Journal of Systems Science and Complexity

, Volume 26, Issue 6, pp 991–1001 | Cite as

Dynamic valuation of options on non-traded assets and trading strategies

  • Hui MiEmail author
  • Shuguang Zhang


This paper investigates the pricing of options written on non-traded assets and trading strategies for the stock and option in an exponential utility maximization framework. Under the assumption that the option can be continuously traded without friction just as the stock, a dynamic relationship between their optimal positions is derived by using the stochastic dynamic programming techniques. The dynamic option pricing equations are also established. In particular, the properties of the associated solutions are discussed and their explicit representations are demonstrated via the Feynman-Kac formula. This paper further compares the dynamic option price to the existing price notions, such as the marginal price and indifference price.

Key words

Non-traded asset option pricing portfolio selection stochastic control 


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  1. [1]
    Henderson V, Valuation of claims on nontraded assets using utility maximization, Mathematical Finance, 2002, 12(4): 351–373.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Henderson V and Hobson D, Utility indifference pricing — An overview, Indifference Pricing: Theory and Applications (ed. by Carmona R), Princeton University Press, 2009, 44–72.Google Scholar
  3. [3]
    Musiela M and Zariphopoulou T, An example of indifference prices under exponential preferences, Finance and Stochastics, 2004, 8(2): 229–239.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Davis M H A, Optimal hedging with basis risk, From Stochastic Calculus to Mathematical Finance (ed. by Kabanov Y, et al.), Springer, Berlin Heidelberg, 2006, 169–187.CrossRefGoogle Scholar
  5. [5]
    Ibáñez A, Factorization of European and American option prices under complete and incomplete markets, Journal of Banking and Finance, 2008, 32: 311–325.CrossRefGoogle Scholar
  6. [6]
    Hodges S D and Neuberger A, Optimal replication of contingent claims under portfolio constraints, Review of Futures Markets, 1989, 8: 222–239.Google Scholar
  7. [7]
    Davis M H A, Option pricing in incomplete markets, in Mathematics of Derivative Securities (ed. by Dempster M A H and Pliska S R), Cambridge University Press, 1997, 216–227.Google Scholar
  8. [8]
    Ilhan A, Jonsson M, and Sircar R, Portfolio optimization with derivatives and indifference pricing, Indifference Pricing: Theory and Applications (ed. by Carmona R), Princeton University Press, 2009, 183–210 (abbreviated title in volume: Portfolio Optimization).Google Scholar
  9. [9]
    Rouge R and El Karoui N, Pricing via utility maximization and entropy, Mathematical Finance, 2000, 10(2): 259–276.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Ankirchner S, Imkeller P, and Reis G, Pricing and hedging of derivatives based on nontradable underlyings, Mathematical Finance, 2010, 20(2): 289–312.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    Ilhan A, Jonsson M, and Sircar R, Optimal investment with derivative securities, Finance and Stochastics, 2005, 9(4): 585–595.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Yang D, Quantitative Strategies for Derivatives Trading, ATMIF LLC, New Jersey, USA, 2006.Google Scholar
  13. [13]
    Zariphopoulou T, A solution approach to valuation with unhedgeable risks, Finance and Stochastics, 2001, 5(1): 61–82.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    Karatzas I and Shreve S E, Methods of Mathematical Finance, Springer-Verlag, New York, 1998.zbMATHGoogle Scholar
  15. [15]
    Monoyios M, The minimal entropy measure and an Esscher transform in an incomplete market model, Statistics and Probability Letters, 2007, 77(11): 1070–1076.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesNanjing Normal UniversityNanjingChina
  2. 2.Department of Statistics and FinanceUniversity of Science and Technology of ChinaHefeiChina

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