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On Interest-Rate Risk in Use of Postal Savings Funds
THE JOURNAL OF CHINA UNIVERSITIES OF POSTS AND TELECOMMUNICATIONS Vol.13, No.2, Jun.2006
On Interest-Rate Risk in Use of Postal Savings Funds DU Chong-dong,
ZHOU Zhi-cui
Finance Department, Shijiazhuang Post and Telecommunication Technical College, Shijiazhuang 050021, P. R. China
Abstract: This paper analyzes interest-rate risks that postal savings bureau may face. Our analysis is b a d on the cash flow characteristics of postal savings funds. The analyzed interest-rate risks consist of re-pricing risks, reinvestment risks, yield curve risks, basis risks and other derivative risks such as credit risks and Liquidity risks . This paper presents alternative methods to control and manage these interest-rate risks. Key words: interat rate; interest-rate risk ; postal savings funds CLC number: F618 Documentcode: A Article ID: 1005-8885(2006)02-0099-04
1
Introduction
With financial system reform and on-going establishment of market-based interest rate system, interest rate is one of the most important factors that affect postal savings performance. Deposit in the People's Bank of China, negotiated deposit in commercial bank, investment in repurchase agreement and government securities in the Inter-bank Bond Market are all interest-rate sensitive"', the change in interest-rate level and volatility changes cash flows of Postal Savings Bureau (PSB), it undertakes interest rate risk. The interest-rate risk of deposit in the central bank was a n a l y ~ e d [ ~ - We ~ ] . focus on interest-rate risk of repurchase agreement, government securities investment and negotiated deposit based on characteristics of cash flows of them.
reinvest funds received at the prevailing interest rates that are unknown exante, but also short interest rates is highly volatile, sometimes magnitude of the change is larget4'. Table 1 exhibits the cash flows of rep0 transactions as interest rate changes. Table 1 The change of cash flows of repurchase agreement due to changes of interest rates Interest rate Repurchase agreement Downward
Interest
-
-
Principal
-
-
Interest
J
t
Principal
J
f
Total changes
4 4
t
Characteristics of cash flows
Value of cash flows
Value of collateral Notes:
2 Interest-Rate Risk of Investment and Negotiated Deposit
Upward
f
f showing the rise of rhose variables; 4 showing the decrease of those variables; - denoting that those variables remain unchanged
In general, each repurchase agreement has little default risk because it has government securities as its col2.1 Interest-Rate Risk of Funds Invested in the Repo lateral. Once borrower defaults, PSB can recover funds by selling the collateral. But if interest rates on governMarket There are thirteen kinds of repurchase agreements in ment securities increase sharply subsequent to the rep0 the rep0 market. The value of repurchase agreements is transaction, the market value of them will declines, influenced by the change of interest rates, but is high PSB will own securities with market value less than the related to maturity: repurchase agreements with 1 day, amount that it lend to borrower, it is exposed to credit 2 days, 3 days, 7 days, 14 days, 21 days, 1 month and risk. 2 months bear little effect due to very short maturity, 2 . 2 Interest-Rate Risk of Funds Invested in Governthe others ( 3 months, 4 months, 6 months, 9 months, ment Security The cash flow that PSB can expect to receive from 12 months) bear more effect. The repurchase agreements with very short maturity bear high reinvestment any government security may consist of the periodic risk, not only because the maturities of those contracts coupon interest payments, interests generated from are very short, as long as they are due, PSB must reinvestment of periodic cash flows and any capital gain Received date:
2005-06-28
The Journal of CHUPT
100
or loss when bond matures or is sold. The price of any government security will change in opposite direction with the change of interest rates in spite of fixed periodic coupon interest payments and principal with maturity. If PSB has to sell a government security before maturity, an increase in interest rates will mean a realization of capital loss. So it faces repricing risk. Repricing risk is major risk that PSB faces in the government security market. Interest on interests also depends on the prevailing interest-rate level at time of coupon payments and reinvestment. It should be noted that repricing risk and reinvestment risk have off< itig effects. See Table 2 . L
able 2 Characteristics and value of cash flow of government security due to changes of interest rates Interest rate Government security Upward Downward
-
-
f
J
Principal
-
-
Coupon
J
t
Coupon Characteristics of cash flows Interest on interests
Value of cash flows
t
J
Capital gain or loss
t
4
Value of government security
repricing risk and reinvestment r i ~ k ' ~ - ~As ' . for a portfolio of government securities with different maturity, term is one of the most basic factors that influence interest rates, interest rates will have different levels and directions of volatility with different term at different time, those changes is described by change in shape of yield curve173, the relevant risk is yield curve risk that PSB faces. It has empirical evidence that those shifts exist in the Inter-Bank Bond Market: parallel shifts, twist shifts and butterfly shifts" - '"I. According to term structure of portfolio, there are three basic categories of government security portfolio"" : 1 ) bullet portfolio; 2 barbell portfolio; 3 ) ladder portfolio. Table 3 exhibits the shift effects. In practice of interestrate risk management, PSB may use Monte Carlo simulation to investigate the value change of the portfolio based on expected yield curve shifts and deduce the yield curve risk"' - l3] .
