Peter Ritchken - Academia.edu (original) (raw)
Papers by Peter Ritchken
Working paper (Federal Reserve Bank of Cleveland), 1992
The linkages between term structures separated by finite time periods can be complex. Indeed, in ... more The linkages between term structures separated by finite time periods can be complex. Indeed, in general, the dynamics of the term structure could depend on the entire set of information revealed since the earlier date. This path dependence, which causes difficulties in pricing interest rate claims, is usually eliminated by making specific assumptions on investment behavior or on the evolution of interest rates. In contrast, this article identifies the class of volatility structures that permits the path dependence to be captured by a single sufficient statistic. An equilibrium framework is provided where beliefs and technologies are restricted so that the resulting term structures have volatilities that belong to the restricted class. The models themselves can be characterized by a parsimonious set of parameters and can be initialized to an observed term structure without the introduction of ad-hoc time-varying parameters. Furthermore, since the dynamics of the resulting term structures are two-state Markovian, simple pricing mechanisms can be developed for interest rate claims. clevelandfed.org/research/workpaper/index.cfm Additional examples of such models include Brennan and Schwartz [1977], CIR [1980], Cox and Ross [1976], Dothan [I9781 and Vasicek [1977]. Such pricing problems have become increasingly more important, primarily due to the rapid growth of the overthe-counter market, where the majority of prices are quoted relative to the term structure. Indeed, in 1991, over-the-counter trading comprised a larger than 4trillionmarketofnotionalprincipal.Thisexceededthe4 trillion market of notional principal. This exceeded the 4trillionmarketofnotionalprincipal.Thisexceededthe2.2 trillion interest rate futures market and the $77 billion stock index futures market. Examples of such approaches include Amin and Jarrow [1991], Musiela, Turnbull and Wakeman [I9921 and Ritchken and Sankarasubramanian [1992].
SSRN Electronic Journal, 2001
the Western Finance Association meetings, the European Financial Management Association meetings,... more the Western Finance Association meetings, the European Financial Management Association meetings, the European Finance Association meetings and the Financial Management Association meetings for comments and suggestions. The usual disclaimer applies.
ABSTRACT Optimal equityholder decisions involve trade-offs between risk-minimizing strategies, wh... more ABSTRACT Optimal equityholder decisions involve trade-offs between risk-minimizing strategies, which reduce the likelihood of losing the charter, and risk-maximizing strategies, which exploit the insured-deposit base. When banks cannot respond dynamically to market information, we have seen that the bank optimally selects extreme positions. Given any flat-rate insurance scheme, incentives exist for firms to revise their portfolios dynamically in response to market information. These dynamic revisions are aimed at exploiting the insured-deposit base more fully, thereby mitigating the likelihood of bankruptcy. The additional value captured by equityholders responding dynamically to jointly maximize the charter value and the deposit insurance subsidy, beyond the static value, is captured in the value of the asset flexibility option. In the presence of the asset flexibility option, portfolio decisions may not be extreme and interior solutions may be optimal. The likelihood of interior solutions may increase as the number of portfolio revision opportunities expands. Moreover, the value and the insured deposit base, provided at a flat rate, increases with the number of portfolio revision opportunities. Our results suggest that the value of flat-rate deposit insurance established by static models underestimates the true value because it completely ignores the flexibility option. The impact of the flexibility option can be significant and, if ignored, may lead to understating the value of deposit insurance by as much as 40 percent. The results suggest that bank regulators should factor the flexibility option into any risk-adjusted capital guidelines and also into closure policies.
SSRN Electronic Journal, 2001
This article examines how the number of stochastic drivers and their associated volatility struct... more This article examines how the number of stochastic drivers and their associated volatility structures affect pricing accuracy and hedging performance in the swaption market. In spite of the fact that low dimensional one and two-factor models do not reflect historical correlations that exist among forward rates, we show that they are capable of accurately pricing swaptions as well as higher order multifactor models, across all expiry dates and over all underlying swap maturities. Effective out-of-sample pricing is necessary but not sufficient for good hedging. Indeed, regarding hedging, we show there are significant benefits in using multifactor models. This is true even if one accounts for the fact that fewer hedging instruments are required when single factor models are used to hedge swaptions. Our empirical findings have strong implications for the modeling and risk management of an array of actively traded derivatives that closely relate to swaptions.
