Introduction to Credit Risk

1. Introduction to Credit Risk • Credit Risk vs Market Risk • Credit Risk is the risk of the other side not paying! This is a “default”… • Failure to pay an interest amount or return all of principal amount • How do we typically measure it? • How do we manage it? • Pledged collateral, posted margin, keep loss reserves, hedging with CDS • You can think of “credit risk” as: • Issuer Risk • Counterparty Risk • Settlement Risk (the time it takes until it’s inventory) • Counterparties are sometimes Issuers… • Probability of Default : “PD” • Loss Given Default : “LGD” • Expected Loss : “EL” • Simplified Formula : EL = PD * LGD • Look up LGD’s by quality code (in SBB_ratings.h/cc - an example is ifdef’d) • LGD is a fraction so the total LGD of the position = Amount * LGD • This is the amount we would lose if counterparty defaulted • A type of credit risk sensitivity: • How does my credit risk change on a ratings downgrade?

2. Mid-Term Submission Reqs – Due Oct 23 • An executable which will build and run on either Linux or Mac using GNU • Deliver an archive tar file named “yourname.tar” - create using: “tar cvf yourname.tar .” in your directory • Build by typing “make all”, launch with shell script “run.sh” • Direct debug to stderr, file descriptor 2 (see run.sh) • Encapsulate your main with “START_TIMER() and END_TIMER() • Price and calculate for each for bond position in file • Given YIELD or SPREAD, compute price, dv01 and risk • Handle both coupon bearing and zero coupon types (key off coupon value - either zero or non-zero) • Our definition of “risk” is: “dv01/100 * amount” - dv01 is in percent and amount is in thousands • Search positions in our portfolio according to below criteria and write out to separate file (“results.txt”) • Largest long position (write out the Amount) • Largest short position (write out the Amount) • Position with most risk (can be either long/positive) or short/negative (Write out the Risk number) • Total risk for the whole portfolio (write out the total Risk number) • Load input files will be called: “tradingbook.txt” and “yieldcurve.txt” • For spread priced bonds find closest maturity treasury bond. On a tie choose shorter maturity treasury. • Required output format • For the individual bond results append to the end of each line read in from tradingbook.txt • … Price dv01 risk LGD • LGD will be adjusted by amount (like risk) • For portfolio measures write out 4 numbers (one per line) to file “results.txt” • The timer output writes out to stdout by default so: • Execute run.sh to call your executable and the only thing displayed should be the timer output • Units: • Show 3 decimal places for all measures • Amounts will be in thousands - 1,000 means 1 million “face amount” • Code example

3. Upcoming deliverables after mid term… • One week before mid-term submission • NYU is officially closed HOWEVER I will have office hours to answer questions. I’ll have my laptop to show examples. • Reachable by email • Mid-term submission lecture • First phase submission of project on thumb drive (done individually) • Have teams formed for upcoming phases (from here on we will work in teams) • Surgeon (lead) • Tester (second graded phase will be a test harness client-side driver that hits our to be built server, Co-pilot/toolsmith/language lawyer… • One week after mid-term lecture • Second quiz of MMM chapters 7-13 • Three weeks after mid term lecture: • Second phase submission • Server built with version 1 of your message set defined • Stub client in python • Your regression harness is now your executable loading tradingbook.txt with answers inserted • The tradingbook.txt and results.txt file will be posted on class page after mid term submission • Submission will be a server and a client • The client will write results to stdout • Specification of results to follow…

4. The “Risk” Measure (market) • Position adjusted sensitivity using 1 basis point change • Example of “bond risk”: • Price (pv): 85.731991 (that’s a total amount of $857.31 the bond is worth) • DV01: 0.092519 (how much price moves with a 1/100 of 1% change in yield = .01) • amount: 10000 (10,000 is 10MM “position”) • Position risk: 9.251928 (that’s $9,251 change to position value given a 1bp move) static double bond_risk( const SBB_bond_calculator_interface* bond_calc_ptr, const SBB_instrument_fields* bond_record_ptr, double dv_bump_amount) { double pv = bond_calc_ptr->PV(bond_record_ptr->Yield() ); double dv = bond_calc_ptr->dv_bump(bond_record_ptr->Yield(), pv, dv_bump_amount); double position_risk = bond_record_ptr->Amount() * dv/100.0; return position_risk; }

5. Units examples • $10,000,000 of a bond • 9% coupon, 20 years to maturity - current price: 134.672 and yield is: 6% • Market value is: $10,000,000 * 1.346722 = $13,467,220 • Bump yield by up by 100 basis points (1%) and price is now: 121.3551 • Our data file has amounts in 000’s so $10,000,000 would be entered as 10000 • Dollar Value of an “01” (DV01) - price diff between starting yield and 1/100th of a percent move of yield, or 1 basis point, (1/100th of above example). Additionally, it is the average of two shifts: the absolute value of the differences resulting from both an up and down move. • “Risk” for us is defined as Amount * DV01/100 and thus stays in thousands since Amount is in thousands. • Risk of 44.123 means for every basis point change in yield we would gain/lose $44,123. • double yield_delta_abs = fabs(bump_amount); • // yield goes up, price goes down • double down_price = PV(base_yield + yield_delta_abs); • double price_delta_down = base_price - down_price; • // yield goes down, price goes up • double up_price = PV(base_yield - yield_delta_abs); • double price_delta_up = up_price - base_price; • dv01 = (price_delta_up + price_delta_down ) / 2.0;