Interest rates risk-premium and shape of the yield curve

Previous Article
A generalization of the Blaschke-Lebesgue problem to a kind of convex domains
DCDS-B Home
This Issue
Next Article
Local strong solutions to the compressible viscous magnetohydrodynamic equations

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
Related Papers

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. Google Scholar
[2]	F. Black and M. Scholes, The pricing of options and corporate liabilities,, J. Political Econ., 81 (1973), 637. doi: 10.1086/260062. Google Scholar
[3]	D. Brigo and F. Mercurio, Interest Rate Models Theory and Practice,, Springer, (2001). doi: 10.1007/978-3-662-04553-4. Google Scholar
[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. Google Scholar
[5]	A. Friedman, Stochastic Differential Equations,, Vol 1 & 2, (1975). Google Scholar
[6]	S. D. Hodges and A. Neuberger, Optimal replication of contingent claims under transaction costs,, Review of Futures Markets, 8 (1989), 222. Google Scholar
[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. Google Scholar
[8]	L. Jiang, Mathematical Modeling and Methods of Option Pricing,, World Scientific Publishing, (2005). doi: 10.1142/5855. Google Scholar
[9]	J. Kallsen, Utility-based derivative pricing in incomplete markets,, Mathematical Finance-Bachelier Congress 2000, (2000), 313. Google Scholar
[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. Google Scholar
[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. Google Scholar
[12]	R. C. Merton, Theory of rational option pricing,, Bell Journal of Economics and Management Science, 4 (1973), 141. doi: 10.2307/3003143. Google Scholar
[13]	R. C. Merton, Continuous-Time Finance,, Wiley-Blackwell, (1990). Google Scholar
[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. Google Scholar
[15]	R. Rouge and N. El Karoui, Pricing via utility maximization and entropy,, Mathematical Finance, 10 (2000), 259. doi: 10.1111/1467-9965.00093. Google Scholar
[16]	S. Stojanovic, Computational Financial Mathematics using MATHEMATICA®,, Birkhauser, (2003). doi: 10.1007/978-1-4612-0043-7. Google Scholar
[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. Google Scholar
[18]	S. Stojanovic, Stochastic Volatility & Risk Premium,, Lecture Notes, (2005). Google Scholar
[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. Google Scholar
[20]	S. Stojanovic, Advanced Financial Engineering for Interest Rates, Equity, and FX,, Lecture Notes, (2007). Google Scholar
[21]	S. Stojanovic, Any-utility neutral and indifference pricing and hedging,, Risk and Decision Analysis, 4 (2013), 103. Google Scholar
[22]	S. Stojanovic, Neutral and Indifference Portfolio Pricing, Hedging and Investing,, Springer, (2011). Google Scholar
[23]	O. Vasicek, An equilibrium characterization of the term structure,, Journal of Financial Economics, 5 (1977), 177. doi: 10.1002/9781119186229.ch6. Google Scholar

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. Google Scholar
[2]	F. Black and M. Scholes, The pricing of options and corporate liabilities,, J. Political Econ., 81 (1973), 637. doi: 10.1086/260062. Google Scholar
[3]	D. Brigo and F. Mercurio, Interest Rate Models Theory and Practice,, Springer, (2001). doi: 10.1007/978-3-662-04553-4. Google Scholar
[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. Google Scholar
[5]	A. Friedman, Stochastic Differential Equations,, Vol 1 & 2, (1975). Google Scholar
[6]	S. D. Hodges and A. Neuberger, Optimal replication of contingent claims under transaction costs,, Review of Futures Markets, 8 (1989), 222. Google Scholar
[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. Google Scholar
[8]	L. Jiang, Mathematical Modeling and Methods of Option Pricing,, World Scientific Publishing, (2005). doi: 10.1142/5855. Google Scholar
[9]	J. Kallsen, Utility-based derivative pricing in incomplete markets,, Mathematical Finance-Bachelier Congress 2000, (2000), 313. Google Scholar
[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. Google Scholar
[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. Google Scholar
[12]	R. C. Merton, Theory of rational option pricing,, Bell Journal of Economics and Management Science, 4 (1973), 141. doi: 10.2307/3003143. Google Scholar
[13]	R. C. Merton, Continuous-Time Finance,, Wiley-Blackwell, (1990). Google Scholar
[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. Google Scholar
[15]	R. Rouge and N. El Karoui, Pricing via utility maximization and entropy,, Mathematical Finance, 10 (2000), 259. doi: 10.1111/1467-9965.00093. Google Scholar
[16]	S. Stojanovic, Computational Financial Mathematics using MATHEMATICA®,, Birkhauser, (2003). doi: 10.1007/978-1-4612-0043-7. Google Scholar
[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. Google Scholar
[18]	S. Stojanovic, Stochastic Volatility & Risk Premium,, Lecture Notes, (2005). Google Scholar
[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. Google Scholar
[20]	S. Stojanovic, Advanced Financial Engineering for Interest Rates, Equity, and FX,, Lecture Notes, (2007). Google Scholar
[21]	S. Stojanovic, Any-utility neutral and indifference pricing and hedging,, Risk and Decision Analysis, 4 (2013), 103. Google Scholar
[22]	S. Stojanovic, Neutral and Indifference Portfolio Pricing, Hedging and Investing,, Springer, (2011). Google Scholar
[23]	O. Vasicek, An equilibrium characterization of the term structure,, Journal of Financial Economics, 5 (1977), 177. doi: 10.1002/9781119186229.ch6. Google Scholar

