Chapter 12 Flashcards
(169 cards)
1
Q
What is the primary objective of the chapter on valuation of investments?
A
To describe how to value several types of derivatives including interest rate caps, floors, swaptions, and credit derivatives.
2
Q
What does Section I of the chapter describe?
A
A general formula that can be used to price derivatives, applied to bond options, interest rate caps and floors, and swaptions.
3
Q
What factors are considered when evaluating a securitisation?
A
Factors include the structure of the securitisation, the underlying assets, and the risk associated with cash flows.
4
Q
What is the focus of Section 3 in the chapter?
A
Evaluation of credit derivatives and a model to price corporate debt allowing for credit risk.
5
Q
What is the Black-Scholes formula used for?
A
Valuing options on shares.
6
Q
Why are interest rate derivatives more difficult to value than equity derivatives?
A
Because the behavior of an individual interest rate is more complicated than that of a stock price, and interest rates vary by term.
7
Q
What are the main classes of yield curve models mentioned?
A
- Vasicek model
- Cox-Ingersoll-Ross model
8
Q
Define arbitrage opportunity in this context.
A
An arbitrage opportunity exists when it is possible to make a risk-free profit by exploiting price differences in different markets.
9
Q
What is Black’s model used for?
A
Valuing European options assuming a lognormal distribution for the value of the underlying asset.
10
Q
What is the maturity date of an option?
A
The date at which the option expires and the payoff is determined.
11
Q
What does the variable F represent in the context of options?
A
Forward price of the underlying asset V for a contract with maturity n.
12
Q
Fill in the blank: The value of the option at time 0 is given by: _______.
A
The Black-Scholes formula
13
Q
What is the expected value of VT in the model?
A
E[VT] = F0
14
Q
What is the formula for the value of a European call option on a bond?
A
c = P(0, T*)[F0Φ(d1) - XΦ(dz)]
15
Q
What is required to be aware of regarding formulae in the gold tables?
A
Knowing exactly which formulae are given.
16
Q
What does the term ‘dirty price’ refer to?
A
The price actually paid for bonds, including accrued interest.
17
Q
What does a higher standard deviation in bond prices indicate?
A
Greater uncertainty in the bond’s price at maturity.
18
Q
True or False: Interest rates are used only for determining payoffs from derivatives.
A
False
19
Q
What assumption is made about the expected value of Vr in a risk-neutral world?
A
It is assumed equal to its forward price F0.
20
Q
What is the significance of the cumulative standard normal distribution function in option pricing?
A
It is used to determine the probability of the option being in-the-money at expiration.
21
Q
How do you obtain the put option formula from the call option formula?
A
By switching the XΦ(.) and F0Φ(.) terms and reversing the signs on d1 and dz.
22
Q
What is the role of the discount factor P(0, T*) in option pricing?
A
It accounts for the time value of money when payoffs are made at a later date.
23
Q
In the context of bond options, what does the variable I represent?
A
The present value of the coupons that will be paid during the life of the option.
24
Q
What is the price of a 5-year fixed interest bond that has just paid its annual coupon of 7?
A
106
This is the price before any option pricing is considered.
25
What is the strike price of the 18-month call option on the bond?
104
26
What is the spot yield assumed for the calculations in the example?
4% pa compounded continuously
27
Calculate the present value of the coupons due to be paid by the bond between now and the option strike date.
6.7255
## Footnote
Calculated using the formula I = 7e^(-1*0.04) for the present value.
28
What is the 18-month discount factor calculated in the example?
0.94176
29
What is the current forward price of the bond at the option strike date?
105.413
## Footnote
Calculated as (106 - 6.7255) / 0.94176.
30
What does the volatility in the option-pricing formula represent?
Price volatility
31
How are yield volatilities expressed in practice?
As yield volatilities
32
What is the expression used to convert yield volatilities to price volatilities?
O' = DYoO'y
33
Define the terms in the expression O' = DYoO'y.
* a' - forward price volatility
* ay - corresponding forward yield volatility
* Yo - initial forward yield on the bond
* D - modified duration of the forward bond
34
What is the formula for modified duration?
D = Duration / (1 + y/m)
## Footnote
Where m is the frequency per annum with which y is compounded.
35
What is the price of a 6-year zero-coupon bond priced at 74.62%?
74.62%
36
What is an interest rate cap?
An over-the-counter interest rate option that provides insurance against interest rates rising above a specified level.
37
What is the cap rate in an interest rate cap?
Rx
38
How does an interest rate cap work?
It caps the variable interest rate paid on a floating rate note.
39
What is the principal amount in the example of a 3-year interest rate cap?
$1,000,000
40
What happens when the LIBOR rate exceeds the cap rate?
A payment equal to the difference between the two payments is made.
