CS计算机代考程序代写 finance Financial Engineering

Financial Engineering
IC302
9. Structured Products
David Oakes

Autumn Term 2020/1

Structured Finance
2

Structured Finance
• Structured finance involves the use of advanced techniques and legal structures to solve problems not easily solved by ordinary debt and equity financing.
• The structures created are often tailored to the needs or constraints of specific issuers or groups of investors.
• In some cases, structured finance may involve financial engineering in which vanilla or exotic derivatives are combined with underlying assets to create products with specific risk profiles or return characteristics.

Structured Finance
• Securitisation
• Tranching
• Structured Investment Products
4

Securitisation
5

Securitisation
• Securitisation is a structured finance technique in which assets or receivables that generate cash flows are
purchased by a special purpose vehicle (SPV) that simultaneously issues securities that are sold to investors.
• The purchase price paid by investors for the securities is used to fund the purchase of the assets.
• The cash flows generated by the assets are used to pay interest and principal on the securities sold to investors.
6

Securitisation
• The securitised assets or receivables are sometimes
referred to as the collateral or the collateral pool.
• The purpose of securitisation is to convert illiquid assets
into a security or securities that can be sold to investors.
7

Securitisation Types
• Mortgage-backed securities (MBS) based on residential (RMBS) or commercial (CMBS) mortgage loans
• Asset backed securities (ABS) based on consumer loans (e.g. credit cards or auto loans) or commercial receivables
• Whole business securitisation (WBS) based on entire receivables of an operating business (e.g. ticket revenue)
• Collateralised debt obligations (CDO) with multiple classes or tranches of securities, each with a different exposure to credit risk or priority of access to cash flows
8

Motives for Securitisation
• Cheaper funding and credit arbitrage
• Alternative funding source
• Balance sheet benefits
• Reduce required regulatory capital
9

Originator
Source: R. Wall, J. Richardson, and H. Bowkett, Guide to a standard securitisation, Thomson Reuters UK Practical Law
10

Originator
Total Business Receipts
Source: R. Wall, J. Richardson, and H. Bowkett, Guide to a standard securitisation, Thomson Reuters UK Practical Law
11

Originator
Total Business Receipts
Receivables to be securitized
Source: R. Wall, J. Richardson, and H. Bowkett, Guide to a standard securitisation, Thomson Reuters UK Practical Law
12

Originator
Total Business Receipts
Receivables to be securitized
Obligors in respect of receivables
Source: R. Wall, J. Richardson, and H. Bowkett, Guide to a standard securitisation, Thomson Reuters UK Practical Law
13

Originator
Originator establishes SPV
Source: R. Wall, J. Richardson, and H. Bowkett, Guide to a standard securitisation, Thomson Reuters UK Practical Law
SPV
Total Business Receipts
Receivables to be securitized
Obligors in respect of receivables
14

Originator
Source: R. Wall, J. Richardson, and H. Bowkett, Guide to a standard securitisation, Thomson Reuters UK Practical Law
15

Originator
SPV
Transfers rights to receivables
Source: R. Wall, J. Richardson, and H. Bowkett, Guide to a standard securitisation, Thomson Reuters UK Practical Law
16

Originator
SPV
Transfers rights to receivables
Purchase price
Source: R. Wall, J. Richardson, and H. Bowkett, Guide to a standard securitisation, Thomson Reuters UK Practical Law
17

SPV
Source: R. Wall, J. Richardson, and H. Bowkett, Guide to a standard securitisation, Thomson Reuters UK Practical Law
18

Securitised receivables
SPV
Income
Source: R. Wall, J. Richardson, and H. Bowkett, Guide to a standard securitisation, Thomson Reuters UK Practical Law
19

ABS
Investors
Securitised receivables
SPV
Income
Source: R. Wall, J. Richardson, and H. Bowkett, Guide to a standard securitisation, Thomson Reuters UK Practical Law
20

