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Financial market with no riskless (safe) asset

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  • Svetlozar Rachev
  • Frank Fabozzi

Abstract

We study markets with no riskless (safe) asset. We derive the corresponding Black-Scholes-Merton option pricing equations for markets where there are only risky assets which have the following price dynamics: (i) continuous diffusions; (ii) jump-diffusions; (iii) diffusions with stochastic volatilities, and; (iv) geometric fractional Brownian and Rosenblatt motions. No arbitrage and market completeness conditions are derived in all four cases.

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  • Svetlozar Rachev & Frank Fabozzi, 2016. "Financial market with no riskless (safe) asset," Papers 1612.02112, arXiv.org.
    • Handle: RePEc:arx:papers:1612.02112
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    1. Aoki, Kosuke & Nakajima, Tomoyuki & Nikolov, Kalin, 2014. "Safe asset shortages and asset price bubbles," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 164-174.
    2. Ricardo J. Caballero & Emmanuel Farhi, 2013. "A Model of the Safe Asset Mechanism (SAM): Safety Traps and Economic Policy," Working Paper 70936, Harvard University OpenScholar.
    3. Anderson, Nicola & Noss, Joseph, 2013. "Financial Stability Paper No 23: The Fractal Market Hypothesis and its implications for the stability of financial markets," Bank of England Financial Stability Papers 23, Bank of England.
    4. Pierre-Olivier Gourinchas & Olivier Jeanne, 2012. "Global safe assets," BIS Working Papers 399, Bank for International Settlements.
    5. Gauti B. Eggertsson & Paul Krugman, 2012. "Debt, Deleveraging, and the Liquidity Trap: A Fisher-Minsky-Koo Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1469-1513.
    6. Christian Bender & Tommi Sottinen & Esko Valkeila, 2008. "Pricing by hedging and no-arbitrage beyond semimartingales," Finance and Stochastics, Springer, vol. 12(4), pages 441-468, October.
    7. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
    8. Hiroshi Konno & Hiroshi Shirakawa, 1995. "Existence Of A Nonnegative Equilibrium Price Vector In The Mean‐Variance Capital Market," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 233-246, July.
    9. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    10. Stefan Rostek, 2009. "Option Pricing in Fractional Brownian Markets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-00331-8, December.
    11. Kim, Y.S. & Stoyanov, S. & Rachev, S. & Fabozzi, F., 2016. "Multi-purpose binomial model: Fitting all moments to the underlying geometric Brownian motion," Economics Letters, Elsevier, vol. 145(C), pages 225-229.
    12. Allingham, Michael, 1991. "Existence Theorems in the Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 59(4), pages 1169-1174, July.
    13. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    14. Bank for International Settlements, 2013. "Sovereign risk: a world without risk-free assets?," BIS Papers, Bank for International Settlements, number 72.
    15. Gary B. Gorton, 2016. "The History and Economics of Safe Assets," NBER Working Papers 22210, National Bureau of Economic Research, Inc.
    16. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    17. Lars Tyge Nielsen, 1990. "Equilibrium in CAPM Without a Riskless Asset," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(2), pages 315-324.
    18. Arif Billah Dar & Niyati Bhanja & Aviral Kumar Tiwari, 2017. "Do global financial crises validate assertions of fractal market hypothesis?," International Economics and Economic Policy, Springer, vol. 14(1), pages 153-165, January.
    19. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    20. Epaminondas Panas & Vassilia Ninni, 2010. "The Distribution of London Metal Exchange Prices: A Test of the Fractal Market Hypothesis," European Research Studies Journal, European Research Studies Journal, vol. 0(2), pages 192-210.
    21. Ning Sun & Zaifu Yang, 2003. "Existence of Equilibrium and Zero-Beta Pricing Formula in the Capital Asset Pricing Model with Heterogeneous Beliefs," Annals of Economics and Finance, Society for AEF, vol. 4(1), pages 51-71, May.
    22. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
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    Cited by:

    1. Davide Lauria & W. Brent Lindquist & Stefan Mittnik & Svetlozar T. Rachev, 2022. "ESG-Valued Portfolio Optimization and Dynamic Asset Pricing," Papers 2206.02854, arXiv.org.
    2. Nancy Asare Nyarko & Bhathiya Divelgama & Jagdish Gnawali & Blessing Omotade & Svetlozar Rachev & Peter Yegon, 2023. "Exploring Dynamic Asset Pricing within Bachelier Market Model," Papers 2307.04059, arXiv.org.
    3. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2023. "Option pricing using a skew random walk pricing tree," Papers 2303.17014, arXiv.org.
    4. Abootaleb Shirvani & Frank J. Fabozzi & Stoyan V. Stoyanov, 2020. "Option Pricing in an Investment Risk-Return Setting," Papers 2001.00737, arXiv.org.
    5. Svetlozar Rachev & Nancy Asare Nyarko & Blessing Omotade & Peter Yegon, 2023. "Bachelier's Market Model for ESG Asset Pricing," Papers 2306.04158, arXiv.org.

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