and Roll of a single interest rate swap. In the current post I will describe the Profit and Loss (PnL) as a mathematical quantity that is defined in a way like that of the Carry and Roll-Down. Table Of Contents​ PnL Definition and Relationship with the Ca...
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Dependence of USD Interest Rate Swaps Price & Risk on Modelling Assumptions affecting the Curve Building

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In my post about USD Interest Rate Swaps in Excel, I have explained in detail how to calculate the price and risk of a single USD interest rate swap using a multi-curve approach and actual market data from Bloomberg as of 22 May 2019.A comparative analysis between the single-curve and multi-curve approach has been laid out in my post focusing on sw...
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Pricing of Cross-Currency Collateralized Swaps using OIS vs non-OIS Discounting: The Mexican case.

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Last week I described the unique problem faced by interest rate swap traders when the collateral is kept in a currency different than the one where the swaps are denominated. You may want to visit that post for details on how the appropriate discounting (basis) curve in the Mexican case is constructed out of several market rates that include t...
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Building in Excel the Implied Risk-Free Discounting Curve when the Collateral is kept in another Currency. Example: Mexico, where no Local OIS Market exists.

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Before the 2007-08 financial crisis, all swap cash flows were discounted with the same yield curve used in "forecasting" the future Libor rates and thus the amounts of the floating cash flows.At any given time, this yield curve was constructed so that it reproduced the market prices of the swaps traded at that time.After its construction, the yield...
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Using Bloomberg Tenor Basis Swap Spreads in Excel to calculate 1M USD Libor Forward Rates

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Until the 2007-08 financial crisis, forward interest rates of any tenor had been calculated off one single yield curve. In the US, traders had been building one USD yield curve out of market-traded deposits, futures and fixed-to-3M-Libor swaps and used that curve for all purposes involving interest rate calculations, such as extracting discount fac...
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Carry and Roll-Down of USD Interest Rate Swaps in Excel with Bloomberg Comparison

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In my previous two posts I have shown how to calculate the price and DV01 of a single interest rate swap and how to do so with a book containing thousands of swaps.Now I turn my attention to the calculation of the Carry and Roll-Down of a single swap. Table Of Contents​ Carry and Roll-Down Definition Deriscope Computation Method Bloomberg Math...
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Trading Blotter and Book Risk Management of USD Interest Rate Swaps in Excel: Example of a Book with 10,000 Trades.

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In my previous post about USD Interest Rate Swaps in Excel, I explained how to calculate the price and risk of a single USD interest rate swap using actual market data from Bloomberg as of 22 May 2019.In the current post, I will make use of the same market data to calculate the prices and DV01s (both flat and bucket) of two different swap collectio...
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USD Interest Rate Swap: Cash Flows and DV01 in Excel using Bloomberg Market Data

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In this post I will make use of the realistic yield curves I built in Excel out of Bloomberg OIS, deposit, futures and Libor swap rates as of May 22, 2019 towards calculating the price and producing the detailed cash flows, flat DV01 and maturity-dependent DV01s of a bespoke forward starting 3-year swap.You may want to visit the respective article,...
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OIS Discounted USD Libor Curve Production in Excel for Front Office Trading

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I have already explained in my earlier yield curve building post how one can use the Excel Deriscope addin to derive the discount factors and zero rates implied by any given market rates of deposits, futures and swaps.At another post about dual bootstrapping, I calculated in Excel the price of an actual 50-year EUR collateralized swap held by ...
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Almost Corporate-Ready Unlimited-Currency FX Option Portfolio Pricing with and without Excel

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The question whether Excel can be trusted for pricing and risk managing derivative transactions seems to be a never ending one.If you are curious about my own opinion on this matter, you may jump to the end of this article. In the sequel, I will confront this issue through the real-world case of pricing and managing a book of FX options.In my last ...
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Valuing a Portfolio of Multi-Currency FX Options and Producing its Value at Risk in Excel using Deriscope

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The topic here is not about simple option pricing but rather about dealing with the complexity introduced by the simultaneous existence of several different currencies in the context of calculating the Price and Value at Risk of a portfolio of European FX options.If you are not familiar with the basics of European option pricing in Excel using Deri...
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Floating Rate Notes (FRN) in Excel: Understanding Duration, Discount Margin and KRD

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Deriscope exports in Excel over 30 functions that deal with bonds, as I have described in an earlier document about bond risk management functions.In spite of the fact that the referred functions apply to all types of bonds, including interest rate and inflation linked bonds, one should be cautious when the referenced bond does not pay a fixed rate...
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Combining Randomized Quasi Monte Carlo (Sobol) and Parallel Processing (Multithreading) when Pricing Derivatives in Excel

