- Interest Rate Swap-Derivative Pricing in ExcelAn interest rate swap (IRS) is a financial derivative instrument that involves an exchange of a fixed interest rate for a floating interest rate. More specifically,An interest rate swap's (IRS's) effective description is a derivative contract, agreed between two counterparties, which specifies the nature of an exchange of payments benchmarked against an interest rate index. The most common IRS is a fixed for floating swap, whereby one party will make payments to the other based on an initially agreed fixed rate of interest, to receive back payments based on a floating interest rate index. Each of these series of payments is termed a 'leg', so a typical IRS has both a fixed and a floating leg. The floating index is commonly an interbank offered rate (IBOR) of specific tenor in the appropriate currency of the IRS, for example LIBOR in USD, GBP, EURIBOR in EUR or STIBOR in SEK. To completely determine any IRS a number of parameters must be specified for each leg; the notional principal amount (or varying notional schedule), the start and end dates and date scheduling, the fixed rate, the chosen floating interest rate index tenor, and day count conventions for interest calculations. Read moreThe above description refers to a plain vanilla IRS. However, interest rate swaps can come in many different flavors. These include, (but are not limited to)Amortizing notional IRSCross-currency swapFloat-for-float (basis) swapOvernight index swapInflation swap etc.Interest rate swaps are often used to hedge the fluctuation in the interest rate. To value an IRS, fixed and floating legs are priced separately using the discounted cash flow approach.Below is an example of a hypothetical plain vanilla IRSMaturity: 5 yearsNotional: 10 Million EURFixed rate: 3.5%Floating rate: EuriborThe values of the fixed, floating legs and the IRS are calculated using an Excel spreadsheet. Table below presents their valuesClick on the link below to download the Excel spreadsheet.Article Source Here: Interest Rate Swap-Derivative Pricing in Excel
- Valuing an American Option Using Binomial Tree-Derivative Pricing in ExcelIn a previous post, we provided an example of pricing American options using an analytical approximation. Such a pricing model is fast and accurate enough for risk management purposes. However, sometimes more accurate results are required. For this purpose, the binomial (lattice) model can be used. Wikipedia describes the binomial tree model as follows,In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein in 1979. Essentially, the model uses a "discrete-time" (lattice based) model of the varying price over time of the underlying financial instrument...The binomial pricing model traces the evolution of the option's key underlying variables in discrete-time. This is done by means of a binomial lattice (tree), for a number of time steps between the valuation and expiration dates. Each node in the lattice represents a possible price of the underlying at a given point in time.Valuation is performed iteratively, starting at each of the final nodes (those that may be reached at the time of expiration), and then working backwards through the tree towards the first node (valuation date). The value computed at each stage is the value of the option at that point in time.We utilized the lattice model previously to price convertible bonds. In this post, we’re going to use it to value an American equity option. We use the same input parameters as in the previous example. Using our Excel workbook, we obtain a price of $3.30, which is smaller than the price determined by the analytical approximation (Barone-Andesi-Whaley) approach.[caption id="attachment_561" align="aligncenter" width="335"] American option valuation in Excel using Binomial Tree[/caption]Click on the link below to download the Excel Workbook.Originally Published Here: Valuing an American Option Using Binomial Tree-Derivative Pricing in Excel
- Credit Risk Management Using Merton ModelR. Merton published a seminal paper [1] that laid the foundation for the development of structural credit risk models. In this post, we’re going to provide an example of how it can be used for managing credit risks.Within the Merton model, equity of a firm is considered a call option on its asset, and it is expressed as follows,where E denotes the equity of the firm, V is the firm’s asset, is the asset volatility, B is the notional amount of the debt, r is the risk-free interest rate, andWe note that both asset (V) and its volatility are not observable. However, the asset volatility can be related to equity and its volatility through the following equation,where denotes the volatility of equity.These 2 equations can be solved simultaneously in order to obtain V and its volatility which are then used to determine the credit spreadHaving the credit spread, we will be able to calculate the probability of default (PD). Loss given default (LGD) can also be derived under Merton framework.Graph below shows the term structures of credit spread under various scenarios for the leverage ratio (B/V).[caption id="attachment_541" align="aligncenter" width="564"] Term structure of credit spread[/caption]It’s worth mentioning that the Merton model usually underestimates credit spreads. This is due to several factors such as the volatility risk premium, firm’s idiosyncratic risks and the assumptions embedded in the Merton model. This phenomenon is called the credit spread puzzle. Research is being conducted actively in order to improve the model.References[1] Merton, R. C. 1974, On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, Journal of Finance, Vol. 29, pp. 449–470. Originally Published Here: Credit Risk Management Using Merton Model
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