41
What is the formula for the payoff provided by the cap?
L x 0.25 x max(RK - Rx, 0)
42
What does the term 'tenor' refer to in the context of interest rate caps?
The time between resets of the floating rate note.
43
What is a caplet?
A call option on the LIBOR rate observed at time tk.
44
What is the general expression for the price of a European call option?
Refer to Equation (2) in Section 1.1
45
What is spot volatility?
Different forward rate volatility used to value each caplet.
46
What is flat volatility?
The same average volatility used for all caplets within a given cap.
47
What is the typical shape of a plot of spot volatilities against term?
A humped curve.
48
What is the annual effective yield on a bond priced at 74.62%?
To be calculated based on specific bond pricing formulas.
49
What is the duration of a bond?
A measure of the sensitivity of the price of a bond to changes in interest rates.
50
What is the relationship between bond price and modified duration?
Modified duration measures the price sensitivity of a bond to interest rate changes.
51
What is flat volatility?
A flat volatility is a constant value across different terms of an option.
52
How do spot and flat volatilities typically vary?
They usually vary with the term of the option.
53
What type of curve is produced when plotting spot volatilities against term?
A humped curve.
54
What is the relationship between spot volatilities and flat volatilities?
Flat volatilities are cumulative averages of spot volatilities.
55
What does an interest rate floor contract provide?
It provides a payoff when the interest rate on an underlying floating rate note falls below a certain rate.
56
In what way is a floor contract similar to a cap?
A floor contract is otherwise identical to a cap.
57
What is the purpose of an interest rate floor?
To provide insurance against a fall in a floating rate.
58
What is the pricing approach for an interest rate floor contract?
It uses an equivalent approach to that used for pricing interest rate caps.
59
What is the put-call parity relationship for caps and floors?
Cap price = Floor price + Value of Swap.
60
What is an interest rate collar?
A combination of caps and floors designed to guarantee that the interest rate on an underlying floating rate note lies between two levels.
61
How is an interest rate collar typically constructed?
So that the price of the long position in the cap equals the price of the short position in the floor.
62
What is the effect of a collar on cashflows?
It ensures that total cashflow remains within a specified range.
63
How can an interest rate cap be characterized?
As a portfolio of put options on zero-coupon bonds.
64
What is a swaption?
An option to exchange a fixed rate bond for a floating rate bond, with the same principal.
65
What is the significance of the swap rate?
It is the fixed interest rate that would be exchanged for LIBOR in a new swap.
66
What does the payoff from a swaption consist of?
A series of cashflows equal to -L max(R-Rx,0) where R is the swap rate.
67
Fill in the blank: A floor can be seen as a portfolio of ______ options on similar bonds.
call
68
True or False: The value of a floating rate bond always equals the principal amount of the swap at the start of a swap.
True.
69
What is the relationship between caps, floors, and portfolios of bond options?
Caps are portfolios of put options, while floors are portfolios of call options.
70
What is the present value of a zero-coupon bond characterized by?
It is characterized by the exercise date and price related to the underlying bond.
71
What does the expression max[L(l+Rxok)] represent?
The present value at time tk of a zero-coupon bond that pays L(l+Rxok) at time tk+1.
72
What is the typical cashflow sequence for a swaption?
Cashflows consist of fixed payments determined by the swap rate.
73
What is the formula for the value of the cashflow received at time fk?
The formula involves the forward swap rate and the volatility of the swap rate.
74
What is a swaption?
A financial derivative that gives the holder the right, but not the obligation, to enter into an interest rate swap agreement
75
How are payments structured in a swaption?
A series of m payments will be made in each of n years
76
What is the purpose of discount factors in a swaption?
To account for the present value of future cash flows
77
Define annuity in the context of financial derivatives.
A series of equal payments made at regular intervals
78
What does the value of a swaption depend on?
The fixed rate Rx and the structure of the swap agreement
79
If a swaption allows annual payments of 4.75% pa fixed, what is being exchanged?
Receiving a floating rate income
80
What is evaluated when considering securitisation?
The predictability and sustainability of adequate cash flow
81
List factors considered in the evaluation of securitised assets.
* Lease terms
* Rental prospects
* Degree of potential competition
* Barriers to competitive entry
82
What does EBITDA stand for?
Earnings Before Interest, Taxes, Depreciation, and Amortisation
83
What is a debt service-to-EBITDA ratio covenant?
A measure to ensure earnings are sufficient to cover interest payments
84
What has reduced currency exchange risk in securitisation?
The adoption of Euro and the elimination of barriers for pan-European securitisation
85
What do auditors verify in securitised assets?
The cash flows, tax positions, and contingent liabilities
86
Why is cash flow volatility important in securitisation?
