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Optimal venture capital entry–exit strategy with jump–diffusion risk

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  • Zuo, Si
  • Wang, Haijun

Abstract

This paper introduces a double exponential jump–diffusion process to model the pre-expansion value of a start-up firm. Within this framework, we present a dynamic model for studying the entry and exit decisions of venture capitalists (VCs). The model returns an analytical solution for the entry trigger, a semi-analytical solution for the exit trigger, the post-money optimum ownership, the (raw) cash multiple and a new time-adjusted version. Significantly, we uncover a direct correlation between the optimal premium upon exit through the trade sale (M&A) and the start-up firm’s value during the M&A offer. Additionally, we theoretically demonstrate that the exit trigger is larger than the value of the start-up firm when the VC makes a M&A offer to the buyer. Our numerical analysis discusses the following empirical implications: (i) postponing the M&A offer results in an increased optimal premium, leading to a strategically delayed divestment. This delay corresponds to an amplified (raw) cash multiple but triggers a notable decrease in the adjusted cash multiple; (ii) considering jump risk enhances the expected investment performance; (iii) the post-money optimum ownership is not influenced by jump risk; (iv) greater uncertainty associated with jump intensity and volatility prompts delayed entry and exit decisions, producing larger cash multiples; (v) a higher VC’s optimism leads to an increased (raw) cash multiple and a decreased adjusted cash multiple.

Suggested Citation

  • Zuo, Si & Wang, Haijun, 2025. "Optimal venture capital entry–exit strategy with jump–diffusion risk," The North American Journal of Economics and Finance, Elsevier, vol. 76(C).
  • Handle: RePEc:eee:ecofin:v:76:y:2025:i:c:s1062940824002845
    DOI: 10.1016/j.najef.2024.102359
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    More about this item

    Keywords

    Real options; Growth options; Venture capital; Start-ups; Double exponential jump–diffusion process;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • G34 - Financial Economics - - Corporate Finance and Governance - - - Mergers; Acquisitions; Restructuring; Corporate Governance
    • L26 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Entrepreneurship
    • M13 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - New Firms; Startups

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