Richard Stapleton - Academia.edu (original) (raw)
Papers by Richard Stapleton
We consider portfolios whose returns depend on at least three variables and show the effect of th... more We consider portfolios whose returns depend on at least three variables and show the effect of the correlation structure on the probabilities of the extreme outcomes of the portfolio return, using a multivariate binomial approximation. The portfolio risk is then managed by using derivatives. We illustrate this risk management both with simple options, whose payoff depends upon only one of
We present a necessary and sufficient condition on an agent’s utility function for a simple mean ... more We present a necessary and sufficient condition on an agent’s utility function for a simple mean preserving spread in an independent background risk to increase the agent’s risk aversion (incremental risk vulnerability). Gollier and Pratt (1996) have shown that declining and convex risk aversion as well as standard risk aversion are sufficient for risk vulnerability. We show that these conditions
In this paper we investigate models of the term structure where the factors are interest rates. A... more In this paper we investigate models of the term structure where the factors are interest rates. As an example, we derive a no-arbitrage model of the term structure in which any two futures (as opposed to forward) rates act as factors. The term structure shifts and tilts as the factor rates vary. The cross-sectional properties of the model derive from
The Journal of Derivatives, 1994
SSRN Electronic Journal, 2000
We derive general properties of two-factor models of the term structure of interest rates and, in... more We derive general properties of two-factor models of the term structure of interest rates and, in particular, the process for futures prices and rates. Then, as a special case, we derive a no-arbitrage model of the term structure in which any two futures rates act as factors. In this model, the term structure shifts and tilts as the factor rates vary. The cross-sectional properties of the model derive from the solution of a two-dimensional, autoregressive process for the short-term rate, which exhibits both mean-reversion and a lagged persistence parameter. We show that the correlation of the futures rates is restricted by the no-arbitrage conditions of the model. In addition, we investigate the determinants of the volatilities and the correlations of the futures rates of various maturities. These are shown to be related to the volatility of the short rate, the volatility of the second factor, the degree of meanreversion and the persistence of the second factor shock. We also discuss the extension of our model to three or more factors. We obtain specific results for futures rates in the case where the logarithm of the short-term rate [e.g., the London Inter-Bank Offer Rate (LIBOR)] follows a two-dimensional process. We calibrate the model using data from Eurocurrency interest rate futures contracts.
SSRN Electronic Journal, 2000
We examine the effects of non-portfolio risks on optimal portfolio choice. Examples of non-portfo... more We examine the effects of non-portfolio risks on optimal portfolio choice. Examples of non-portfolio risks include, among others, uncertain labor income, uncertainty about the terminal value of fixed assets such as housing and uncertainty about future tax liabilities . In particular, while some of these risks are added to portfolio value and have been amply studied, others are multiplicative in nature and have received far less attention. Moreover, the combined effects of multiple risks lead to some seemingly paradoxical choice behavior. We rationalize such behavior and we show how non-portfolio risks might lead to seemingly U-shaped relative risk aversion for a representative investor, as found empirically by Ait-Sahilia and Lo (2000) and Jackwerth (2000). JEL classification: G 11
We define a class of risk-taking-neutral (RTN) background risks. These background risks have the ... more We define a class of risk-taking-neutral (RTN) background risks. These background risks have the property that they will not alter decisions made with respect to another risk, for individuals with HARA utility. If we wish to compare a decision made with and without some exogenous background risk, it is often easier to compare the decision made to one made with a RTN background risk. We use this methodology to prove and extend a well-known theorem about dynamic investment strategy, due to Mossin (1968a). We also use this methodology to analyze investment behavior in the presence of an income tax as well as to analyze investment behavior in the presence of particular types of background risks.
Review of Derivatives Research, 2002
In this paper, we present a methodology for approximating a correlated multivariate-lognormal pro... more In this paper, we present a methodology for approximating a correlated multivariate-lognormal process with a recombining or “simple” multivariate-binomial process. The method represents an extension and implementation of previous work by Nelson and Ramaswamy (1990) and Ho, Stapleton and Subrahmanyam (1995) on diffusion approximation. The general method is illustrated by pricing a Bermudan-style put option on the minimum of three
We build a three-factor term-structure of interest rates model and use it to price corporate bond... more We build a three-factor term-structure of interest rates model and use it to price corporate bonds. The first two factors allow the risk-free term structure to shift and tilt. The third factor generates a stochastic credit-risk premium. To implement the model, we apply the Peterson and Stapleton (2002) diffusion approximation methodology. The method approximates a correlated and lagged-dependent lognormal diffusion
A Two-factor Lognormal Model of the Term Structure andthe Valuation of American-Style Options on ... more A Two-factor Lognormal Model of the Term Structure andthe Valuation of American-Style Options on BondsWe build a no-arbitrage model of the term structure, using two stochastic factors, the shortterminterest rate and the premium of the forward rate over the short-term interest rate.The model extends the lognormal interest rate model of Black and Karasinski #1991# totwo factors. It allows for mean
SSRN Electronic Journal, 2002
Investors choosing a portfolio strategy, in order to secure a pension at a future date for exampl... more Investors choosing a portfolio strategy, in order to secure a pension at a future date for example, are faced with many uncertainties. One major uncertainty is the amount by which their pension fund will be supplemented by personal savings from a variety of sources such as life insurance contracts, bequests, or property sales. Over long periods of time these uncertainties are likely to be large and difficult to hedge, and hence may have a significant effect on the dynamic portfolio strategy. Drawing on the results of previous literature on the reaction of investors to non-unhedgeable background risk, and on the theory of stochastic dynamic programming, this article derives optimal strategies for investors maximising the expected utility of terminal wealth, where this wealth consists of the value of a pension fund plus accumulated personal savings. Numerical results, assuming that the market portfolio and the expectation of personal savings follow possibly correlated geometric Brownian motions, are derived to illustrate the effects of the size and uncertainty of the personal savings, as well as the effect of the resolution of the uncertainty in them over time. The computation uses a new technique for implementing the stochastic dynamic programming. This involves a binomial approximation, in two dimensions, which ensures that the computations are feasible for relatively long-term problems.