Review of Financial Studies, 2012
We develop a model of nominal and real bond yield curves that has four stochastic drivers but sev... more We develop a model of nominal and real bond yield curves that has four stochastic drivers but seven factors: three factors primarily determine the cross-section of yields, whereas four volatility factors solely determine risk premia. The model is estimated using nominal Treasury yields, survey inflation forecasts, and inflation swap rates and has attractive empirical properties. Time-varying volatility is particularly apparent in shortterm real rates and expected inflation. Also, we detail the different economic forces that drive short-and long-term real and inflation risk premia and provide evidence that Treasury inflation-protected securities were undervalued prior to 2004 and during the recent financial crisis. (JEL G01, G12, G13) Policymakers and finance professionals often use the term structure of Treasury yields to infer expectations of inflation and real interest rates. Inflation expectations can gauge the credibility of a government's fiscal and monetary policies, whereas real rates measure the economic cost of financing investments and the tightness of monetary policy. However, Treasury yields embed time-varying risk premia that make it difficult to extract measures of expected inflation and real rates. This article presents a new methodology for decomposing Treasury yields and analyzes the determinants of the term structures of real rates, expected inflation, and inflation risk premia. The article The views expressed in this article do not necessarily represent those of the Federal Reserve Bank of Cleveland or the Federal Reserve System. For valuable comments, we thank Editor Pietro Veronesi and an anonymous referee, as well as seminar participants at the
The Journal of Finance, 1988
ABSTRACTThis article generalizes the single‐period linear‐programming bounds on option prices by ... more ABSTRACTThis article generalizes the single‐period linear‐programming bounds on option prices by allowing for a finite number of revision opportunities. It is shown that, in an incomplete market, the bounds on option prices can be derived using a modified binomial option‐pricing model. Tighter bounds are developed under more restrictive assumptions on probabilities and risk aversion. For this case the upper bounds are shown to coincide with the upper bounds derived by Perrakis, while the lower bounds are shown to be tighter.
The Journal of Finance, 1985
ABSTRACTThe purpose of this article is to compare the Perrakis and Ryan bounds of option prices i... more ABSTRACTThe purpose of this article is to compare the Perrakis and Ryan bounds of option prices in a single‐period model with option bounds derived using linear programming. It is shown that the upper bounds are identical but that the lower bounds are different. A comparison of these bounds, together with Merton's bounds and the Black‐Scholes prices in a lognormal securities market, is presented.
The Journal of Finance, 1990
ABSTRACT
The Journal of Finance, 1995
ABSTRACTThis article establishes efficient lattice algorithms for pricing American interest‐sensi... more ABSTRACTThis article establishes efficient lattice algorithms for pricing American interest‐sensitive claims in the Heath, Jarrow, and Morton paradigm, under the assumption that the volatility structure of forward rates is restricted to a class that permits a Markovian representation of the term structure. The class of volatilities that permits this representation is quite large and imposes no severe restrictions on the structure for the spot rate volatility. The algorithm exploits the Markovian property of the term structure and permits the efficient computation of all types of interest rate claims. Specific examples are provided.
Management Science, 1989
Merton, Perrakis and Ryan, Levy, and Ritchken have established option pricing bounds under first ... more Merton, Perrakis and Ryan, Levy, and Ritchken have established option pricing bounds under first and second stochastic dominance preferences. These bounds are particularly important for valuing contingent claims when continuous trading in the claim and/or underlying security does not exist. This article provides option bounds under higher orders of dominance. Specifically, option bounds are obtained by solving mathematical programs where preference structures on prices are represented by constraints. For first, second, third and higher orders of stochastic dominance preferences, the special linear structure of the mathematical programs allow analytical solutions to be obtained for the bounds. For DARA preferences, third order stochastic dominance, while being necessary, is not sufficient and additional constraints must be imposed. Unfortunately these additional constraints are nonlinear. While in this case closed form analytical solutions for the option bounds are not obtained, nume...