It is a key feature in evaluating credit risk
87
What standard approach is followed in the evaluation of a securitisation?
Modeling anticipated cash flows and discounting at an appropriate interest rate
88
What are the main classes of asset-backed securities?
Not specified in the text
89
How is the price of a plain vanilla credit default swap (CDS) derived?
From the yield on an associated bond in excess of the risk-free rate
90
If the face value of a bond is $100 and the yield is 7.25% pa with a risk-free rate of 6% pa, what is P?
$1.25
91
What should Bank X do if P is less than the calculated value?
Reconsider the terms of the CDS
92
What should Bank Z do if P is greater than the calculated value?
Reassess the risk associated with the bond
93
What does the basis refer to in credit derivatives?
The CDS price less the yield in excess of risk-free on the bond
94
What are the risks associated with a bond and a CDS package?
* Counterparty credit risk
* Changes in interest rates
* Documentation differences
95
What is a structural model in the context of credit risk?
A model that estimates the price of credit risk based on equity derivative market information
96
What is the Merton model used for?
Pricing corporate debt
97
What happens if the value of a company's assets is less than the debt at maturity?
The company rationally defaults on its debt
98
How is the value of equity at time T determined?
max(Vr - D, 0)
99
What does the Black-Scholes formula provide in this context?
The current value of the equity
100
What is the Black-Scholes formula used for?
To give the current value of the equity, E0
## Footnote
The Black-Scholes formula is a mathematical model for pricing options.
101
What does V0 represent in the context of company valuation?
The current value of the company's assets
## Footnote
V0 includes the market value of equity, debt, and other obligations.
102
What does cf>(d2) represent in the valuation formula?
A survival probability, indicating the probability that the company does not default on its debt.
103
What is the risk-neutral probability that a company will default?
<1>(-d2)
## Footnote
This requires knowledge of both V0 and ov, which are not directly observable.
104
What equation is used to derive the value of corporate debt considering default?
V0 - E0
105
What is Ito's lemma used for in this context?
To differentiate equations governing the evolution of equity and debt over time.
106
What can be estimated by solving the second equation derived from Merton's work?
The risk-neutral probability of default.
107
What is the payoff from a vanilla credit default swap per annum?
The excess return on the bond over the risk-free rate.
108
What is the evaluation of assets for securitisation based on?
Predictability and sustainability of adequate cashflow
## Footnote
Factors include lease terms, rental prospects, potential competition, and barriers to entry.
109
What approach is used for evaluating a securitisation?
Discounted cash flow approach.
110
What is a major difficulty in evaluating a securitisation?
Choice of discount rate to use.
111
What do bond options allow for in valuation?
They can be valued using equations for European call and put options.
112
What defines the payoff from an interest rate cap?
A payoff at time tk+1, which is a call option on the LIBOR rate observed at time tk.
113
What is the relationship between cap and floor prices?
Cap price = Floor price + Value of swap.
114
What does the value of a total return swap represent?
The difference between the values of the assets generating returns on each side of the swap.
115
What is the significance of the company's share price in bond valuation?
It provides information necessary to determine V0 - E0.
116
What is the formula for the value of a European call option?
A general expression involving the stock price, strike price, risk-free rate, and time to expiration.
117
Fill in the blank: The value of a bond allowing for its credit risk can be found using information provided by the company's share price as _______.
V0 - E0
118
What do the terms 'interest rate caps' and 'floors' refer to?
Financial derivatives that provide payoffs based on interest rate movements.
119
True or False: The volatilities of different points on the yield curve are the same.
False
120
What is the purpose of evaluating investment alternatives?
To assess various types of investments and determine potential returns.
121
What are the assumptions to state when evaluating returns from investments?
Assumptions related to market conditions, interest rates, and company performance.
122
What is the effect of estimating O'E in finding the risk-neutral probability of default?
It allows for an alternative figure for the theoretical price of a CDS contract.
123
What is the risk-neutral probability of default derived from?
cf>(-d2)
124
What can be derived from the difference between the market value of a bond and its value at the strike spread?
The value of a credit spread option.
125
What does lnF0 equal in terms of lnS0 and rT?
lnF0 = lnS0 + rT
126
What does the equality of variance between lnF0 and lnS0 imply?
lnF0 and lnS0 have the same variance
127
In the context of volatility, what is
128
What is the general formula for the price of a European call option on a bond?
The price formula involves the cumulative standard normal distribution function
129
What is the 18-month discount factor denoted as?
P(0, 1½) = 0.94176
130
What is the forward price of the bond denoted as?
F0 = 105.413
131
What is the option strike price denoted as?
X = 104
132
What is the forward volatility denoted as?
133
What is the strike date denoted as?
T = 1½
134
Fill in the blank: The modified duration of a bond with price P is defined as _______.