SSRN Electronic Journal, 2000
ABSTRACT Huang and Stapleton (2012) characterize cautiousness as a measure of skewness preference... more ABSTRACT Huang and Stapleton (2012) characterize cautiousness as a measure of skewness preferences using a simple portfolio problem with a risk-free bond, a stock, and an option on the stock. In this paper, we explain the link between cautiousness and skewness preferences in a more general context where agents face two risks with one of them being a convex (or concave) function of the other.
SSRN Electronic Journal, 2000
The Valuation of American-style Swaptions in a Two-factor Spot-Futures Model.
Asset Allocation Given Non-Market Wealth and Rollover Risks. We show the eect, on optimal portfol... more Asset Allocation Given Non-Market Wealth and Rollover Risks. We show the eect, on optimal portfolio strategy, of a combination of addi-
We build a no-arbitrage model of the term structure, using two stochastic factors on each date, t... more We build a no-arbitrage model of the term structure, using two stochastic factors on each date, the short-term interest rate and the forward premium. The model is essentially an extension to two factors of the lognormal interest rate model of Black-Karazinski. It allows for mean reversion in the short rate and in the forward premium. The method is computationally efficient
Review of Financial Studies, 1995
... USA. We are grateful to participants at these presen-tations and to John Chang, Chi-fu Huang ... more ... USA. We are grateful to participants at these presen-tations and to John Chang, Chi-fu Huang (the editor), Apoorva Koticha, Ser-Huang Poon, Steven Tsay, and an anonymous referee for comments on previous drafts. Address ...
We consider portfolios whose returns depend on at least three variables and show the effect of th... more We consider portfolios whose returns depend on at least three variables and show the effect of the correlation structure on the probabilities of the extreme outcomes of the portfolio return, using a multivariate binomial approximation. The portfolio risk is then managed by using derivatives. We illustrate this risk management both with simple options, whose payoff depends upon only one of
We present a necessary and sufficient condition on an agent’s utility function for a simple mean ... more We present a necessary and sufficient condition on an agent’s utility function for a simple mean preserving spread in an independent background risk to increase the agent’s risk aversion (incremental risk vulnerability). Gollier and Pratt (1996) have shown that declining and convex risk aversion as well as standard risk aversion are sufficient for risk vulnerability. We show that these conditions
In this paper we investigate models of the term structure where the factors are interest rates. A... more In this paper we investigate models of the term structure where the factors are interest rates. As an example, we derive a no-arbitrage model of the term structure in which any two futures (as opposed to forward) rates act as factors. The term structure shifts and tilts as the factor rates vary. The cross-sectional properties of the model derive from
The Journal of Derivatives, 1994
SSRN Electronic Journal, 2000
We derive general properties of two-factor models of the term structure of interest rates and, in... more We derive general properties of two-factor models of the term structure of interest rates and, in particular, the process for futures prices and rates. Then, as a special case, we derive a no-arbitrage model of the term structure in which any two futures rates act as factors. In this model, the term structure shifts and tilts as the factor rates vary. The cross-sectional properties of the model derive from the solution of a two-dimensional, autoregressive process for the short-term rate, which exhibits both mean-reversion and a lagged persistence parameter. We show that the correlation of the futures rates is restricted by the no-arbitrage conditions of the model. In addition, we investigate the determinants of the volatilities and the correlations of the futures rates of various maturities. These are shown to be related to the volatility of the short rate, the volatility of the second factor, the degree of meanreversion and the persistence of the second factor shock. We also discuss the extension of our model to three or more factors. We obtain specific results for futures rates in the case where the logarithm of the short-term rate [e.g., the London Inter-Bank Offer Rate (LIBOR)] follows a two-dimensional process. We calibrate the model using data from Eurocurrency interest rate futures contracts.