IIE Transactions, 1997
ABSTRACT
Financial Management, 1990
European Journal of Operational Research, 1994
ABSTRACT This article considers the problem of valuing a supply contract that requires the manufa... more ABSTRACT This article considers the problem of valuing a supply contract that requires the manufacturer to deliver fixed quantities of a product according to a predetermined schedule at fixed prices. Given that the raw material costs fluctuate randomly, the producer has capacity constraints, production costs depend on production rates, and that switching production rates result in additional charges, the problem is to establish an optimal production and inventory policy such that the schedule is met, and the value of the contract to the firm is maximized.
European Journal of Operational Research, 1991
Recently techniques of continuous time arbitrage and stochastic control theory have been used to ... more Recently techniques of continuous time arbitrage and stochastic control theory have been used to value risky ventures characterized by significant operating flexibility. While the advantages of these methods over the used discounted cash flow approaches have been well documented, implementation problems have emerged, primarily due to the immence mathematical and computational complexity inherent in these approaches and due to the fact that the methodology is not easily understood by management. This article uses a simple binomial framework which not only provides an easily understandable introduction to these, say, new methods, but also provides useful valuations in their own right.
European Journal of Operational Research, 2012
The authors wish to thank two anonymous referees for their valuable comments and suggestions that... more The authors wish to thank two anonymous referees for their valuable comments and suggestions that help improve the paper.
Decision Sciences, 1985
Current stochastic dominance algorithms use step functions to approximate the cumulative distribu... more Current stochastic dominance algorithms use step functions to approximate the cumulative distributions of the alternatives, even when the underlying random variables are known to be continuous. Since stochastic dominance tests require repeated integration of the cumulative distribution functions, a compounding of errors may result from this type of approximation. This article introduces a new stochastic dominance algorithm that approximates the cumulative distribution function by piccmise hear approximations. Comparisons between the new and old algorithms are performed for normally distributed alternatives. In about 95 percent of all cases, the two algorithms produce the same result. Subject A w Lkcidon Analysis Yogah Agamal is enrolled in the Ph.D. program in operations research at Case %tern Reserve Alok K. Gupta is enrolled in the Ph.D. program in operations research at Case Western Reserve include portfolio and risk management, option pricing theory, and computer simulation. University and is employed by Lcaseway 'Ramportation in Cleveland, Ohio. University and is employed by Bell Labs in Holmdel, New Jersey.
Decision Sciences, 1984
ABSTRACTIn many applications involving the construction of efficient sets, the parameters of the ... more ABSTRACTIn many applications involving the construction of efficient sets, the parameters of the alternatives are estimated using small examples. As a result, inefficient alternatives may be included in the sample efficient set and efficient alternatives left out. This paper investigates the effects of estimation risk when there are more than two alternatives and limited information. The study reveals that estimation risk is a severe handicap to the practical implementation of stochastic dominance and mean‐variance efficiency analysis.
We study the effects of credit risk in a supply chain where one retailer deals with competing ris... more We study the effects of credit risk in a supply chain where one retailer deals with competing risky suppliers who may default during their production lead-times. The suppliers, who compete for business with the retailer by establishing wholesale prices, are leaders in a Stackelberg game with the retailer. The retailer, facing uncertain future demand, chooses order quantities while weighing the benefits of procuring from the cheapest supplier against the advantages of reducing credit risk through diversification. Although, in general, the timing of the retailer-to-suppliers payments is important, we identify a family of wholesale pricing policies for which, in equilibrium, the suppliers and the retailer are indifferent between up-front and on-delivery payment schedules. Our analysis reveals that the equilibrium firms' profits decline as default risk increases. Furthermore, the decline rates for firms in different echelons of the supply chain depend on the shape of the demand distribution. If the wholesale prices were fixed, the retailer would benefit from the decreasing correlation of the defaults. However, if prices are endogenous to the model, the decreasing defaults' correlation alters the nature of the competition among the suppliers and lowers the equilibrium wholesale prices. We show that, in equilibrium, the retailer prefers suppliers with positively correlated default events. In contrast, the suppliers and the supply chain prefer defaults that are negatively correlated.