[1]	María Teresa V. Martínez-Palacios, Adrián Hernández-Del-Valle, Ambrosio Ortiz-Ramírez. On the pricing of Asian options with geometric average of American type with stochastic interest rate: A stochastic optimal control approach. Journal of Dynamics & Games, 2019, 6 (1) : 53-64. doi: 10.3934/jdg.2019004
[2]	Linlin Tian, Xiaoyi Zhang, Yizhou Bai. Optimal dividend of compound poisson process under a stochastic interest rate. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-17. doi: 10.3934/jimo.2019047
[3]	Lin Xu, Rongming Wang. Upper bounds for ruin probabilities in an autoregressive risk model with a Markov chain interest rate. Journal of Industrial & Management Optimization, 2006, 2 (2) : 165-175. doi: 10.3934/jimo.2006.2.165
[4]	Dingjun Yao, Kun Fan. Optimal risk control and dividend strategies in the presence of two reinsurers: Variance premium principle. Journal of Industrial & Management Optimization, 2018, 14 (3) : 1055-1083. doi: 10.3934/jimo.2017090
[5]	Xin Jiang, Kam Chuen Yuen, Mi Chen. Optimal investment and reinsurance with premium control. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-17. doi: 10.3934/jimo.2019080
[6]	Roya Soltani, Seyed Jafar Sadjadi, Mona Rahnama. Artificial intelligence combined with nonlinear optimization techniques and their application for yield curve optimization. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1701-1721. doi: 10.3934/jimo.2017014
[7]	Haixiang Yao, Zhongfei Li, Yongzeng Lai. Dynamic mean-variance asset allocation with stochastic interest rate and inflation rate. Journal of Industrial & Management Optimization, 2016, 12 (1) : 187-209. doi: 10.3934/jimo.2016.12.187
[8]	Tien-Yu Lin, Ming-Te Chen, Kuo-Lung Hou. An inventory model for items with imperfect quality and quantity discounts under adjusted screening rate and earned interest. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1333-1347. doi: 10.3934/jimo.2016.12.1333
[9]	Yan Zhang, Yonghong Wu, Benchawan Wiwatanapataphee, Francisca Angkola. Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-31. doi: 10.3934/jimo.2018141
[10]	Jingzhen Liu, Lihua Bai, Ka-Fai Cedric Yiu. Optimal investment with a value-at-risk constraint. Journal of Industrial & Management Optimization, 2012, 8 (3) : 531-547. doi: 10.3934/jimo.2012.8.531
[11]	Bei Hu, Lishang Jiang, Jin Liang, Wei Wei. A fully non-linear PDE problem from pricing CDS with counterparty risk. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 2001-2016. doi: 10.3934/dcdsb.2012.17.2001
[12]	Kegui Chen, Xinyu Wang, Min Huang, Wai-Ki Ching. Compensation plan, pricing and production decisions with inventory-dependent salvage value, and asymmetric risk-averse sales agent. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1397-1422. doi: 10.3934/jimo.2018013
[13]	Bopeng Rao. Optimal energy decay rate in a damped Rayleigh beam. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 721-734. doi: 10.3934/dcds.1998.4.721
[14]	Jianxiong Zhang, Zhenyu Bai, Wansheng Tang. Optimal pricing policy for deteriorating items with preservation technology investment. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1261-1277. doi: 10.3934/jimo.2014.10.1261
[15]	Guodong Yi, Xiaohong Chen, Chunqiao Tan. Optimal pricing of perishable products with replenishment policy in the presence of strategic consumers. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1579-1597. doi: 10.3934/jimo.2018112
[16]	Gang Xie, Wuyi Yue, Shouyang Wang. Optimal selection of cleaner products in a green supply chain with risk aversion. Journal of Industrial & Management Optimization, 2015, 11 (2) : 515-528. doi: 10.3934/jimo.2015.11.515
[17]	Linyi Qian, Lyu Chen, Zhuo Jin, Rongming Wang. Optimal liability ratio and dividend payment strategies under catastrophic risk. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1443-1461. doi: 10.3934/jimo.2018015
[18]	Yong Ma, Shiping Shan, Weidong Xu. Optimal investment and consumption in the market with jump risk and capital gains tax. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1937-1953. doi: 10.3934/jimo.2018130
[19]	Chao Deng, Haixiang Yao, Yan Chen. Optimal investment and risk control problems with delay for an insurer in defaultable market. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-17. doi: 10.3934/jimo.2019070
[20]	Tak Kuen Siu, Yang Shen. Risk-minimizing pricing and Esscher transform in a general non-Markovian regime-switching jump-diffusion model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2595-2626. doi: 10.3934/dcdsb.2017100

2018 Impact Factor: 1.008

American Institute of Mathematical Sciences