Interest rates risk-premium and shape of the yield curve

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July 2016, 21(5): 1603-1615. doi: 10.3934/dcdsb.2016013

Interest rates risk-premium and shape of the yield curve

1.	Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025, United States

Received April 2015 Revised December 2015 Published April 2016

Abstract
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We apply the general theory of pricing in incomplete markets, due to the author, on the problem of pricing bonds for the Hull-White stochastic interest rate model. As pricing in incomplete markets involves more market parameters than the classical theory, and as the derived risk premium is time-dependent, the proposed methodology might offer a better way for replicating different shapes of the empirically observed yield curves. For example, the so-called humped yield curve can be obtained from a normal yield curve by only increasing the investors risk aversion.

Keywords: optimal pricing., yield curve, risk premium, Interest rate.

Mathematics Subject Classification: Primary: 60H10, 60G40, 93E2.

Citation: Srdjan Stojanovic. Interest rates risk-premium and shape of the yield curve. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1603-1615. doi: 10.3934/dcdsb.2016013

References:

[1]	D. Becherer, Utility-indifference hedging and valuation via reaction-diffusion systems,, Proc. R. Soc. Lond. A, 460 (2004), 27. doi: 10.1098/rspa.2003.1234.
[2]	F. Black and M. Scholes, The pricing of options and corporate liabilities,, J. Political Econ., 81 (1973), 637. doi: 10.1086/260062.
[3]	D. Brigo and F. Mercurio, Interest Rate Models Theory and Practice,, Springer, (2001). doi: 10.1007/978-3-662-04553-4.
[4]	M. Davis, V. G. Panas and T. Zariphopoulou, European option pricing with transaction costs,, SIAM Journal on Control and Optimization, 31 (1993), 470. doi: 10.1137/0331022.
[5]	A. Friedman, Stochastic Differential Equations,, Vol 1 & 2, (1975).
[6]	S. D. Hodges and A. Neuberger, Optimal replication of contingent claims under transaction costs,, Review of Futures Markets, 8 (1989), 222.
[7]	J. Hull and A. White, Pricing interest-rate derivative securities,, The Review of Financial Studies, 3 (1990), 573. doi: 10.1093/rfs/3.4.573.
[8]	L. Jiang, Mathematical Modeling and Methods of Option Pricing,, World Scientific Publishing, (2005). doi: 10.1142/5855.
[9]	J. Kallsen, Utility-based derivative pricing in incomplete markets,, Mathematical Finance-Bachelier Congress 2000, (2000), 313.
[10]	Z. Kang and S. Stojanovic, Interest rate risk premium and equity valuation,, Journal of Systems Science and Complexity, 23 (2010), 484. doi: 10.1007/s11424-010-0142-y.
[11]	G. Liang and L. Jiang, A modified structural model for credit risk,, IMA Journal of Management Mathematics, 23 (2012), 147. doi: 10.1093/imaman/dpr004.
[12]	R. C. Merton, Theory of rational option pricing,, Bell Journal of Economics and Management Science, 4 (1973), 141. doi: 10.2307/3003143.
[13]	R. C. Merton, Continuous-Time Finance,, Wiley-Blackwell, (1990).
[14]	M. Musiela and T. Zariphopoulou, An example of indifference prices under exponential preferences,, Finance and Stochastics, 8 (2004), 229. doi: 10.1007/s00780-003-0112-5.
[15]	R. Rouge and N. El Karoui, Pricing via utility maximization and entropy,, Mathematical Finance, 10 (2000), 259. doi: 10.1111/1467-9965.00093.
[16]	S. Stojanovic, Computational Financial Mathematics using MATHEMATICA®,, Birkhauser, (2003). doi: 10.1007/978-1-4612-0043-7.
[17]	S. Stojanovic, Risk premium and fair option prices under stochastic volatility: The HARA solution,, C. R. Acad. Sci. Paris Ser. I, 340 (2005), 551. doi: 10.1016/j.crma.2004.11.002.
[18]	S. Stojanovic, Stochastic Volatility & Risk Premium,, Lecture Notes, (2005).
[19]	S. Stojanovic, Pricing and hedging of multi type contracts under multidimensional risks in incomplete markets modeled by general Itô SDE systems,, Asia Pacific Financial Markets, 13 (2006), 345.
[20]	S. Stojanovic, Advanced Financial Engineering for Interest Rates, Equity, and FX,, Lecture Notes, (2007).
[21]	S. Stojanovic, Any-utility neutral and indifference pricing and hedging,, Risk and Decision Analysis, 4 (2013), 103.
[22]	S. Stojanovic, Neutral and Indifference Portfolio Pricing, Hedging and Investing,, Springer, (2011).
[23]	O. Vasicek, An equilibrium characterization of the term structure,, Journal of Financial Economics, 5 (1977), 177. doi: 10.1002/9781119186229.ch6.

