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

Si Zuo and Haijun Wang

The North American Journal of Economics and Finance, 2025, vol. 76, issue C

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.

Keywords: Real options; Growth options; Venture capital; Start-ups; Double exponential jump–diffusion process (search for similar items in EconPapers)
JEL-codes: G13 G24 G34 L26 M13 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecofin:v:76:y:2025:i:c:s1062940824002845

DOI: 10.1016/j.najef.2024.102359

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