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September  2012, 17(6): 1809-1829. doi: 10.3934/dcdsb.2012.17.1809

Equity valuation under stock dilution and buy-back

Yaling Cui 1, and  Srdjan D. Stojanovic 2,

1. 

Financial Engineering Research Center, Soochow University, Suzhou, Jiangsu 215006, China
2. 

Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, United States

Received  May 2011 Revised  December 2011 Published  May 2012

Employing and generalizing the (continuous time, incomplete market) equity valuation (and hedging) theory introduced recently by one of the authors, the effect of stock dilution and buy-back on the equity value is quantified. Both, neutral and indifference pricing methodologies are considered, and results of different levels of complexity are provided. Hedging results are provided as well. Both pricing and hedging results are obtained as special cases of the general methodology of pricing and hedging in incomplete markets recently developed by one of the authors.
Keywords: Indifference pricing, SDE, neutral pricing, equity valuation, PDE..
Mathematics Subject Classification: Primary: 91G20, 91G80; Secondary: 35K5.
Citation: Yaling Cui, Srdjan D. Stojanovic. Equity valuation under stock dilution and buy-back. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1809-1829. doi: 10.3934/dcdsb.2012.17.1809
References:
[1]

F. Black and M. Scholes, The pricing of options and corporate liabilities,, J. Political Econ. \textbf{81} (1973), 81 (1973), 637.   Google Scholar

[2]

F. Black, The dividend puzzle,, Journal of Portfolio Management, 2 (1976), 5.   Google Scholar

[3]

Mark H. A. Davis, Vassilios G. Panas and Thaleia Zariphopoulou, European option pricing with transaction costs,, SIAM J. Control Optim., 31 (1993), 470.  doi: 10.1137/0331022.  Google Scholar

[4]

Avner Friedman, "Stochastic Differential Equations and Applications," Vol. 1,, Probability and Mathematical Statistics, (1975).   Google Scholar

[5]

S. D. Hodges and A. Neuberger, Optimal replication of contingent claims under transaction costs,, Review of Futures Markets, 8 (1989), 222.   Google Scholar

[6]

Jiang Lishang, "Mathematical Modeling and Methods of Option Pricing,", World Scientific Publishing Co., (2005).   Google Scholar

[7]

Jan Kallsen, Utility-based derivative pricing in incomplete markets,, in, (2002), 313.   Google Scholar

[8]

Zhuang Kang and Srdjan D. Stojanovic, Interest rate risk premium and equity valuation,, J. Syst. Sci. Complex, 23 (2010), 484.  doi: 10.1007/s11424-010-0142-y.  Google Scholar

[9]

Robert C. Merton, Theory of rational option pricing,, Bell J. Econom. and Management Sci., 4 (1973), 141.   Google Scholar

[10]

R. C. Merton, "Continuous-Time Finance,", Wiley-Blackwell, (1990).   Google Scholar

[11]

M. H. Miller and F. Modigliani, Dividend Policy, Growth, and the Valuation of Shares,, Journal of Business, 34 (1961), 411.  doi: 10.1086/294442.  Google Scholar

[12]

Marek Musiela and Thaleia Zariphopoulou, An example of indifference prices under exponential preferences,, Finance Stoch., 8 (2004), 229.   Google Scholar

[13]

Richard Rouge and Nicole El Karoui, Pricing via utility maximization and entropy,, Mathematical Finance, 10 (2000), 259.  doi: 10.1111/1467-9965.00093.  Google Scholar

[14]

Srdjan D. Stojanovic, Risk premium and fair option prices under stochastic volatility: The HARA solution,, C. R. Math. Acad. Sci. Paris, 340 (2005), 551.  doi: 10.1016/j.crma.2004.11.002.  Google Scholar

[15]

Srdjan D. Stojanovic, "Stochastic Volatility & Risk Premium,", Lecture Notes, (2005).   Google Scholar

[16]

Srdjan D. 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.  doi: 10.1007/s10690-007-9049-6.  Google Scholar

[17]

Srdjan D. Stojanovic, The dividend puzzle unpuzzled,, 2007., ().   Google Scholar

[18]