A negative sign included to give a positive number
135
What does the relationship dP/dy = -Dy/Py suggest?
Forward price volatility can be related to forward yield volatility
136
What is the duration of a zero-coupon bond equal to?
The duration is equal to its outstanding term
137
What is the annual effective yield on the bond found from?
s6 = 0.05, ie 5% pa
138
What is the modified duration of the zero-coupon bond?
D = -6 / 1.05 = 5.71 years
139
What leads to a payoff at the end of each quarter for a cap?
The cap leads to a payoff equal to the difference between LIBOR and the cap rate
140
What does a floorlet provide?
A payoff if the actual LIBOR rate RK is less than the floor rate Rx
141
What does a swaption provide its holder?
The right, but not the obligation, to enter into a swap agreement on specified terms
142
True or False: A swaption that gives the holder the right to pay fixed and receive floating can be thought of as a put option on a fixed rate bond.
True
143
What is the expression for the value of the swaption simplified with an annuity A?
A = -2,P(0, ti) where i=1 to m
144
What is the volatility of cashflow important for?
To determine the sufficiency of cashflows to cover coupon payments
145
What are the main classes of asset-backed securities?
* Residential mortgage-backed securities (MBS)
* Commercial mortgage-backed securities (MBS)
* Credit card receivables (CCABS)
* Collateralised loan, bond and debt obligations (CLO, CBO and CDOs)
146
Fill in the blank: If the face value of the bond is $100, the yield is 7.25% pa, and the risk-free rate is 6% pa, then the excess yield p is _______.
0.0125 X 100 = $1.25
147
What should Bank X do if P is less than the value calculated?
Bank X should buy the bond and enter into the credit default arrangement
148
What should Bank Z do if P is greater than the value calculated?
Bank Z can make an arbitrage profit by short selling the bond
149
What is the value of the bond found as?
V0 - E0
150
What is the conversion option in a convertible debenture?
Converts £100 nominal of debenture into 150 shares
151
What is the intrinsic value of the conversion option when the share price is £0.57?
No intrinsic value because 150 x £0.57 = £85.50 < £100
152
If the share rises at 10% pa, what would the share price be after five years?
£0.92
153
What annual return does a share price rise of 10% pa represent?
6.6% pa
154
What annual return does a share price rise of 20% pa equate to?
16.3% pa
155
Fill in the blank: If the share price does not rise above £0.67 per share, then the _______.
debenture remains unprofitable
156
What is the annual return on a debenture if the share price rises by 20% per annum?
16.3%
## Footnote
This return reflects the increased value of the debenture as a result of the share price rise.
157
What happens if the share price does not rise above £0.67 per share?
The debenture will be repaid at par and investors will get their money back.
## Footnote
This indicates the security of the investment in the debenture.
158
Why is the return from a convertible debenture typically less than from shares when prices rise strongly?
The convertible guarantees the investor's money back whereas the share does not.
## Footnote
This reflects the risk-return trade-off between different types of investments.
159
What is the yield on preference shares?
3.5% per annum
## Footnote
This yield is above the dividend yield of other options.
160
In the event of a wind-up, where do preference shares rank compared to bond investors?
Preference shares rank below bond investors.
## Footnote
This indicates the priority of claims on assets during liquidation.
161
Which type of investors may prefer equity shares and why?
Investors seeking cash flow may prefer equity shares due to their 3.5% dividend yield.
## Footnote
This yield provides regular income which is attractive for cash flow-focused investors.
162
What is the appeal of convertible debentures to risk-averse investors?
They offer a money-back guarantee with potential upside if the company performs well.
## Footnote
This combination of security and growth potential attracts conservative investors.
163
What is the minimum share price rise required to give any return on capital?
Greater than 3.3% per annum.
## Footnote
This is necessary to cover costs and provide a return over the investment period.
164
What fixed nominal return do preference shares offer?
6.6% per annum.
## Footnote
This fixed return may suit investors with known future cash flow needs.
165
Why might life insurance companies or pension funds prefer preference shares?
They are looking for nominal returns to match known cash flows.
## Footnote
This aligns with the liabilities these institutions manage.
166
What is a key characteristic of preference shares regarding income over a 5-year period?
They offer no income over the 5-year period.
## Footnote
This feature may appeal to investors without immediate cash flow requirements.
167
What may influence the preference for debentures over preference shares?
Tax reasons.
## Footnote
Different tax treatments can make one investment more favorable than another.
168
What do preference shares offer that may appeal to certain investors?
A fixed nominal return rather than a real return.
## Footnote
This can be attractive for investors prioritizing predictable income.
169
What is the investment appeal of convertible debentures to pension funds?
They offer real returns with downside protection.
## Footnote
This feature helps pension funds manage their liabilities effectively.
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