Working paper (Federal Reserve Bank of Cleveland), 2007
Working paper (Federal Reserve Bank of Cleveland), 1997
Working paper (Federal Reserve Bank of Cleveland), 1992
The linkages between term structures separated by finite time periods can be complex. Indeed, in ... more The linkages between term structures separated by finite time periods can be complex. Indeed, in general, the dynamics of the term structure could depend on the entire set of information revealed since the earlier date. This path dependence, which causes difficulties in pricing interest rate claims, is usually eliminated by making specific assumptions on investment behavior or on the evolution of interest rates. In contrast, this article identifies the class of volatility structures that permits the path dependence to be captured by a single sufficient statistic. An equilibrium framework is provided where beliefs and technologies are restricted so that the resulting term structures have volatilities that belong to the restricted class. The models themselves can be characterized by a parsimonious set of parameters and can be initialized to an observed term structure without the introduction of ad-hoc time-varying parameters. Furthermore, since the dynamics of the resulting term structures are two-state Markovian, simple pricing mechanisms can be developed for interest rate claims. clevelandfed.org/research/workpaper/index.cfm Additional examples of such models include Brennan and Schwartz [1977], CIR [1980], Cox and Ross [1976], Dothan [I9781 and Vasicek [1977]. Such pricing problems have become increasingly more important, primarily due to the rapid growth of the overthe-counter market, where the majority of prices are quoted relative to the term structure. Indeed, in 1991, over-the-counter trading comprised a larger than 4trillionmarketofnotionalprincipal.Thisexceededthe4 trillion market of notional principal. This exceeded the 4trillionmarketofnotionalprincipal.Thisexceededthe2.2 trillion interest rate futures market and the $77 billion stock index futures market. Examples of such approaches include Amin and Jarrow [1991], Musiela, Turnbull and Wakeman [I9921 and Ritchken and Sankarasubramanian [1992].
SSRN Electronic Journal, 2001
the Western Finance Association meetings, the European Financial Management Association meetings,... more the Western Finance Association meetings, the European Financial Management Association meetings, the European Finance Association meetings and the Financial Management Association meetings for comments and suggestions. The usual disclaimer applies.
ABSTRACT Optimal equityholder decisions involve trade-offs between risk-minimizing strategies, wh... more ABSTRACT Optimal equityholder decisions involve trade-offs between risk-minimizing strategies, which reduce the likelihood of losing the charter, and risk-maximizing strategies, which exploit the insured-deposit base. When banks cannot respond dynamically to market information, we have seen that the bank optimally selects extreme positions. Given any flat-rate insurance scheme, incentives exist for firms to revise their portfolios dynamically in response to market information. These dynamic revisions are aimed at exploiting the insured-deposit base more fully, thereby mitigating the likelihood of bankruptcy. The additional value captured by equityholders responding dynamically to jointly maximize the charter value and the deposit insurance subsidy, beyond the static value, is captured in the value of the asset flexibility option. In the presence of the asset flexibility option, portfolio decisions may not be extreme and interior solutions may be optimal. The likelihood of interior solutions may increase as the number of portfolio revision opportunities expands. Moreover, the value and the insured deposit base, provided at a flat rate, increases with the number of portfolio revision opportunities. Our results suggest that the value of flat-rate deposit insurance established by static models underestimates the true value because it completely ignores the flexibility option. The impact of the flexibility option can be significant and, if ignored, may lead to understating the value of deposit insurance by as much as 40 percent. The results suggest that bank regulators should factor the flexibility option into any risk-adjusted capital guidelines and also into closure policies.
SSRN Electronic Journal, 2001
This article examines how the number of stochastic drivers and their associated volatility struct... more This article examines how the number of stochastic drivers and their associated volatility structures affect pricing accuracy and hedging performance in the swaption market. In spite of the fact that low dimensional one and two-factor models do not reflect historical correlations that exist among forward rates, we show that they are capable of accurately pricing swaptions as well as higher order multifactor models, across all expiry dates and over all underlying swap maturities. Effective out-of-sample pricing is necessary but not sufficient for good hedging. Indeed, regarding hedging, we show there are significant benefits in using multifactor models. This is true even if one accounts for the fact that fewer hedging instruments are required when single factor models are used to hedge swaptions. Our empirical findings have strong implications for the modeling and risk management of an array of actively traded derivatives that closely relate to swaptions.
