Equity valuation under stock dilution and buy-back

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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

Abstract
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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 and 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. 81 (1973), 637-659.
[2]	F. Black, The dividend puzzle, Journal of Portfolio Management, 2 (1976), 5-8.
[3]	Mark H. A. Davis, Vassilios G. Panas and Thaleia Zariphopoulou, European option pricing with transaction costs, SIAM J. Control Optim., 31 (1993), 470-493. doi: 10.1137/0331022.
[4]	Avner Friedman, "Stochastic Differential Equations and Applications," Vol. 1, Probability and Mathematical Statistics, Vol. 28, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975.
[5]	S. D. Hodges and A. Neuberger, Optimal replication of contingent claims under transaction costs, Review of Futures Markets, 8 (1989), 222-239.
[6]	Jiang Lishang, "Mathematical Modeling and Methods of Option Pricing," World Scientific Publishing Co., Inc., River Edge, NJ, 2005.
[7]	Jan Kallsen, Utility-based derivative pricing in incomplete markets, in "Mathematical Finance-Bachelier Congress," 2000 (Paris), Springer Finance, Springer, Berlin, (2002), 313-338.
[8]	Zhuang Kang and Srdjan D. Stojanovic, Interest rate risk premium and equity valuation, J. Syst. Sci. Complex, 23 (2010), 484-498. doi: 10.1007/s11424-010-0142-y.
[9]	Robert C. Merton, Theory of rational option pricing, Bell J. Econom. and Management Sci., 4 (1973), 141-183.
[10]	R. C. Merton, "Continuous-Time Finance," Wiley-Blackwell, 1990.
[11]	M. H. Miller and F. Modigliani, Dividend Policy, Growth, and the Valuation of Shares, Journal of Business, 34 (1961), 411-433. doi: 10.1086/294442.
[12]	Marek Musiela and Thaleia Zariphopoulou, An example of indifference prices under exponential preferences, Finance Stoch., 8 (2004), 229-239.
[13]	Richard Rouge and Nicole El Karoui, Pricing via utility maximization and entropy, Mathematical Finance, 10 (2000), 259-276. doi: 10.1111/1467-9965.00093.
[14]	Srdjan D. Stojanovic, Risk premium and fair option prices under stochastic volatility: The HARA solution, C. R. Math. Acad. Sci. Paris, 340 (2005), 551-556. doi: 10.1016/j.crma.2004.11.002.
[15]	Srdjan D. Stojanovic, "Stochastic Volatility & Risk Premium," Lecture Notes, GARP, New York, 2005.
[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), 345-372. doi: 10.1007/s10690-007-9049-6.
[17]	Srdjan D. Stojanovic, The dividend puzzle unpuzzled, 2007.
[18]	Srdjan D. Stojanovic, "Advanced Financial Engineering for Interest Rates, Equity, and FX," Lecture Notes, GARP, New York, 2007.
[19]	Srdjan D. Stojanovic, Any-utility neutral and indifference pricing and hedging, International Research Forum, Hong Kong Polytechnic University, Hong Kong, 2010.
[20]	Srdjan D. Stojanovic, "Neutral and Indifference Pricing, Hedging and Investing," Springer, New York, 2011.
[21]	Srdjan D. Stojanovic and Zhuang Kang, General difussive neutral pricing under non-zero portfolio position, work in progress.

show all references

References:

[1]	F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Political Econ. 81 (1973), 637-659.
[2]	F. Black, The dividend puzzle, Journal of Portfolio Management, 2 (1976), 5-8.
[3]	Mark H. A. Davis, Vassilios G. Panas and Thaleia Zariphopoulou, European option pricing with transaction costs, SIAM J. Control Optim., 31 (1993), 470-493. doi: 10.1137/0331022.
[4]	Avner Friedman, "Stochastic Differential Equations and Applications," Vol. 1, Probability and Mathematical Statistics, Vol. 28, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975.
[5]	S. D. Hodges and A. Neuberger, Optimal replication of contingent claims under transaction costs, Review of Futures Markets, 8 (1989), 222-239.
[6]	Jiang Lishang, "Mathematical Modeling and Methods of Option Pricing," World Scientific Publishing Co., Inc., River Edge, NJ, 2005.
[7]	Jan Kallsen, Utility-based derivative pricing in incomplete markets, in "Mathematical Finance-Bachelier Congress," 2000 (Paris), Springer Finance, Springer, Berlin, (2002), 313-338.
[8]	Zhuang Kang and Srdjan D. Stojanovic, Interest rate risk premium and equity valuation, J. Syst. Sci. Complex, 23 (2010), 484-498. doi: 10.1007/s11424-010-0142-y.
[9]	Robert C. Merton, Theory of rational option pricing, Bell J. Econom. and Management Sci., 4 (1973), 141-183.
[10]	R. C. Merton, "Continuous-Time Finance," Wiley-Blackwell, 1990.
[11]	M. H. Miller and F. Modigliani, Dividend Policy, Growth, and the Valuation of Shares, Journal of Business, 34 (1961), 411-433. doi: 10.1086/294442.
[12]	Marek Musiela and Thaleia Zariphopoulou, An example of indifference prices under exponential preferences, Finance Stoch., 8 (2004), 229-239.
[13]	Richard Rouge and Nicole El Karoui, Pricing via utility maximization and entropy, Mathematical Finance, 10 (2000), 259-276. doi: 10.1111/1467-9965.00093.
[14]	Srdjan D. Stojanovic, Risk premium and fair option prices under stochastic volatility: The HARA solution, C. R. Math. Acad. Sci. Paris, 340 (2005), 551-556. doi: 10.1016/j.crma.2004.11.002.
[15]	Srdjan D. Stojanovic, "Stochastic Volatility & Risk Premium," Lecture Notes, GARP, New York, 2005.
[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), 345-372. doi: 10.1007/s10690-007-9049-6.
[17]	Srdjan D. Stojanovic, The dividend puzzle unpuzzled, 2007.
[18]	Srdjan D. Stojanovic, "Advanced Financial Engineering for Interest Rates, Equity, and FX," Lecture Notes, GARP, New York, 2007.
[19]	Srdjan D. Stojanovic, Any-utility neutral and indifference pricing and hedging, International Research Forum, Hong Kong Polytechnic University, Hong Kong, 2010.
[20]	Srdjan D. Stojanovic, "Neutral and Indifference Pricing, Hedging and Investing," Springer, New York, 2011.
[21]	Srdjan D. Stojanovic and Zhuang Kang, General difussive neutral pricing under non-zero portfolio position, work in progress.

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