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The beauty of Monte Carlo simulation is that it can be used to price any European financial derivative contract, of which the terminal payoff is expressed as a function of D terminal underlying factors by simulating the terminal values of these factors as of the contract's maturity date.It turns out, the successful execution of a Monte Carlo simula...
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Monte Carlo Pricing of any European Structured Product in Excel: Revisiting the Morgan Stanley Trigger Plus 2024 Note

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In my previous article I showed how one can use Deriscope in Excel to calculate the price of a particular type of a structured product that pays the minimum of two equity indices observed at some specified future terminal time. As example was used the Trigger Plus note issued by Morgan Stanley on April 1, 2019, which is based on the value of t...
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Perfect Bloomberg Price Match of an Interest Rate Swap in Excel by using Dual Bootstrapping

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Up until the financial crisis of 2008, the price calculation of an interest rate swap involved only the so-called Libor curve. The latter was essentially the discount factors (or equivalently zero rates or forward rates) implied by market-traded instruments, such as deposits, futures, forwards and swaps. The Libor curve was used to derive everythin...
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Pricing Structured Products in Excel: The Morgan Stanley Trigger Plus 2024 Note

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Various structured products can be precisely priced in Excel using Deriscope and its underlying QuantLib analytics. In this article I will focus on the Trigger Plus product issued by Morgan Stanley on April 1, 2019. It is based on the value of the worst performing of the Dow Jones Industrial Average and the Russel 2000 Index due April 4, 2024. It o...
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Currency Swaps and Basis Curves in Excel

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​The basic concepts of spot fx rates, forward fx contracts, fx swaps and the construction of foreign yield curves out of fx forward rates have been described in detail in my previous fx rates article.While these instruments cover the short end of the maturity spectrum – typically about a year -, the tenor of so-called currency swaps (also known as ...
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FX Spots, Forwards, Swaps and Curves in Excel

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​Assume you possess Nd units of a currency DOM regarded as domestic currency. For example, you live in the US and hold 1,000 USD, ie. Nd = 1,000 and DOM = USD.For whatever reasons, you want to replace this money with their equivalent number of units Nf of another currency FOR regarded as foreign currency. For concreteness think of FOR like if it we...
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Bond Key Rate Duration (KRD) in Excel: Calculating and Understanding

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You are all familiar with the concept of bond Duration, which tells us how much a bond's price changes if its yield goes up or down by a small amount.  In this post I will look into a less common but related concept that goes by the name Key Rate Duration. Table Of Contents​ Understanding the Duration ConceptDefinition and Rationale of Ke...
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Risk free Yield Curve Building in Excel using Negative Overnight Index Swap (OIS) Rates

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Long are the dates when all-purpose risk free yield curves were produced out of deposits, futures and swaps. Since the credit crisis of 2007/08, banks realized they should use different curves for different purposes. In the intervening years, quants have proven mathematically that uncollateralized contingent flows should be discounted using a curve...
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Overnight Index Swap (OIS): Pricing and Understanding using Excel

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Overnight Index Swaps (OIS) may be priced in Excel using the free and open source derivatives analytics QuantLib library through the Deriscope Excel interface.  Table Of Contents​ Overnight Index Swap (OIS) Description Mathematical Calculation of the OIS Present ValueCreating a 5-year OIS object in Excel in less than 18 seconds Getti...
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How to compute the VaR: Step-by-Step Excel Guide

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The purpose of this article is to show you step-by-step how you can calculate the Value at Risk (VaR) of any portfolio by generating all simulation samples in the spreadsheet. This is great for understanding what's going on but it becomes too complex and slow when the number of samples generated by the simulation exceeds 100.If you don't ...
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Pricing of Risk Scaling Options in Excel

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You are all familiar with simple European call options that are securities promising to pay their holders at some agreed future time T the difference S(T) – K between the price S(T) realized by a monitored underlying S at time T and a fixed amount K, under the condition that S(T) is greater than K. The last long sentence may be compressed to t...
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Using Quantos to gain exposure on Foreign Assets without the Currency Risk: Yes, but be careful!