Srdjan D. Stojanovic, "Advanced Financial Engineering for Interest Rates, Equity, and FX,", Lecture Notes, (2007).   Google Scholar

[19]

Srdjan D. Stojanovic, Any-utility neutral and indifference pricing and hedging,, International Research Forum, (2010).   Google Scholar

[20]

Srdjan D. Stojanovic, "Neutral and Indifference Pricing, Hedging and Investing,", Springer, (2011).   Google Scholar

[21]

Srdjan D. Stojanovic and Zhuang Kang, General difussive neutral pricing under non-zero portfolio position,, work in progress., ().   Google Scholar

show all references

References:
[1]

F. Black and M. Scholes, The pricing of options and corporate liabilities,, J. Political Econ. \textbf{81} (1973), 81 (1973), 637.   Google Scholar

[2]

F. Black, The dividend puzzle,, Journal of Portfolio Management, 2 (1976), 5.   Google Scholar

[3]

Mark H. A. Davis, Vassilios G. Panas and Thaleia Zariphopoulou, European option pricing with transaction costs,, SIAM J. Control Optim., 31 (1993), 470.  doi: 10.1137/0331022.  Google Scholar

[4]

Avner Friedman, "Stochastic Differential Equations and Applications," Vol. 1,, Probability and Mathematical Statistics, (1975).   Google Scholar

[5]

S. D. Hodges and A. Neuberger, Optimal replication of contingent claims under transaction costs,, Review of Futures Markets, 8 (1989), 222.   Google Scholar

[6]

Jiang Lishang, "Mathematical Modeling and Methods of Option Pricing,", World Scientific Publishing Co., (2005).   Google Scholar

[7]

Jan Kallsen, Utility-based derivative pricing in incomplete markets,, in, (2002), 313.   Google Scholar

[8]

Zhuang Kang and Srdjan D. Stojanovic, Interest rate risk premium and equity valuation,, J. Syst. Sci. Complex, 23 (2010), 484.  doi: 10.1007/s11424-010-0142-y.  Google Scholar

[9]

Robert C. Merton, Theory of rational option pricing,, Bell J. Econom. and Management Sci., 4 (1973), 141.   Google Scholar

[10]

R. C. Merton, "Continuous-Time Finance,", Wiley-Blackwell, (1990).   Google Scholar

[11]

M. H. Miller and F. Modigliani, Dividend Policy, Growth, and the Valuation of Shares,, Journal of Business, 34 (1961), 411.  doi: 10.1086/294442.  Google Scholar

[12]

Marek Musiela and Thaleia Zariphopoulou, An example of indifference prices under exponential preferences,, Finance Stoch., 8 (2004), 229.   Google Scholar

[13]

Richard Rouge and Nicole El Karoui, Pricing via utility maximization and entropy,, Mathematical Finance, 10 (2000), 259.  doi: 10.1111/1467-9965.00093.  Google Scholar

[14]

Srdjan D. Stojanovic, Risk premium and fair option prices under stochastic volatility: The HARA solution,, C. R. Math. Acad. Sci. Paris, 340 (2005), 551.  doi: 10.1016/j.crma.2004.11.002.  Google Scholar

[15]

Srdjan D. Stojanovic, "Stochastic Volatility & Risk Premium,", Lecture Notes, (2005).   Google Scholar

[16]

Srdjan D. 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.  doi: 10.1007/s10690-007-9049-6.  Google Scholar

[17]

Srdjan D. Stojanovic, The dividend puzzle unpuzzled,, 2007., ().   Google Scholar

[18]

Srdjan D. Stojanovic, "Advanced Financial Engineering for Interest Rates, Equity, and FX,", Lecture Notes, (2007).   Google Scholar

[19]

Srdjan D. Stojanovic, Any-utility neutral and indifference pricing and hedging,, International Research Forum, (2010).   Google Scholar

[20]

Srdjan D. Stojanovic, "Neutral and Indifference Pricing, Hedging and Investing,", Springer, (2011).   Google Scholar

[21]

Srdjan D. Stojanovic and Zhuang Kang, General difussive neutral pricing under non-zero portfolio position,, work in progress., ().   Google Scholar

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