Review of Financial Studies, 2012
We develop a model of nominal and real bond yield curves that has four stochastic drivers but sev... more We develop a model of nominal and real bond yield curves that has four stochastic drivers but seven factors: three factors primarily determine the cross-section of yields, whereas four volatility factors solely determine risk premia. The model is estimated using nominal Treasury yields, survey inflation forecasts, and inflation swap rates and has attractive empirical properties. Time-varying volatility is particularly apparent in shortterm real rates and expected inflation. Also, we detail the different economic forces that drive short-and long-term real and inflation risk premia and provide evidence that Treasury inflation-protected securities were undervalued prior to 2004 and during the recent financial crisis. (JEL G01, G12, G13) Policymakers and finance professionals often use the term structure of Treasury yields to infer expectations of inflation and real interest rates. Inflation expectations can gauge the credibility of a government's fiscal and monetary policies, whereas real rates measure the economic cost of financing investments and the tightness of monetary policy. However, Treasury yields embed time-varying risk premia that make it difficult to extract measures of expected inflation and real rates. This article presents a new methodology for decomposing Treasury yields and analyzes the determinants of the term structures of real rates, expected inflation, and inflation risk premia. The article The views expressed in this article do not necessarily represent those of the Federal Reserve Bank of Cleveland or the Federal Reserve System. For valuable comments, we thank Editor Pietro Veronesi and an anonymous referee, as well as seminar participants at the
The Journal of Finance, 1988
ABSTRACTThis article generalizes the single‐period linear‐programming bounds on option prices by ... more ABSTRACTThis article generalizes the single‐period linear‐programming bounds on option prices by allowing for a finite number of revision opportunities. It is shown that, in an incomplete market, the bounds on option prices can be derived using a modified binomial option‐pricing model. Tighter bounds are developed under more restrictive assumptions on probabilities and risk aversion. For this case the upper bounds are shown to coincide with the upper bounds derived by Perrakis, while the lower bounds are shown to be tighter.
The Journal of Finance, 1985
ABSTRACTThe purpose of this article is to compare the Perrakis and Ryan bounds of option prices i... more ABSTRACTThe purpose of this article is to compare the Perrakis and Ryan bounds of option prices in a single‐period model with option bounds derived using linear programming. It is shown that the upper bounds are identical but that the lower bounds are different. A comparison of these bounds, together with Merton's bounds and the Black‐Scholes prices in a lognormal securities market, is presented.
The Journal of Finance, 1990
ABSTRACT
The Journal of Finance, 1995
ABSTRACTThis article establishes efficient lattice algorithms for pricing American interest‐sensi... more ABSTRACTThis article establishes efficient lattice algorithms for pricing American interest‐sensitive claims in the Heath, Jarrow, and Morton paradigm, under the assumption that the volatility structure of forward rates is restricted to a class that permits a Markovian representation of the term structure. The class of volatilities that permits this representation is quite large and imposes no severe restrictions on the structure for the spot rate volatility. The algorithm exploits the Markovian property of the term structure and permits the efficient computation of all types of interest rate claims. Specific examples are provided.
Management Science, 1989
Merton, Perrakis and Ryan, Levy, and Ritchken have established option pricing bounds under first ... more Merton, Perrakis and Ryan, Levy, and Ritchken have established option pricing bounds under first and second stochastic dominance preferences. These bounds are particularly important for valuing contingent claims when continuous trading in the claim and/or underlying security does not exist. This article provides option bounds under higher orders of dominance. Specifically, option bounds are obtained by solving mathematical programs where preference structures on prices are represented by constraints. For first, second, third and higher orders of stochastic dominance preferences, the special linear structure of the mathematical programs allow analytical solutions to be obtained for the bounds. For DARA preferences, third order stochastic dominance, while being necessary, is not sufficient and additional constraints must be imposed. Unfortunately these additional constraints are nonlinear. While in this case closed form analytical solutions for the option bounds are not obtained, nume...