2.3
c
Interst on interests
For any government security, modified duration or effective duration is a good approximate measure of
2006
Interest-Rate Risk of Negotiated Deposit
The negotiated deposit is funds that PSB lends to some commercial banks with negotiated interest rate. The cash flows of each negotiated deposit consists of interests based on floating interest rate adjusted periodically or occasionally depending on changes of the base interest rate and general level of interest rates, interests generated from reinvestment of periodic cash flows, the full or part payment of principal depending on whether default happens or not, and contingent claims on collaterals underlying the negotiated deposit contracts.
The shift effects on three kind of portfolio
Table 3
Parallel shifts Portfolio
Twist shifts
Butterfly shifts
Maturity Upward
Downward
Flattening
Steepening
Positive
Negative
Short
3
t
J
f
J-
t
Intermediate
J
t
Long
J
f
t
c
Total value
4
f
Uncertain
Uncertain
Uncertain
Uncertain
Short
J
f
3.
f
J-
t
Intermediate
J
t
-
-
t
J-
Long
3.
t
t
J
J
f
Total value
J
t
Uncertain
Uncertain
Uncertain
Uncertain
Short
J
4
J
f
J
f
-
f
4
Bullet
Barbell
Intermediate
4
f
-
Imng
J
f
J
t
J
t
Total value
J
t
Uncertain
Uncertain
Uncertain
Uncertain
Ladder
DU Chong-dong, et a1 . : On Interest-Rate Risk in Use of Postal Savings Funds
No.2
Table 4 Characteristics and value of cash flow of negotiated deposits due to changes of interest rates Interest rate Negotiated deposits Upward Downward
f
J
f -
J-
Interest
-
-
Interest on interests
f
J
Capital gain or loss
4
4
J
f
Interest Characteristics of cash flows Interest on interests Principal
Value of cash flows
Value of collaterals
As interest rate of negotiated deposit is floating, there is no reinvestment risk because interests adjust with the base interest rate; but the value of principal will change, so will the value of collaterals. Especially, as interest rate increases sharply, the value of collaterals may be less than the loss of principal, PSB faces credit risk. Furthermore, the collaterals consists of various kinds of assets with different liquidity, PSB faces liquidity risk when it deals with the collaterals. Negotiated interest rates have different level base on different reference interest rates and different margins which reflect borrowers' different credit level, change of interest rates includes both different base interest rates and margins. As interest rates change, variation of those base interest rates and margins is different, PSB faces basis risk['41. Interest-Rate Risk When Considering Interest Rates of Postal Savings Deposit
2.4
From the above discussing, we can see that postal savings deposit is neglected. For understanding interestrate risk, it is necessary to take interest rates of postal savings deposit into account. Interest rates of all kinds of postal savings deposit are regulated and adjusted by the People' Bank of China, they are semi-fixed and adjusted irregularly, but those of assets of PSB are mixture of fixed and floating rates, they do not change at same amount and time, so PSB faces basis risk. When market interest rate or term structure of interest rate of postal savings deposits changes, deposit balance and structure may change because individuals withdraw or save money, it causes mismatch between assets and liabilities due to different maturity and different balance at same maturity, and is also sources of reinvestment risk and liquidity risk.