SSRN Electronic Journal, 2000
We examine the effects of non-portfolio risks on optimal portfolio choice. Examples of non-portfo... more We examine the effects of non-portfolio risks on optimal portfolio choice. Examples of non-portfolio risks include, among others, uncertain labor income, uncertainty about the terminal value of fixed assets such as housing and uncertainty about future tax liabilities . In particular, while some of these risks are added to portfolio value and have been amply studied, others are multiplicative in nature and have received far less attention. Moreover, the combined effects of multiple risks lead to some seemingly paradoxical choice behavior. We rationalize such behavior and we show how non-portfolio risks might lead to seemingly U-shaped relative risk aversion for a representative investor, as found empirically by Ait-Sahilia and Lo (2000) and Jackwerth (2000). JEL classification: G 11
We define a class of risk-taking-neutral (RTN) background risks. These background risks have the ... more We define a class of risk-taking-neutral (RTN) background risks. These background risks have the property that they will not alter decisions made with respect to another risk, for individuals with HARA utility. If we wish to compare a decision made with and without some exogenous background risk, it is often easier to compare the decision made to one made with a RTN background risk. We use this methodology to prove and extend a well-known theorem about dynamic investment strategy, due to Mossin (1968a). We also use this methodology to analyze investment behavior in the presence of an income tax as well as to analyze investment behavior in the presence of particular types of background risks.
Review of Derivatives Research, 2002
In this paper, we present a methodology for approximating a correlated multivariate-lognormal pro... more In this paper, we present a methodology for approximating a correlated multivariate-lognormal process with a recombining or “simple” multivariate-binomial process. The method represents an extension and implementation of previous work by Nelson and Ramaswamy (1990) and Ho, Stapleton and Subrahmanyam (1995) on diffusion approximation. The general method is illustrated by pricing a Bermudan-style put option on the minimum of three
We build a three-factor term-structure of interest rates model and use it to price corporate bond... more We build a three-factor term-structure of interest rates model and use it to price corporate bonds. The first two factors allow the risk-free term structure to shift and tilt. The third factor generates a stochastic credit-risk premium. To implement the model, we apply the Peterson and Stapleton (2002) diffusion approximation methodology. The method approximates a correlated and lagged-dependent lognormal diffusion
A Two-factor Lognormal Model of the Term Structure andthe Valuation of American-Style Options on ... more A Two-factor Lognormal Model of the Term Structure andthe Valuation of American-Style Options on BondsWe build a no-arbitrage model of the term structure, using two stochastic factors, the shortterminterest rate and the premium of the forward rate over the short-term interest rate.The model extends the lognormal interest rate model of Black and Karasinski #1991# totwo factors. It allows for mean
SSRN Electronic Journal, 2002
Investors choosing a portfolio strategy, in order to secure a pension at a future date for exampl... more Investors choosing a portfolio strategy, in order to secure a pension at a future date for example, are faced with many uncertainties. One major uncertainty is the amount by which their pension fund will be supplemented by personal savings from a variety of sources such as life insurance contracts, bequests, or property sales. Over long periods of time these uncertainties are likely to be large and difficult to hedge, and hence may have a significant effect on the dynamic portfolio strategy. Drawing on the results of previous literature on the reaction of investors to non-unhedgeable background risk, and on the theory of stochastic dynamic programming, this article derives optimal strategies for investors maximising the expected utility of terminal wealth, where this wealth consists of the value of a pension fund plus accumulated personal savings. Numerical results, assuming that the market portfolio and the expectation of personal savings follow possibly correlated geometric Brownian motions, are derived to illustrate the effects of the size and uncertainty of the personal savings, as well as the effect of the resolution of the uncertainty in them over time. The computation uses a new technique for implementing the stochastic dynamic programming. This involves a binomial approximation, in two dimensions, which ensures that the computations are feasible for relatively long-term problems.
SSRN Electronic Journal, 2000
ABSTRACT Huang and Stapleton (2012) characterize cautiousness as a measure of skewness preference... more ABSTRACT Huang and Stapleton (2012) characterize cautiousness as a measure of skewness preferences using a simple portfolio problem with a risk-free bond, a stock, and an option on the stock. In this paper, we explain the link between cautiousness and skewness preferences in a more general context where agents face two risks with one of them being a convex (or concave) function of the other.
SSRN Electronic Journal, 2000
The Valuation of American-style Swaptions in a Two-factor Spot-Futures Model.
Asset Allocation Given Non-Market Wealth and Rollover Risks. We show the eect, on optimal portfol... more Asset Allocation Given Non-Market Wealth and Rollover Risks. We show the eect, on optimal portfolio strategy, of a combination of addi-
We build a no-arbitrage model of the term structure, using two stochastic factors on each date, t... more We build a no-arbitrage model of the term structure, using two stochastic factors on each date, the short-term interest rate and the forward premium. The model is essentially an extension to two factors of the lognormal interest rate model of Black-Karazinski. It allows for mean reversion in the short rate and in the forward premium. The method is computationally efficient
Review of Financial Studies, 1995
... USA. We are grateful to participants at these presen-tations and to John Chang, Chi-fu Huang ... more ... USA. We are grateful to participants at these presen-tations and to John Chang, Chi-fu Huang (the editor), Apoorva Koticha, Ser-Huang Poon, Steven Tsay, and an anonymous referee for comments on previous drafts. Address ...