Publish on 25th October 2019
Category: Birds
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Credit Default Swaps atFABPart 1:

Who are the players in this Case?

Charles Bank International (CBI) is a lending institution that has in place a limit regarding loan exposure with any one client (between $100 million and $150 million is the assumed limit).CapEx Unlimited (CEU) is a loyal banking client of CBI who wants an additional $50 million loan on top of the $100 million they already have with CBI.First American Bank (FAB) is a large financial services firm with a division that offers credit derivatives (First American Credit Derivatives – FACD).

What problem does each party have?

CEU needs to borrow more money for expansion of its business enterprise.CBI wants to keep a loyal client (CEU) happy, but will have to turn away its additional business because of an internal risk practice that limits loan exposure. Wants to make loan, yet not face the risk of loan default.FAB can offer to secure the credit default risk of CEU so that it removes risk form CBI’s balance sheet. It must figure out how much to charge for this service and whether to keep or remove the risk from its own books.

Credit Default Swap

FAB

CBI

????

CEU

Periodic Fee

$ If Default Occurs

$50 mil loan

Loan Pmts

What if default occurs?

If default occurs, CBI will approach FAB to claim their “insurance.”CBI will deliver the loan to FAB and collect a payment to cover their loss from the loan (physical delivery).FAB will then retain the loan and wait for the bankruptcy courts to decide if any assets are available to repay the loan (recovery).

Should FAB keep ortransfer the risk from the CDS?

Keep: FAB holds on to the CDS and may eventually find another partially or fully offsetting position. Or, they may simply hold the risk (bet against the default happening).Transfer: FAB tries to get someone on the “other side” of the trade and just play facilitator. No (or little) risk kept on FAB’s books.

If they transfer risk…

FAB’s Problem with transferring:There is only one client willing to buy this position off of FAB. And their credit isn’t great… so you could have a situation in which CEU folds at the same time that this other firm folds. So, FAB would be stuck with the “hot potato” of risk exposure.

Possible Solution:Credit Linked Note

FAB could issue a credit linked note that will raise money from the counterparty. FAB will promise to pay a high return on this bond. The high return comes from the payments that CBI is paying.If CEU defaults and so does the new counterparty, FAB will deduct any losses from the principal of the credit linked note and will no longer be responsible for payments on the note.

Credit Linked Note

FAB

CBI

New Counterparty

CEU

Periodic Fee

$ If Default Occurs

$50 mil loan

Loan Pmts

Pays periodic Interest on Note

FAB Issues Credit Linked Note

What if Default Occurs with CEU?

FAB

CBI

New Counterparty

CEU

Periodic Fee

$ If Default Occurs

$50 mil loan

Loan Pmts

Pays periodic Interest on Note

FAB Issues Credit Linked Note

X

X

YES

FAB doesn’t pay Principal back to New Counterparty

What Periodic Fee should FAB charge for a Credit Default Swap?

Credit Default Swaps are like insurance. The Swap Bank offers to insure the event of default.A Put is also like insurance (it is the right to sell something at a given price, even if the value of the “something” has fallen).You have priced Put Options using the Black-Scholes and Binomial Pricing Models.Perhaps we can use these models to help us price FAB’s Credit Default Swap. We want a semi-annual fixed fee.

Our Roadmap for Fee Calculation

Expected Costs = Expected Revenues

Our plan of attack:

Calculate the probability of default for CEU.Given this probability, what is the expected cash flows that FAB might have to pay in the future?What is the probability that a fee will be paid? (Note: if CEU defaults and FAB pays the “insurance benefit” to CBI, the fees on the CDS will stop)Determine the appropriate rate to discount these cash flows back to today.Set the fee so that the PV of expected cash out flows for FAB equals the PV of expected cash inflows for FAB (fees received from CBI)

Probability of default for CEU

Consider the Black-Scholes Option Pricing Model for a Put:

Probabilityof Put going“in the money”

Can we Relate a Risky Bond to a Put Option?

Principal Amount

Firm/Asset Value

Payoff to Bondholder

How is a Risky Bond like a Risk Free Bond + a Short Put?

Firm/Asset Value

Payoff

Risk Free Bond

Short Put

Add these together to get the graph on previous slide… The Risky Bond!

The Put Represents the Credit Risk of the Risky Bond

Risky Bond = Risk-Free Bond + (Short Put)The risk-free bond is the price of waiting. The short put is the price of the credit risk.So, probability of default of the issuing firm is the same as the probability of the Put being “in the money.”

What’s next?

Risky Bond = Risk-Free Bond + (Short Put)

Black-Scholes assumes no cash flows paid by the underlying asset.

CEU’s Risky Bonds Pay Cash Flows (coupons). We’ll need to convert risky debt to “equivalent” zero-coupon bonds.

This will be the estimated market value of CEU’s “equivalent” zero-coupon bonds if they were Risk Free

CEU Summary Data

Face Value of Debt: $5 billionMarket Value of Debt: $4.1 billionMaturity of Debt: 5 yearsSemiannual Coupons $130 milCalculate YTM of Debt at 9.84%Equity Market Value: $6.8 billionCurrent CEU firm market value (V = D+E)… $4.1 + $6.8 = $10.9 billion

What’s next?

Risky Bond = Risk-Free Bond + (Short Put)

Black-Scholes assumes no cash flows paid by the underlying asset.

CEU’s Risky Bonds Pay Cash Flows (coupons). We’ll need to convert risky debt to “equivalent” zero-coupon bonds.

This will be the estimated market value of CEU’s “equivalent” zero-coupon bonds if they were Risk Free

$4.1 billion

Convert Risky Coupon-paying Debt to Risky Zero-Coupon Debt

We must retain 1) the bond sensitivity to interest rate risk (duration), 2) current market value of debt, and 3) current YTM.At this point, we must take a detour to explain the concept of duration.

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455_O1 Financial Markets Prof. Suman Banerjee Fall 1999