3
Interest-Rate Risk Management
At present, PSB is not a financial agency. It can't manage interest-rate risk as same way as commercial banks. It can determine the maximal amount of risk
101
undertaking and allocate it into counterpart of different kinds of asset^"^].
3.1
Matching Assets with Liabilities
In using postal savings funds, it is important to match assets with liabilities based on duration of them, especially for government bonds and deposit. When interest rates change, the value change of them is same in direction and amount, it can mitigate interest-rate risks. Of course, the match should adjust regularly in accordance with change of maturity of assets and liabilities.
3.2
Prediction of Interest-Rate Movements
Repricing risk, reinvestment risk, yield curve risk, basis risk, credit risk and liquidity risk is induced by variations of interest rate. Prediction of interest-rate movements is base for managing interest-rate risk. PSB adjusts structure of different kinds of assets in response to expectations of future interest rate so as to maximize the returns under certain level of risks.
3.3
Reserve Maintenance
Reserve withdrawn from revenue of PSB each year is alternative way to manage risks"']. When loss occurs, those funds can be utilized to offset them.
3.4 Limiting Credit Risk The methods to limit credit risk include: 1 ) Select high-liquidity and value-stable collateral. 2 ) Considerable margin. The value of collateral exceeds the principal of loan in consistence with different credit level. 3 ) Market the collateral to market on a regular basis. As collateral market value change by a certain percentage, the negotiated deposit or rep0 position is adjusted accordingly.
3.5 Hedging PSB may use financial derivatives such as forward contracts of government securities to control interestrate risks"61. By way of derivative transactions, PSB can transfer those risks to other party with cost of paying relevant fees.
4
Conclusions
This paper analyzes interest-rate risks that PSB faces based on the characteristics of cash flows of three ways of using postal saving funds. The interest-rate risks consist of repricing risk, reinvestment risk, yield curve risk, basis risk and other derivative risks such as credit risk and liquidity risk. PSI3 may manage and control those risks by determining maximal amount of riskundertaking, matching assets with liabilities, prediction of interest rate movements, maintaining reserve, limiting credit risk and hedging.
102
The Journal of CHUPT
References: The People’s Bank of China. Executive reports of monetary policy in 2004[EB/OL]. www. pbc. gov. cn, 2004. DU Chong-dong, IaI Su-man, Sun Hao. A study on pricing deposits of postal savings in the central bank[J] . The Journal of China Universities of Posts and Telecommunications, 2003, lO(2): 38-45. LANG Qiu-hong, DU Chong-dong, DU Yu-wei. A study of effectiveness of postal financial assets services [ J ] . The Journal of Chongqing University of Posts and Telecommunications, 2002, 9 (1): 18-23. FABOZZI F J . Bond markets, analysis and strategies[ M I . Upper Saddle River, NJ, USA: Prentice Hall, 2000. MILES L, CAKS J. A “duration” fallacy[J] . Journal of Fib nance, 1997,32(1): 185-187. FABOZZI F J. The handbook of fixed income securities[M]. 5th ed. New York, NY, USA: McGraw Hill, 1997. MCCUILOCH J H. Measuring the term structure of interest rates [ J ] . Journal of Business, 1971,44(1): 19-31. DENG Zhen-long, LIN Hai. Static approximation of China’s interest rate term structure [ J 1. Wuhan Finance, 20O3(3) :33 - 36. JONES F J . Yield curve strategies[J] . The Journal of Fixed Income. 1991,1(1): 43-48.
From p. 89 [21 AHN J, LEE H S. Frequency domain equalization of OFDM signal over frequency nonselective Rayleigh fading channels[ J 1. Electronics Letters, 1993, 29 ( 16) : 1476 1477. Y P, HAGGMAN S G. Intercarrier interference ZHAO [31 self-cancellation scheme for OFDM mobile communication systems [ J 1. IEEE Trans on Communications, 2001, 49(7): 1185-1191. L41 MUSCHALLIK C . Improving an OFDM reception using an adaptive Nyquitst windowing[J] . IEEE Trans on Consumer Electronics, 1996,42(8): 259 - 269. [51 MUILER-WEINFURTNER S H. Optimum Nyquist windowing in OFDM receivers[J] . IEEE Trans on Communications, 2001, 49(3): 417 - 420. [61 TAN P, BEAULIEU N C. Reduced ICI in OFDM systems using the “better than” raised cosine pulse[J]. IEEE Communications Letteers, 2004, 8(3): 135 - 137.
