Structured products occupy a distinctive space in modern capital markets, sitting at the intersection of derivatives engineering, quantitative finance, and investment product design. Unlike standard financial instruments such as vanilla options, swaps, or bonds—which are typically defined by relatively simple payoff formulas and well-establish...
In my previous article I showed how one can use Deriscope in Excel to calculate through Monte Carlo simulation the price of a European style equity linked note that paid once at maturity an amount linked to the minimum of two equity indices observed at that time. With the current article I start a series of posts that address the valuation of ...
Setting up an interest rate swaption trading desk is a complex endeavor. 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) s...
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...
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 ...
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...
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 ...
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...
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...
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 trade...
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-...
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...
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...
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...
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...
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 C...
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 s...
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...
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 yie...
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...