Investors
Securitised receivables
SPV
Income
ABS ABS price
Source: R. Wall, J. Richardson, and H. Bowkett, Guide to a standard securitisation, Thomson Reuters UK Practical Law
21

Investors
Securitised receivables
SPV
Income
ABS ABS price
ABS interest and principal payments
Source: R. Wall, J. Richardson, and H. Bowkett, Guide to a standard securitisation, Thomson Reuters UK Practical Law
22

Collateral Transfer and the SPV
• Securitisation often involves a true sale of the underlying
receivables (sometimes called the collateral) to the SPV.
• SPV must be established so as to ensure that it is:
– Insolvency remote (i.e. that it is unlikely to be subject to insolvency proceedings and that, in any event, it will be unaffected by the insolvency of the originator)
– Treated separately from the originator
• This protects investors in the ABS from any claims made by creditors of the originator, should the originator become insolvent.
23

Collateral Transfer and the SPV
• In some cases, economic interest in receivables is transferred to SPV through a sub-participation rather than
a true sale, or the originator may place the receivables in a trust with the SPV as the beneficiary.
24

Credit Enhancement
• Over-collateralisation: the total value of the collateral assets held by the SPV may be greater than the nominal value of the asset-backed securities it issues
• Retained spread: difference between what the SPV earns on the collateral and what it pays investors in its securities
• Insurance: monoline insurance industry severely damaged by credit crisis, so reliance on external insurers is no longer common
25

Credit Enhancement
• Tranching: SPV can enhance the credit quality of some of the securities that it issues by creating other securities that are linked to the same collateral but subordinated to them. This is a collateralised debt obligation (CDO).
• We look at tranching and CDOs in the next section.
26

Tranching

Collateralised Debt Obligations
• A collateralised debt obligation (CDO) is a securitisation in which the SPV issues multiple classes or tranches of securities that are linked to the same pool of collateral assets but have claims of differing priority over the assets.
• The subordinated tranches absorb the initial losses on the collateral, and the senior tranches only suffer losses once the tranches subordinated to them are exhausted.
• This reduces the expected loss on the senior tranches, improving their credit quality.
28

Collateralised Debt Obligations
• The more senior tranches have less credit risk, so attract a higher credit rating and pay a lower coupon interest rate.
• Different tranches have different degrees of exposure to the credit risk of the collateral pool, so they can be sold to investors with different appetites for that risk.
• We saw this same mechanism at work in lecture 4 when we discussed CDS index tranches.
29

CDO Tranches
Securi8sed” receivables”
Income”
SPV”
Note”issuance”
Cash”
AAA”
AA”
A”
Principal” and”interest” payments”
Senior”
Mezzanine” Equity”
BBB”
BB”
Equity”
30

CDO Tranches
• The CDO illustrated above contains a senior tranche, which is rated AAA; mezzanine tranches of varying
degrees of subordination that carry ratings ranging from AA to BB; and an equity tranche that is not rated.
• Some CDOs have multiple senior tranches, the most senior of which is called the super-senior tranche.
31

Defining CDO Tranches
• Attachment point: the fraction of the total notional amount of securities issued in the CDO that consists of tranches that are subordinated to the tranche
• Detachment point: the fraction of the total notional amount of securities issued in the CDO that consists of the tranche itself and the tranches that are subordinated to it.
• Difference between attachment point and detachment point for a tranche is the tranche width.
32

Tranche Losses
• A tranche will begin to suffer losses when credit losses on the receivables exceed a level defined by its attachment point multiplied by the total notional amount.
• A tranche will be exhausted when losses reach a level defined by its detachment point multiplied by the total notional amount.
• For example, a 5-10% tranche will begin to suffer losses once 5% of the notional amount is lost to default and will be exhausted when losses reach 10% of the notional.
33

Tranche Losses
• The attachment point is sometimes called the
subordination level of the tranche.
• It reflects the level of credit support that the tranche
enjoys because of the tranches that are subordinated to it.
34