show all references

References:

[1]	D. Becherer, Utility-indifference hedging and valuation via reaction-diffusion systems,, Proc. R. Soc. Lond. A, 460 (2004), 27. doi: 10.1098/rspa.2003.1234.
[2]	F. Black and M. Scholes, The pricing of options and corporate liabilities,, J. Political Econ., 81 (1973), 637. doi: 10.1086/260062.
[3]	D. Brigo and F. Mercurio, Interest Rate Models Theory and Practice,, Springer, (2001). doi: 10.1007/978-3-662-04553-4.
[4]	M. Davis, V. G. Panas and T. Zariphopoulou, European option pricing with transaction costs,, SIAM Journal on Control and Optimization, 31 (1993), 470. doi: 10.1137/0331022.
[5]	A. Friedman, Stochastic Differential Equations,, Vol 1 & 2, (1975).
[6]	S. D. Hodges and A. Neuberger, Optimal replication of contingent claims under transaction costs,, Review of Futures Markets, 8 (1989), 222.
[7]	J. Hull and A. White, Pricing interest-rate derivative securities,, The Review of Financial Studies, 3 (1990), 573. doi: 10.1093/rfs/3.4.573.
[8]	L. Jiang, Mathematical Modeling and Methods of Option Pricing,, World Scientific Publishing, (2005). doi: 10.1142/5855.
[9]	J. Kallsen, Utility-based derivative pricing in incomplete markets,, Mathematical Finance-Bachelier Congress 2000, (2000), 313.
[10]	Z. Kang and S. Stojanovic, Interest rate risk premium and equity valuation,, Journal of Systems Science and Complexity, 23 (2010), 484. doi: 10.1007/s11424-010-0142-y.
[11]	G. Liang and L. Jiang, A modified structural model for credit risk,, IMA Journal of Management Mathematics, 23 (2012), 147. doi: 10.1093/imaman/dpr004.
[12]	R. C. Merton, Theory of rational option pricing,, Bell Journal of Economics and Management Science, 4 (1973), 141. doi: 10.2307/3003143.
[13]	R. C. Merton, Continuous-Time Finance,, Wiley-Blackwell, (1990).
[14]	M. Musiela and T. Zariphopoulou, An example of indifference prices under exponential preferences,, Finance and Stochastics, 8 (2004), 229. doi: 10.1007/s00780-003-0112-5.
[15]	R. Rouge and N. El Karoui, Pricing via utility maximization and entropy,, Mathematical Finance, 10 (2000), 259. doi: 10.1111/1467-9965.00093.
[16]	S. Stojanovic, Computational Financial Mathematics using MATHEMATICA®,, Birkhauser, (2003). doi: 10.1007/978-1-4612-0043-7.
[17]	S. Stojanovic, Risk premium and fair option prices under stochastic volatility: The HARA solution,, C. R. Acad. Sci. Paris Ser. I, 340 (2005), 551. doi: 10.1016/j.crma.2004.11.002.
[18]	S. Stojanovic, Stochastic Volatility & Risk Premium,, Lecture Notes, (2005).
[19]	S. Stojanovic, Pricing and hedging of multi type contracts under multidimensional risks in incomplete markets modeled by general Itô SDE systems,, Asia Pacific Financial Markets, 13 (2006), 345.
[20]	S. Stojanovic, Advanced Financial Engineering for Interest Rates, Equity, and FX,, Lecture Notes, (2007).
[21]	S. Stojanovic, Any-utility neutral and indifference pricing and hedging,, Risk and Decision Analysis, 4 (2013), 103.
[22]	S. Stojanovic, Neutral and Indifference Portfolio Pricing, Hedging and Investing,, Springer, (2011).
[23]	O. Vasicek, An equilibrium characterization of the term structure,, Journal of Financial Economics, 5 (1977), 177. doi: 10.1002/9781119186229.ch6.

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