2006
[ 101 DUFFEE G R. Term premia and interest rate forecasts in affine models [ J 1. Journal of Finance, 2002, 57 ( 1 ) : 405 - 443. 1113 ANTHONY S. Financial institutions management: a m d ern perspective[M]. 2nd ed. Ncw York, NY, USA: McGraw Hill, 1997. [12] FABOZZI F J . Fixed income mathematics: analytical & statistical techniques[M]. 3rd ed. New York, NY, USA: McGraw Hill, 1997. [13] DUFFIE D. Dynamic asset pricing theory[M] . Princeton, NJ, USA: Princeton University Press, 1996. [ 141 MORRISON J B, PYLE D H. Interest rate risk and the regulation of financial institutions[ R] . NBER Working Paper, 1978: 266. [151 MORRISON J B. PYLE D H. Bank income taxes and interest rate risk management: a note [ J ]. Journal of Finance, 1984, 39(4): 1199 - 1206. 161 HULL J C. Options, futures and other deraivatives[ M I . 4th ed. Upper Saddle River, NJ, USA: Prentice Hall: 2000. Biography: DU Chong-dong, Ph. D., Shijiazhuang Post and Telecommunication Technical College, interested in the research of finance and postal finance.
[71 BEAULIEU N C, Tan C C , Damen M 0. A “better than” Nyquist pulse[J]. IEEE Communication.. Letters, 2001, 5 ( 9 ) : 367-368. [ 81 HOLTZMANN J M. A simple accurate method to calculate spread-spectrum multiple-accesserror probabilities[ J ] . IEEE Trans on Communications, 1992, 40(3) : 461 - 464. [9] SONG R F, LEUNG S H. A unified analysis of quaternary DSCDMA systems with arbitrary chip waveforms and its applications[ J ] . Wireless Personal Communications, 2004, 31(1): 111 - 129. Biography: SONG Rong-fang, male, Ph. r). , Professor, Tutor of Doctorial Graduate, Nanjing University of Posts and Telecommunications, interested in the research into key technology in future broadband mobile communications.
On Interest-Rate Risk in Use of Postal Savings Funds DU Chong-dong,
ZHOU Zhi-cui
Finance Department, Shijiazhuang Post and Telecommunication Technical College, Shijiazhuang 050021, P. R. China
Abstract: This paper analyzes interest-rate risks that postal savings bureau may face. Our analysis is b a d on the cash flow characteristics of postal savings funds. The analyzed interest-rate risks consist of re-pricing risks, reinvestment risks, yield curve risks, basis risks and other derivative risks such as credit risks and Liquidity risks . This paper presents alternative methods to control and manage these interest-rate risks. Key words: interat rate; interest-rate risk ; postal savings funds CLC number: F618 Documentcode: A Article ID: 1005-8885(2006)02-0099-04
1
Introduction
With financial system reform and on-going establishment of market-based interest rate system, interest rate is one of the most important factors that affect postal savings performance. Deposit in the People's Bank of China, negotiated deposit in commercial bank, investment in repurchase agreement and government securities in the Inter-bank Bond Market are all interest-rate sensitive"', the change in interest-rate level and volatility changes cash flows of Postal Savings Bureau (PSB), it undertakes interest rate risk. The interest-rate risk of deposit in the central bank was a n a l y ~ e d [ ~ - We ~ ] . focus on interest-rate risk of repurchase agreement, government securities investment and negotiated deposit based on characteristics of cash flows of them.