IIE Transactions, 1997
ABSTRACT
Financial Management, 1990
European Journal of Operational Research, 1994
ABSTRACT This article considers the problem of valuing a supply contract that requires the manufa... more ABSTRACT This article considers the problem of valuing a supply contract that requires the manufacturer to deliver fixed quantities of a product according to a predetermined schedule at fixed prices. Given that the raw material costs fluctuate randomly, the producer has capacity constraints, production costs depend on production rates, and that switching production rates result in additional charges, the problem is to establish an optimal production and inventory policy such that the schedule is met, and the value of the contract to the firm is maximized.
European Journal of Operational Research, 1991
Recently techniques of continuous time arbitrage and stochastic control theory have been used to ... more Recently techniques of continuous time arbitrage and stochastic control theory have been used to value risky ventures characterized by significant operating flexibility. While the advantages of these methods over the used discounted cash flow approaches have been well documented, implementation problems have emerged, primarily due to the immence mathematical and computational complexity inherent in these approaches and due to the fact that the methodology is not easily understood by management. This article uses a simple binomial framework which not only provides an easily understandable introduction to these, say, new methods, but also provides useful valuations in their own right.
European Journal of Operational Research, 2012
The authors wish to thank two anonymous referees for their valuable comments and suggestions that... more The authors wish to thank two anonymous referees for their valuable comments and suggestions that help improve the paper.
Decision Sciences, 1985
Current stochastic dominance algorithms use step functions to approximate the cumulative distribu... more Current stochastic dominance algorithms use step functions to approximate the cumulative distributions of the alternatives, even when the underlying random variables are known to be continuous. Since stochastic dominance tests require repeated integration of the cumulative distribution functions, a compounding of errors may result from this type of approximation. This article introduces a new stochastic dominance algorithm that approximates the cumulative distribution function by piccmise hear approximations. Comparisons between the new and old algorithms are performed for normally distributed alternatives. In about 95 percent of all cases, the two algorithms produce the same result. Subject A w Lkcidon Analysis Yogah Agamal is enrolled in the Ph.D. program in operations research at Case %tern Reserve Alok K. Gupta is enrolled in the Ph.D. program in operations research at Case Western Reserve include portfolio and risk management, option pricing theory, and computer simulation. University and is employed by Lcaseway 'Ramportation in Cleveland, Ohio. University and is employed by Bell Labs in Holmdel, New Jersey.
Decision Sciences, 1984
ABSTRACTIn many applications involving the construction of efficient sets, the parameters of the ... more ABSTRACTIn many applications involving the construction of efficient sets, the parameters of the alternatives are estimated using small examples. As a result, inefficient alternatives may be included in the sample efficient set and efficient alternatives left out. This paper investigates the effects of estimation risk when there are more than two alternatives and limited information. The study reveals that estimation risk is a severe handicap to the practical implementation of stochastic dominance and mean‐variance efficiency analysis.
We study the effects of credit risk in a supply chain where one retailer deals with competing ris... more We study the effects of credit risk in a supply chain where one retailer deals with competing risky suppliers who may default during their production lead-times. The suppliers, who compete for business with the retailer by establishing wholesale prices, are leaders in a Stackelberg game with the retailer. The retailer, facing uncertain future demand, chooses order quantities while weighing the benefits of procuring from the cheapest supplier against the advantages of reducing credit risk through diversification. Although, in general, the timing of the retailer-to-suppliers payments is important, we identify a family of wholesale pricing policies for which, in equilibrium, the suppliers and the retailer are indifferent between up-front and on-delivery payment schedules. Our analysis reveals that the equilibrium firms' profits decline as default risk increases. Furthermore, the decline rates for firms in different echelons of the supply chain depend on the shape of the demand distribution. If the wholesale prices were fixed, the retailer would benefit from the decreasing correlation of the defaults. However, if prices are endogenous to the model, the decreasing defaults' correlation alters the nature of the competition among the suppliers and lowers the equilibrium wholesale prices. We show that, in equilibrium, the retailer prefers suppliers with positively correlated default events. In contrast, the suppliers and the supply chain prefer defaults that are negatively correlated.
Working paper (Federal Reserve Bank of Cleveland), 2007
Working paper (Federal Reserve Bank of Cleveland), 1997