Tranche Width and Loss Severity
• Other things remaining equal, a tranche with a higher attachment point will be less risky than a tranche with a
lower attachment point, since the securitised receivables must suffer a larger amount of losses before the tranche with the higher attachment point is affected.
• But the expected loss on a tranche, and therefore its credit risk, is also affected by the tranche width.
35

Tranche Width and Loss Severity
• Consider, for example, two hypothetical tranches based on the same collateral pool, each with an attachment
point of 18%, but one with detachment point 20% and the other with detachment point 22%.
• For a given absolute loss beyond the attachment point, the loss severity (i.e. the proportion of the tranche lost) is greater for the narrower tranche.
• For example, if 20% of the notional is lost to default, the 18-20% tranche would suffer a total loss but an 18-22% tranche would have suffered a loss rate of just 50%.
36

CDOs and Default Dependence
• Structuring the credit risk in a collateral pool by issuing tranches with differing subordination creates securities
that are exposed to default dependence as well as to the average or expected pool default probability.
• Higher default dependence or correlation means that entities are more likely to default at the same time.
• This increases the expected loss on the senior tranche, since it will suffer a loss if many entities default.
37

CDOs and Default Dependence
• At the same time, higher correlation means that the most subordinated tranche (also known as the equity tranche) may sometimes escape losses, making it less risky.
• Lower default correlation will have the opposite effect, reducing the expected loss on the senior tranche and increasing the expected loss on the equity tranche.
• We saw this same dependence on default correlation when we discussed CDS index tranches in lecture 4.
38

Correlation and Loss Distribution
Lower default correlation Higher default correlation
39

Correlation and Tranche Spreads
• Coupons or spreads paid to investors in CDO tranches will reflect this dependence on default correlation.
• Spreads on senior tranches will be increasing in default correlation, since higher correlation increases their risk.
• Spreads on deeply subordinated (equity) tranches will be decreasing in default correlation, since higher correlation makes these tranches relatively less risky.
• Spreads for tranches with intermediate subordination may have complex relationships with default correlation.
40

Tranche Spreads and Correlation
41

Modelling CDOs

Modelling CDOs
• When designing CDOs, we need to be able to estimate the expected losses for tranches with specific attachment and detachment points, given the default characteristics (including default correlation) of the collateral pool.
• This can be done through Monte Carlo simulation.
• These simulations are often based on the Gaussian copula model, which offers a simple way of modelling credit losses on a portfolio when the defaults or times to default of different borrowers are correlated (see Hull, ch. 24).
43

Simplified CDO Simulation
Simulation specifications
Simulation results for tranches
Attachment
PD
EL
# trials
100,000
0%
39.1100%
16.670%
3%
0.2400%
0.0650%
7%
0.0000%
0.0000%
Run simCDO
Portfolio
Loan
PD
LGD
EAD
w
1
1.00%
50%
100
0.1
2
1.00%
50%
100
0.1
3
1.00%
50%
100
0.1
4
1.00%
50%
100
0.1
5
1.00%
50%
100
0.1
6
1.00%
50%
100
0.1
7
1.00%
50%
100
0.1
8
1.00%
50%
100
0.1
9
1.00%
50%
100
0.1
10
1.00%
50%
100
0.1
11
1.00%
50%
100
0.1
12
1.00%
50%
100
0.1
13
1.00%
50%
100
0.1
14
1.00%
50%
100
0.1
15
1.00%
50%
100
0.1
44

LHP Model
• LHP model is a limiting case of the Gaussian copula in the sense that it assumes that the reference portfolio contains
infinitely many credits and that the credits have the same default probability, recovery rate and correlation.
LHP assumptions
PD
LGD
w
1.00%
50%
0.9
LHP analysis
Attachment
d(K)
E(Loss(0,K))
Tranche expected loss
0%
-1.83181975
0.16632%
5.54415%
3.00%
-2.06160843
0.26765%
2.53323%
7.00%
0.50000%
0.24983%
100.00%
• It captures the impact of market variables such as average spread, average correlation, and average recovery rate.
45