reinvest funds received at the prevailing interest rates that are unknown exante, but also short interest rates is highly volatile, sometimes magnitude of the change is larget4'. Table 1 exhibits the cash flows of rep0 transactions as interest rate changes. Table 1 The change of cash flows of repurchase agreement due to changes of interest rates Interest rate Repurchase agreement Downward
Interest
-
-
Principal
-
-
Interest
J
t
Principal
J
f
Total changes
4 4
t
Characteristics of cash flows
Value of cash flows
Value of collateral Notes:
2 Interest-Rate Risk of Investment and Negotiated Deposit
Upward
f
f showing the rise of rhose variables; 4 showing the decrease of those variables; - denoting that those variables remain unchanged
In general, each repurchase agreement has little default risk because it has government securities as its col2.1 Interest-Rate Risk of Funds Invested in the Repo lateral. Once borrower defaults, PSB can recover funds by selling the collateral. But if interest rates on governMarket There are thirteen kinds of repurchase agreements in ment securities increase sharply subsequent to the rep0 the rep0 market. The value of repurchase agreements is transaction, the market value of them will declines, influenced by the change of interest rates, but is high PSB will own securities with market value less than the related to maturity: repurchase agreements with 1 day, amount that it lend to borrower, it is exposed to credit 2 days, 3 days, 7 days, 14 days, 21 days, 1 month and risk. 2 months bear little effect due to very short maturity, 2 . 2 Interest-Rate Risk of Funds Invested in Governthe others ( 3 months, 4 months, 6 months, 9 months, ment Security The cash flow that PSB can expect to receive from 12 months) bear more effect. The repurchase agreements with very short maturity bear high reinvestment any government security may consist of the periodic risk, not only because the maturities of those contracts coupon interest payments, interests generated from are very short, as long as they are due, PSB must reinvestment of periodic cash flows and any capital gain Received date:
2005-06-28
The Journal of CHUPT
100
or loss when bond matures or is sold. The price of any government security will change in opposite direction with the change of interest rates in spite of fixed periodic coupon interest payments and principal with maturity. If PSB has to sell a government security before maturity, an increase in interest rates will mean a realization of capital loss. So it faces repricing risk. Repricing risk is major risk that PSB faces in the government security market. Interest on interests also depends on the prevailing interest-rate level at time of coupon payments and reinvestment. It should be noted that repricing risk and reinvestment risk have off< itig effects. See Table 2 . L
able 2 Characteristics and value of cash flow of government security due to changes of interest rates Interest rate Government security Upward Downward
-
-
f
J
Principal
-
-
Coupon
J
t
Coupon Characteristics of cash flows Interest on interests
Value of cash flows
t
J
Capital gain or loss
t
4
Value of government security
repricing risk and reinvestment r i ~ k ' ~ - ~As ' . for a portfolio of government securities with different maturity, term is one of the most basic factors that influence interest rates, interest rates will have different levels and directions of volatility with different term at different time, those changes is described by change in shape of yield curve173, the relevant risk is yield curve risk that PSB faces. It has empirical evidence that those shifts exist in the Inter-Bank Bond Market: parallel shifts, twist shifts and butterfly shifts" - '"I. According to term structure of portfolio, there are three basic categories of government security portfolio"" : 1 ) bullet portfolio; 2 barbell portfolio; 3 ) ladder portfolio. Table 3 exhibits the shift effects. In practice of interestrate risk management, PSB may use Monte Carlo simulation to investigate the value change of the portfolio based on expected yield curve shifts and deduce the yield curve risk"' - l3] .
2.3
c
Interst on interests
For any government security, modified duration or effective duration is a good approximate measure of
2006
Interest-Rate Risk of Negotiated Deposit
The negotiated deposit is funds that PSB lends to some commercial banks with negotiated interest rate. The cash flows of each negotiated deposit consists of interests based on floating interest rate adjusted periodically or occasionally depending on changes of the base interest rate and general level of interest rates, interests generated from reinvestment of periodic cash flows, the full or part payment of principal depending on whether default happens or not, and contingent claims on collaterals underlying the negotiated deposit contracts.
The shift effects on three kind of portfolio
Table 3
Parallel shifts Portfolio
Twist shifts
Butterfly shifts
Maturity Upward
Downward
Flattening
Steepening
Positive
Negative
Short
3
t
J
f
J-
t
Intermediate
J
t
Long
J
f
t
c
Total value
4
f
Uncertain
Uncertain
Uncertain
Uncertain
Short
J
f
3.
f
J-
t
Intermediate
J
t
-
-
t
J-
Long
3.
