Category: Essential Concepts for Level II

09-12-19 Essential Concept 71: Value of a Bond and its Credit Spread, Given Assumptions about the Credit Risk Parameters

For credit analysis of a risky bond in a volatile interest rate environment, we use the arbitrage-free framework. The first step in the arbitrage-free framework is to build the binomial interest rate tree under assumption of no arbitrage. Once the tree is built we need to verify that it is correctly calibrated. Analyzing a fixed-coupon corporate bond: This tree can then be used to analyze a fixed-coupon corporate bond. The steps are: Determine value of bond assuming no default (VND) Calculate credit valuation adjustment (CVA) Fair value of bond = VND – CVA Using fair value determine YTM. Using YTM… Read More

101 concepts level II

09-12-19 Essential Concept 72: Credit Analysis of Securitized Debt

Credit analysis of structured debt requires a different approach compared to credit analysis of other risky bonds. There are three major factors to consider when evaluating asset-backed securities (ABS): Underlying collateral – Granularity and homogeneity describe the underlying collateral. Granularity refers to the number of obligations in the overall structured financial instrument. Homogeneity refers to the degree to which the underlying debt characteristics within a structured financial instrument are similar across individual obligations. Three major credit analysis approaches can be used for ABS: book of loans, portfolio, loan by loan. The appropriate approach depends on the asset type, tenor and… Read More

101 concepts level II

09-12-19 Essential Concept 73: CDS Description; Single Name and Index CDS

A credit default swap is a derivative contract between two parties, a credit protection buyer and credit protection seller, in which the buyer makes a series of cash payments to the seller and receives a promise of compensation for credit losses resulting from the default of a third party. The figure below shows the structure of payment flows. The ISDA master agreement is a document that lays down the rules that all CDS contracts must conform to and other guidelines for the functioning of the CDS market. Each CDS contract has a notional amount and maturity date. The debt… Read More

101 concepts level II

09-12-19 Essential Concept 74: Credit Events and Settlement Protocols

Credit event is an event that defines default by the reference entity. When a credit event occurs, the protection seller makes a payment to the protection buyer. Three general types of credit events include: Bankruptcy Failure to pay Restructuring If credit event has occurred, two parties to a CDS have the right to settle the CDS. Settlement can happen in two ways: Physical settlement: The debt instrument (reference obligation) is delivered by the protection buyer to the protection seller in exchange for a payment equal to the notional amount of the CDS contract Cash settlement: The credit protection seller pays… Read More

101 concepts level II

09-12-19 Essential Concept 75: Principles and Factors which Influence CDS Pricing

Basic pricing concepts: Probability of default: probability of non-payment of an upcoming interest or principal obligation. Since CDS typically cover a multi-year horizon, we use the hazard rate to calculate the probability of default for each year. Hazard rate: probability that an event will occur given that it has not already occurred. It is a conditional probability. Ex: death. Probability of survival: Given the hazard rate, the probability of survival is calculated as: 1 – hazard rate. Loss given default: amount that will be lost if a default occurs. Expected loss: full amount owed minus the expected recovery. It is… Read More

101 concepts level II

09-12-19 Essential Concept 76: FRA Pricing and Valuation

A forward rate agreement is an over-the-counter forward contract in which the underlying is an interest rate. FRAs are usually expressed in the “X x Y” convention, ‘X’ represents the point where the underlying loan starts. This also the point where the FRA expires. ‘Y’ represents the point where the underlying loan ends. A 3 x 9 FRA is depicted in the figure below. The FRA fixed rate i.e. price of an FRA can be calculated using these steps: Set up the time line. Compute the de-annualized fixed rate: Annualize by multiplying by 360/(n2 – n1) The FRA value for… Read More

101 concepts level II

09-12-19 Essential Concept 77: Fixed-Income Forward and Futures Contracts

Unique issues: Quoted priced, accrued interest and full price: The quoted price is the clean price without the interest accrued since the last coupon date. The full price is the quoted price plus interest accrued since the last coupon date. Conversion factor: Fixed-income futures contracts often have more than one bond that can be delivered by the seller. Because bonds trade at different prices based on their maturity and stated coupon, an adjustment known as the conversion factor is used to make all deliverable bonds roughly equal in price. Cheapest to deliver bonds: However, even after applying the conversion factor… Read More

101 concepts level II

09-12-19 Essential Concept 78: Interest Rate Swaps

A swap is an over-the-counter contract between two parties to exchange a series of cash flows based on some pre-determined formula. In a plain vanilla interest rate swap one party pays fixed rate, whereas the other party pays a floating rate. Swap fixed rate = (1 – final discount factor) / (sum of all discount factors) Value of a fixed rate swap at Time t = Sum of the present value of the difference in fixed swap rates x Stated notional amount Example: Suppose two years ago we entered a €100,000,000 seven-year receive-fixed Libor-based interest rate swap with annual… Read More

101 concepts level II

10-12-19 Essential Concept 79: Binomial Model: Expectations Approach

The expectations approach is given by the following equations: c = PV[πc+ + (1 – π)c–] and p = PV[πp+ + (1 – π)p–] π = the risk-neutral probability of an up move = (1 + r – d) / (u – d) The expected terminal option payoffs can be expressed as: E(c1) = πc+ + (1 – π)c– and E(p1) = πp+ + (1 – π)p– The option values can be written as: c = PV[E(c1)] and p = PV[E(p1)] With the expectations approach, The probability, π, is objectively determined and is called the risk-neutral (RN) probability. No assumption… Read More

101 concepts level II

10-12-19 Essential Concept 80: The BSM Model

The inputs to the BSM model are: Price of underlying stock, S Continuously compounded risk-free rate, r Time to maturity in years, T Strike price, X Volatility of the underlying in annual percentage terms, σ The BSM model for non-dividend paying stock is: c = SN(d1) – e–rTXN(d2) p = e–rTXN(–d2) – SN(–d1) where: Using the above inputs, the BSM model can be used to predict: Call option price, c Put option price, p Instructor’s Note: The following tips will help you remember the formulas. c = SN(d1) – e–rTXN(d2) p = e–rTXN(–d2) – SN(–d1) A call option is of… Read More

101 concepts level II