Mortgage-Backed Securities

Mortgage-Backed Securities
• A securitisation in which the collateral pool consists of
mortgage loans is a mortgage-backed security (MBS).
• MBS accounted for 49% of European securitisation
issuance and 85% of US securitisation issuance in 2019.
• Most MBS collateral is residential mortgages.
• The total amount outstanding of mortgage-related securities in the US in 2019 was $10.3 trillion, versus $16.7 trillion of US Treasury debt.
Source: AFME, Securitisation Data Report Q2: 2020.
Source: SIFMA (https://www.sifma.org/resources/research/fixed-income-chart/ accessed 22 November 2020.
47

US Agency MBS
• Most US MBS are issued by US federal government agencies or government sponsored entities (GSEs):
– Government National Mortgage Association (GNMA) (a government agency that is part of the Department of Housing and Urban Development)
– Federal National Mortgage Association (FNMA)
– Federal Home Loan Mortgage Corporation (FHLMC).
• These issuers are known as ‘Ginnie Mae’ (GNMA), ‘Fannie Mae’ (FNMA) and ‘Freddie Mac’ (FHLMC).
48

US Agency MBS
• These entities buy mortgage loans originated by banks and package them into securitisations.
• These may be ‘pass-through’ MBS, tranched collateralized mortgage obligations (CMOs), or other structures.
• Fannie Mae and Freddie Mac have operated under a conservatorship of the US government since October 2008, as a result of losses suffered in the financial crisis.
• Agency MBS carry explicit or implicit guarantees of the US government and have relatively little credit risk.
49

Prepayment Risk in MBS
• In some countries (e.g. USA), borrowers in fixed-rate mortgages may repay their mortgage early or accelerate repayment without financial penalty.
• They have an incentive to do so if rates fall, since they can then refinance by taking out a new loan at a lower rate.
• Financially-motivated prepayment disadvantages lenders, since the value of the mortgage loan (like the price of a bond) would otherwise have increased as rates fell.
50

Prepayment Risk in MBS
• Prepayment also adversely affects MBS investors, since prepayment of the mortgage loans will result in accelerated repayment of principal in the MBS.
• With interest rates at lower levels, the investors would have preferred to keep receiving the scheduled payments rather than having to reinvest the principal at lower rates.
• Investors in MBS are subject to prepayment risk.
51

Price Compression in MBS
• Prepayment risk produces price compression in MBS:
• The impact of prepayment risk on the value of the MBS is very like that of the imbedded option in a callable bond.
MBS’Price’
Early’redemp6on’price’
MBS'(no’prepayment’risk)’ MBS'(with’prepayment’risk)’
Price’compression’due’to’ prepayment’risk’
Interest’Rates’
52

Negative Convexity in MBS
• MBS may have negative convexity at low levels of rates, due to increased value of embedded prepayment option:
• Fall in rates reduces the expected life of the MBS and may reduce, rather than increase, its sensitivity to interest rates as measured by duration or basis point value.
MBS’Price’
Value’of’MBS’without’ prepayment’risk’
Value’of’MBS’with” prepayment’risk’
MBS'(no’prepayment’risk)’ MBS'(with’prepayment’risk)’
Value’of’prepayment’‘op>on’’
Interest’Rates’
53

Cash Flow Waterfall in CMOs
• In our earlier discussion of CDOs, the main objective of tranching was to reallocate exposure to credit risk.
• Subordinated tranches protected senior tranches from default by being the first to absorb losses from default.
• In CMOs, however, the objective of tranching may sometimes be to reallocate cash flows from the collateral pool in order to mitigate the impact of prepayment. The focus of these CMOs is on the cash flow waterfall.
• This is especially true of US agency CMOs.
54

CMO Structures
• Sequential Pay
– ‘Plain vanilla’ CMO in which tranches pay on a fixed
schedule and receive regular interest payments
– Principal payments are applied to the first tranche until it is retired, then to the second tranche, and so on until all the tranches have been retired.
– First tranche may have average life of 2 to 3 years, second tranche 5 to 7 years, third tranche 10 to 12 years, and so on.
55

