Quantifying the Endogeneity in Online Donations

Charitable crowdfunding provides a new channel for people and families suffering from unforeseen events, such as accidents, severe illness, and so on, to seek help from the public. Thus, finding the key determinants which drive the fundraising process of crowdfunding campaigns is of great importance, especially for those suffering. With a unique data set containing 210,907 crowdfunding projects covering a period from October 2015 to June 2020, from a famous charitable crowdfunding platform, specifically Qingsong Chou, we will reveal how many online donations are due to endogeneity, referring to the positive feedback process of attracting more people to donate through broadcasting campaigns in social networks by donors. For this aim, we calibrate three different Hawkes processes to the event data of online donations for each crowdfunding campaign on each day, which allows us to estimate the branching ratio, a measure of endogeneity. It is found that the online fundraising process works in a sub-critical state and nearly 70–90% of the online donations are endogenous. Furthermore, even though the fundraising amount, number of donations, and number of donors decrease rapidly after the crowdfunding project is created, the measure of endogeneity remains stable during the entire lifetime of crowdfunding projects. Our results not only deepen our understanding of online fundraising dynamics but also provide a quantitative framework to disentangle the endogenous and exogenous dynamics in complex systems.

The Theory of Uncertaintism

The stock jumps of the underlying assets underpinning the Margrabe options have been studied by Cheang and Chiarella [Cheang, GH and Chiarella C (2011). Exchange options under jump-diffusion dynamics. Applied Mathematical Finance, 18(3), 245–276], Cheang and Garces [Cheang, GHL and Garces LPDM (2020). Representation of exchange option prices under stochastic volatility jump-diffusion dynamics. Quantitative Finance, 20(2), 291–310], Cufaro Petroni and Sabino [Cufaro Petroni, N and Sabino P (2020). Pricing exchange options with correlated jump diffusion processes. Quantitate Finance, 20(11), 1811–1823], and Ma et al. [Ma, Y, Pan D and Wang T (2020). Exchange options under clustered jump dynamics. Quantitative Finance, 20(6), 949–967]. Although the authors argue that they explored stock jumps under Hawkes processes, those processes are the Poisson process in their applications. Thus, they studied Hawkes processes in-between two assets while this study explores Hawkes process within any asset. Furthermore, the Poisson process can be flipped into Hawkes process and vice versa. In terms of hedging, this study uses specific Greeks (rho and phi) while some of the mentioned studies used other Greeks (Delta, Theta, Vega, and Gamma). Moreover, hedging is carried out under static and dynamic environments. The results illustrate that the jumpy Margrabe option can be extended to complex barrier option and waiting to invest option. In addition, hedging strategies are robust both under static and dynamic environments.