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A common usage of quanto call options is to benefit from the price appreciation of a foreign asset and on the same time stay immune on exchange rate variations.A European style quanto call option on a foreign asset S with strike K is always cash settled and pays its holder on expiry time T the amount max{S(T) – K, 0} converted into domestic currenc...
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USD Swaption Pricing in Excel using SABR Stochastic Volatility and Market Vol Cube from CME

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The pricing of exotic interest rate products cannot ignore the so called market volatility cube that is made daily available by several swaption brokers.Traders often use the SABR Stochastic volatility model in order to estimate vols off the provided grid.In this article I will show you how to price an out-of-the-money swaption by applying SABR cal...
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USD Swaption Pricing in Excel using the Bachelier Model and Market Normal Vols from CME

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The Chicago Mercantile Exchange (CME) clears European swaption trades on 3-month USD LIBOR since April 2016 and has thus become the first major exchange that lists Over-The-Counter (OTC) interest rate products with optionality.The standardized swaption contracts have 5 different expiries - 1M, 3M, 6M, 1Y, 2Y – and 7 underlying swap tenors - 1Y, 2Y,...
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Parametric Yield Curve Fitting to Bond Prices under constraints: The National Bank of Georgia case

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Both the Nelson Siegel method and its Svensson extension are very popular among central and other banks when the time spectrum of interest rates needs to be derived from market bond prices. If you are interested in non-parametric methods favored by relative value traders as they provide an exact fit to observed bond prices, these have been demonstr...
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Asian Option Pricing in Excel using QuantLib: Monte Carlo, Finite Differences, Analytic models for Arithmetic and Geometric Average. Example with live EUR/USD rate

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Asian options come in different flavors as described below, but to the extent they have European exercise rights they can be priced by QuantLib using primarily Monte Carlo, but under certain circumstances using also Finite Differences or even analytic formulas.  Table Of Contents​ Asian Option Description Creating all four types of Asian ...
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Swaption Pricing in Excel: 14 Free QuantLib Models plus Implied Volatility Surface and Cube

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Most people are unaware of the fact that free and open source QuantLib comes with a great variety of modelling approaches when it comes to pricing an interest rate European swaption in Excel that surpasses what is offered by expensive commercial products.In fact, 14 different modelling approaches are implemented, whereby the Black approach does not...
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Credit Default Swap (CDS) Pricing in Excel using QuantLib

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Free and open source QuantLib supports the precise valuation of Credit Default Swaps (CDS) in Excel.  Table Of Contents​ CDS Description Creating a slimmed-down CDS object in 13 secondsCreating a full-fledged CDS objectUnderstanding the main formulaBrowsing the contents of a created CDS objectUsing the CDS objectThe Price functionAddition...
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Over 30 Bond Risk Management Functions in Excel: Clean & Dirty Price, Yield, Duration, Convexity, BPS, DV01, Z-spread etc

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Free and open source QuantLib is capable of calculating several risk measures associated with the pricing of bonds and allows you to get in Excel quantities like clean and dirty price, duration, convexity, BPS, DO01, Z-spread etc.I have already showed you how to build a yield curve out of clean bond prices using either a parametric or non...
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Excel Builder and Cash Flow Viewer for Non-Standard Interest Rates Swaps

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Building, pricing and analyzing even non-standard interest rate swaps in Excel becomes a simple exercise when the Deriscope interface to the open source QuantLib analytics library is employed.We have already encountered a simple interest rate swap contract in the Yield Curve Building in Excel using Swap Rates article, where vanilla swaps were used ...
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Time for a coffee break? Understanding Time and its implications on Interest Rates

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With this article I want to give you an intuitive feeling of the concept of interest rate and also show you how to work with various types of interest rates – such as a compounded interest rate - in Excel as accurately as market professionals do.  Table Of Contents​ The Primitives: Time and Money How did our prehistoric ancestors measure ...
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Parametric Yield Curve Fitting to Bond Prices: The Nelson-Siegel-Svensson method

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When it comes to building a yield curve out of bond prices, QuantLib can handle both non-parametric and parametric methods, both deliverable to Excel through Deriscope.The former have been demonstrated at my articles Yield Curve Building in Excel using Bond Prices (QuantLibXL vs Deriscope and Bootstrapping in Excel a Yield Curve to perfectly fit Bl...
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Yield Curve Building in Excel using Bond Prices (QuantLibXL vs Deriscope)

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With this article I want to show you how to create a yield curve in Excel by bootstrapping bond prices, using the open source QuantLib analytics library. I will present both alternative spreadsheet interfaces to QuantLib, which are the QuantLibXL and Deriscope.For a production-ready setup using actual Bloomberg quotes of US Treasuries, look at Boot...
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Yield Curve Building in Excel using Deposits, Futures and Swaps

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With this article I want to show you how to create a yield curve in Excel using the open source QuantLib analytics library, when the input market data are a mixture of deposit rates, futures prices and swap rates.I have already written how you may build a yield curve using a single type of market instruments, such as deposits, futures or swaps...
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Yield Curve Building in Excel using Swap Rates

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With this article I want to show you how to create a yield curve in Excel using the open source QuantLib analytics library, when the input market data are swap rates. I will also show you how to apply dual bootstrapping when an exogenous yield curve is present.For short term maturities – typically less than a year – the yield curve may be built out...
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