CMO Structures
• Planned Amortization Class (PAC)
– Fixed principal payment schedule directs cash-flow irregularities caused by varying prepayments away from the PAC tranche and toward a companion tranche.
– If prepayments are slow, the PAC will receive principal first and the companion will wait.
– If prepayments are fast, the PAC will get only what
is scheduled, and the companion class will absorb the rest.
• Companion tranche
– Supports PAC tranche by absorbing prepayment variability. – Higher return to compensate investors for uncertain life
56

CMO Structures
• Targeted Amortization Class (TAC)
– PAC tranches maintain their payment schedules over a
range of prepayment speeds
– TAC tranches only do so for a specified prepayment speed
• Z-tranche
– Pay no interest until end of a specified lockout period
– Z-tranche is credited with accrued interest, which increases the face amount of the tranche on each payment date.
– During accrual period, investor does not face the risk of reinvesting at lower rates if the market yield declines.
– Also known as accretion bonds or accrual bonds
57

CMO Structures
• Principal-only (PO) securities
– Investors receive principal-only payments from collateral. – Investors purchase PO tranche at discount to its face value. – Market value fluctuates with changing prepayment rates.
• Interest-only (IO) securities
– IO security is created to complement PO security.
– As principal is prepaid, the cash flow on the IO will decline.
– When interest rates increase, market value of IO securities may also rise (reverse of usual pattern for fixed income).
– IO securities are often used to hedge existing portfolios.
58

Securitisation and the Crisis
• Securitisations based on mortgage loans played a major role in the financial crisis of 2007-9.
• Many investors suffered substantial losses on mortgage- related debt, especially in tranches of CMOs and other structured investment products.
• This triggered a credit and liquidity crisis that spread to other market sectors, causing widespread disruption.
• Financial institutions failed and massive state intervention was required restore markets and aid economic recovery.
59

Contributing Factors
• Moral hazard in ‘originate-to-distribute’ model
• Weakened lending standards
• Problematic assets (e.g. sub-prime mortgages)
• Complex products (e.g. CDO of CDO or CMO of CMO)
• Over-reliance on mathematical models
• Inadequate and poorly understood credit ratings process 60

Default Correlation and the Crisis
• As we have seen, tranched products are highly dependent on default correlation between the underlying assets.
• The collapse in the housing market that began in 2007 not only increased the number and rate of defaults, but also dependence among defaults.
• Default dependence also increased in other types of securitised collateral.

Default Correlation and the Crisis
• This had not been anticipated when the CMOs and CDOs linked to this collateral were designed and rated.
• The increase in default correlation under stressed market conditions led to losses on senior tranches that were much higher than had been expected and much larger than the expected loss consistent with their ratings.
• This effect was magnified in more complex products such as CDOs of CDOs, with disastrous consequences.
62

Structured Products: Capital Protection

Structured Products
• A structured product is an investment that promises a payoff or return that is linked to some underlying asset or
market, but where that payoff has been modified in some way relative to a simple long position in the asset.
• Structured products are created through financial engineering by combining traditional assets (equity, fixed income, commodities) with vanilla or exotic derivatives to produce modified payoffs and risk profiles.
64

Objectives of Structured Products
• Express a client view
• Target a specific risk profile
• Tax optimization
• Capital protection
• Yield enhancement
65

Risk in Structured Products
• Complex payoffs can make it hard for investors to assess properly the risk of structured investment products.
• Most structured products do not trade in liquid markets.
• Investors in structured products therefore face:
– Market risk (exposure to the underlying asset or assets)
– Credit risk (exposure to issuer of structured investment) – Liquidity risk
66

Capital Protected Note
• Capital protected products promise the return of all or a specified fraction of the invested amount at maturity.
• In addition to capital protection, a capital protected equity-linked note offers the investor a return (in the form a coupon paid at maturity) equal to all or a specified fraction of the increase in an equity price or index during the life of the note. This fraction is the participation rate.
67