t
t
J
J
f
Total value
J
t
Uncertain
Uncertain
Uncertain
Uncertain
Short
J
4
J
f
J
f
-
f
4
Bullet
Barbell
Intermediate
4
f
-
Imng
J
f
J
t
J
t
Total value
J
t
Uncertain
Uncertain
Uncertain
Uncertain
Ladder
DU Chong-dong, et a1 . : On Interest-Rate Risk in Use of Postal Savings Funds
No.2
Table 4 Characteristics and value of cash flow of negotiated deposits due to changes of interest rates Interest rate Negotiated deposits Upward Downward
f
J
f -
J-
Interest
-
-
Interest on interests
f
J
Capital gain or loss
4
4
J
f
Interest Characteristics of cash flows Interest on interests Principal
Value of cash flows
Value of collaterals
As interest rate of negotiated deposit is floating, there is no reinvestment risk because interests adjust with the base interest rate; but the value of principal will change, so will the value of collaterals. Especially, as interest rate increases sharply, the value of collaterals may be less than the loss of principal, PSB faces credit risk. Furthermore, the collaterals consists of various kinds of assets with different liquidity, PSB faces liquidity risk when it deals with the collaterals. Negotiated interest rates have different level base on different reference interest rates and different margins which reflect borrowers' different credit level, change of interest rates includes both different base interest rates and margins. As interest rates change, variation of those base interest rates and margins is different, PSB faces basis risk['41. Interest-Rate Risk When Considering Interest Rates of Postal Savings Deposit
2.4
From the above discussing, we can see that postal savings deposit is neglected. For understanding interestrate risk, it is necessary to take interest rates of postal savings deposit into account. Interest rates of all kinds of postal savings deposit are regulated and adjusted by the People' Bank of China, they are semi-fixed and adjusted irregularly, but those of assets of PSB are mixture of fixed and floating rates, they do not change at same amount and time, so PSB faces basis risk. When market interest rate or term structure of interest rate of postal savings deposits changes, deposit balance and structure may change because individuals withdraw or save money, it causes mismatch between assets and liabilities due to different maturity and different balance at same maturity, and is also sources of reinvestment risk and liquidity risk.
3
Interest-Rate Risk Management
At present, PSB is not a financial agency. It can't manage interest-rate risk as same way as commercial banks. It can determine the maximal amount of risk
101
undertaking and allocate it into counterpart of different kinds of asset^"^].
3.1
Matching Assets with Liabilities
In using postal savings funds, it is important to match assets with liabilities based on duration of them, especially for government bonds and deposit. When interest rates change, the value change of them is same in direction and amount, it can mitigate interest-rate risks. Of course, the match should adjust regularly in accordance with change of maturity of assets and liabilities.
3.2
Prediction of Interest-Rate Movements
Repricing risk, reinvestment risk, yield curve risk, basis risk, credit risk and liquidity risk is induced by variations of interest rate. Prediction of interest-rate movements is base for managing interest-rate risk. PSB adjusts structure of different kinds of assets in response to expectations of future interest rate so as to maximize the returns under certain level of risks.
3.3
Reserve Maintenance
Reserve withdrawn from revenue of PSB each year is alternative way to manage risks"']. When loss occurs, those funds can be utilized to offset them.
3.4 Limiting Credit Risk The methods to limit credit risk include: 1 ) Select high-liquidity and value-stable collateral. 2 ) Considerable margin. The value of collateral exceeds the principal of loan in consistence with different credit level. 3 ) Market the collateral to market on a regular basis. As collateral market value change by a certain percentage, the negotiated deposit or rep0 position is adjusted accordingly.
3.5 Hedging PSB may use financial derivatives such as forward contracts of government securities to control interestrate risks"61. By way of derivative transactions, PSB can transfer those risks to other party with cost of paying relevant fees.
4
Conclusions
This paper analyzes interest-rate risks that PSB faces based on the characteristics of cash flows of three ways of using postal saving funds. The interest-rate risks consist of repricing risk, reinvestment risk, yield curve risk, basis risk and other derivative risks such as credit risk and liquidity risk. PSI3 may manage and control those risks by determining maximal amount of riskundertaking, matching assets with liabilities, prediction of interest rate movements, maintaining reserve, limiting credit risk and hedging.