Equity-Linked Note
• Consider the following capital-protected note linked to the S&P 500 equity index.
5-year note
Issue price $100,000
100% capital protection
75% participation in S&P 500
• How would we structure or engineer this note?
68

Structuring the Note
• Capital protection is funded by using part of the initial investment to buy a risk-free zero-coupon bond with face value equal to that of the note.
• Equity-linked return is generated by using the remaining cash (less any fees kept by the structuring bank) to purchase call options on the S&P 500 index.
69

Structuring the Note
s
Zero- Coupon Bond
PV(100)
Initial investment = 100
Issue Date
70

Structuring the Note
s
Capital Protection
100
Zero- Coupon Bond
PV(100)
Initial investment = 100
Issue Date Maturity Date
71

Structuring the Note
S&P 500 Index Calls
Capital Protection
100
Zero- Coupon Bond
PV(100)
Initial investment = 100
Issue Date Maturity Date
72

Structuring the Note
S&P 500 Linked Return
S&P 500 Index Calls
Capital Protection
100
Zero- Coupon Bond
PV(100)
Initial investment = 100
Issue Date Maturity Date
73

Initial Market Conditions
• Suppose that market conditions on the issue date are:
S&P 500 index level 1200 5-year interest rate 2.89% S&P 500 index dividend yield 2.00% S&P 500 index volatility 20%
• Ignore any fees kept by the structuring bank.
• What participation rate can we offer on the note?
74

Capital Protection
• Funding the 100% capital protection means we will need need $100,000 (the note’s face value) to repay the investors when the note mature five years from now.
• With five-year interest rates at 2.89%, the price of a five- year zero coupon bond with face value $100,000 will be:
𝑃𝑉 = 𝐹𝑉 = $100,000 = $86,723 1+𝑟 ! 1+0.0289 ”
• After funding the capital protection, we will be left with $100,000 – $86,723 =$13,277 of the initial investment.
75

Equity Participation
• We use this to buy 5-year call options on the S&P 500, with strike price equal to 1200 (the current index level).
• How many options will we be able to buy?
76

Equity Participation
• At current volatility levels, an option giving full exposure to the index costs 212.48 index points.
• This is 212.48/1200 = 17.707% of the index strike level.
77

Equity Participation
• Buying enough options to give 100% participation in the index on the initial investment of $100,000 would therefore cost 17.707% of $100,000, or $17,707.
• But we have only $13,277 left after funding the capital guarantee, so the most we can offer to investors is $13,277/$17,707 = 75% participation in the index.
78

Payoff at maturity
100
Capital Protected Equity-linked Note
Long index call
Long index
Capital protection
Long index call (75%) Index level
79

Opportunity Costs and Risks
• Investor receives no coupon if the index does not go up. Had she invested in a risk-free bond, she would have earned 2.89% per year, or 15.31% over 5 years. This foregone interest is a significant opportunity cost.
• The note pays a coupon based on a specified participation in any gains in the index. Had the investor been invested in stocks, she would also have earned dividends.
• This is also a significant cost: the note pays 75% of any gains in the index, not 75% of the total return on stocks in the S&P 500 index, which would have included dividends.
80

Opportunity Costs and Risks
• The investor is also exposed to the credit risk of the bank that issues the structured note.
• In a long-dated note, this can be quite significant.
• Note that the investor is long the index level and long the volatility of the index (because she is long options).
81

Factors Affecting Participation
• Interest rate
• Dividend Yield • Volatility
Higher Funding Rate
Higher Volatility
82

Increasing the Participation Rate
• We can modify the structure in any number of ways to increase the apparent participation rate.
• Maturity
• Strike price
• Capital protection level
• Barrier options
• Selling call or put options at other strikes
83

Increasing the Participation Rate
Longer Maturity
Lower Capital Protection Level
84

Structured Products: Yield Enhancement

Reverse Convertible Note
• Some structured products focus on yield enhancement rather than capital protection.
• One example of this is a reverse convertible note.
• A reverse convertible pays an enhanced coupon relative to ordinary notes of similar credit quality, but the issuer may redeem at maturity either in cash or by paying a predetermined number of shares of some linked stock.
86