102
The Journal of CHUPT
References: The People’s Bank of China. Executive reports of monetary policy in 2004[EB/OL]. www. pbc. gov. cn, 2004. DU Chong-dong, IaI Su-man, Sun Hao. A study on pricing deposits of postal savings in the central bank[J] . The Journal of China Universities of Posts and Telecommunications, 2003, lO(2): 38-45. LANG Qiu-hong, DU Chong-dong, DU Yu-wei. A study of effectiveness of postal financial assets services [ J ] . The Journal of Chongqing University of Posts and Telecommunications, 2002, 9 (1): 18-23. FABOZZI F J . Bond markets, analysis and strategies[ M I . Upper Saddle River, NJ, USA: Prentice Hall, 2000. MILES L, CAKS J. A “duration” fallacy[J] . Journal of Fib nance, 1997,32(1): 185-187. FABOZZI F J. The handbook of fixed income securities[M]. 5th ed. New York, NY, USA: McGraw Hill, 1997. MCCUILOCH J H. Measuring the term structure of interest rates [ J ] . Journal of Business, 1971,44(1): 19-31. DENG Zhen-long, LIN Hai. Static approximation of China’s interest rate term structure [ J 1. Wuhan Finance, 20O3(3) :33 - 36. JONES F J . Yield curve strategies[J] . The Journal of Fixed Income. 1991,1(1): 43-48.
From p. 89 [21 AHN J, LEE H S. Frequency domain equalization of OFDM signal over frequency nonselective Rayleigh fading channels[ J 1. Electronics Letters, 1993, 29 ( 16) : 1476 1477. Y P, HAGGMAN S G. Intercarrier interference ZHAO [31 self-cancellation scheme for OFDM mobile communication systems [ J 1. IEEE Trans on Communications, 2001, 49(7): 1185-1191. L41 MUSCHALLIK C . Improving an OFDM reception using an adaptive Nyquitst windowing[J] . IEEE Trans on Consumer Electronics, 1996,42(8): 259 - 269. [51 MUILER-WEINFURTNER S H. Optimum Nyquist windowing in OFDM receivers[J] . IEEE Trans on Communications, 2001, 49(3): 417 - 420. [61 TAN P, BEAULIEU N C. Reduced ICI in OFDM systems using the “better than” raised cosine pulse[J]. IEEE Communications Letteers, 2004, 8(3): 135 - 137.
2006
[ 101 DUFFEE G R. Term premia and interest rate forecasts in affine models [ J 1. Journal of Finance, 2002, 57 ( 1 ) : 405 - 443. 1113 ANTHONY S. Financial institutions management: a m d ern perspective[M]. 2nd ed. Ncw York, NY, USA: McGraw Hill, 1997. [12] FABOZZI F J . Fixed income mathematics: analytical & statistical techniques[M]. 3rd ed. New York, NY, USA: McGraw Hill, 1997. [13] DUFFIE D. Dynamic asset pricing theory[M] . Princeton, NJ, USA: Princeton University Press, 1996. [ 141 MORRISON J B, PYLE D H. Interest rate risk and the regulation of financial institutions[ R] . NBER Working Paper, 1978: 266. [151 MORRISON J B. PYLE D H. Bank income taxes and interest rate risk management: a note [ J ]. Journal of Finance, 1984, 39(4): 1199 - 1206. 161 HULL J C. Options, futures and other deraivatives[ M I . 4th ed. Upper Saddle River, NJ, USA: Prentice Hall: 2000. Biography: DU Chong-dong, Ph. D., Shijiazhuang Post and Telecommunication Technical College, interested in the research of finance and postal finance.
[71 BEAULIEU N C, Tan C C , Damen M 0. A “better than” Nyquist pulse[J]. IEEE Communication.. Letters, 2001, 5 ( 9 ) : 367-368. [ 81 HOLTZMANN J M. A simple accurate method to calculate spread-spectrum multiple-accesserror probabilities[ J ] . IEEE Trans on Communications, 1992, 40(3) : 461 - 464. [9] SONG R F, LEUNG S H. A unified analysis of quaternary DSCDMA systems with arbitrary chip waveforms and its applications[ J ] . Wireless Personal Communications, 2004, 31(1): 111 - 129. Biography: SONG Rong-fang, male, Ph. r). , Professor, Tutor of Doctorial Graduate, Nanjing University of Posts and Telecommunications, interested in the research into key technology in future broadband mobile communications.