Reverse Convertible Note
• Consider a reverse convertible linked to Intel stock:
Maturity
Coupon
Linked share
Stock redemption amount
1 year
C%
Intel (current price $21.75) 45.98 shares per $1000 invested (i.e. $1000 / $21.75)
• Under what conditions will the issuer choose to redeem the note in shares rather than in cash?
• How would we structure this note?
• What coupon rate can we offer?
87

Initial Market Conditions
• Suppose that market conditions when the note is issued are as follows:
Intel stock price 1-year interest rate Intel dividend yield Intel volatility
21.75 0.25% 2.90% 20%
• Ignore any fees kept by the structuring bank.
• In effect, the investor is selling a 1-year put option on Intel
stock to the structuring bank, with strike price $21.75.
88

Embedded Put Option Value
• In current market conditions, this option is worth $2.0042.
• This is $2.0042/$21.75 = 9.21% of the stock price.
89

Structuring the Note
• The amount paid by the investor must be sufficient to finance the whole of the structure, including the coupon:
𝐼𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝐴𝑚𝑜𝑢𝑛𝑡 = 100 + 𝐶 − 𝑃𝑢𝑡 𝑂𝑝𝑡𝑖𝑜𝑛 1+𝑟
100= 100+𝐶 −2.0042 ×100 1 + 0.0025 21.75
→ 𝐶= 100+2.0042 ×100 1+0.0025 −100=9.49 21.75
• Ignoring fees, we can offer an enhanced coupon of 9.49%.
90

Risk and Reward in the Note
• The coupon is paid whether the shares go up or down in price and is higher than the coupon that would usually be offered to investors on debt of the structuring bank.
• But the return earned by the investor will depend on what happens to the share price, since if the share price falls the note will be redeemed in (depreciated) shares.
91

Risk and Reward in the Note
• What view is the investor in the reverse convertible expressing about the price of Intel stock?
• What is her view on Intel volatility?
• To what other risks is the investor exposed?
• Under what market conditions might we be able to offer a higher coupon rate?
92

Factors Affecting Coupon Rate Original Parameters Higher Volatility
93

Reverse Convertible with Barriers
• By varying the structure, we can change the risk and reward characteristics of the note.
• One way of doing this is by using barrier options.
• As we have seen, a barrier option is a call or put option that knocks in or knocks out if, during the option’s life, the underlying stock trades at a specified barrier level.
94

Reverse Convertible with Barriers
• Consider a reverse convertible with a knock-in barrier:
Value of linked share during life of note Return to Investor
Linked share goes up
100% of principal
plus enhanced coupon
Linked share goes down
Barrier (protection) level not hit
100% of principal
plus enhanced coupon
Barrier (protection) level hit
Linked shares
plus enhanced coupon
95

Knock-in Barrier
• We modify the Intel-linked reverse convertible to incorporate a knock-in barrier equal to 80% of the initial share price:
Maturity
Coupon
Linked share
Stock redemption amount
Barrier level
1 year
C%
Intel (current price $21..75)
45.98 shares per $1000 invested
(i.e. $1000 / $21.75)
80% of current share price (i.e. $17.40)
• How will we structure the note?
96

Knock-in Barrier
• Will the option the investor is giving the issuer be worth more or less than the option in the simple reverse convertible we looked at earlier?
• How will this affect the coupon that can be offered?
97

Risk and Reward
• Introducing the barrier reduces the coupon rate.
• The barrier option the investor gives the structuring bank is worth less than the vanilla put in the original structure.
98

Risk and Reward
• Why might the investor be willing to accept this less enhanced coupon?
• Would this structure be harder or easier for the structuring bank to hedge than the ordinary reverse convertible that we analyzed earlier?
99

References Main reading:
• Hull, ch. 8 and 25
• Kosowski and Neftci, ch. 20 and 21
100

101