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Has financial derivatives of financial derivatives ever been considered in academic or practical settings? Is it useless/useful?

Say $C(S_t;K,T)$ is a European call on an underlying $S_t$ with strike $K$ and expiry $T$. Then what is the no-arbitrage price of a European call on the above call, $C^*(C(S_t;K,T);K^*,T^*)$ and questions like these?

Who cares
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    A compound option – Kermittfrog Mar 24 '22 at 09:58
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    Robert Geske, The valuation of compound options. Journal of Financial Economics 7 (1979), 63-81. Academic and as practical as the Black-Scholes model. – Kurt G. Mar 24 '22 at 10:35
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    @KurtG., the CO model is a nice tool to discuss corporate finance, IMO. Equity is a call on assets, and an equity option is a call-on-a-call. Also, can be used in terms of real options. But besides that, yeah, a bit academic. – Kermittfrog Mar 24 '22 at 10:44
  • @Kermittfrog . Correct. In the Merton 76 framework (Asset price of the firm model) the stock becomes an option and the option on stock a compound option. I only mentioned 'academic' because OP asked for academic or practical settings. Geske's paper delivers both. – Kurt G. Mar 24 '22 at 11:57
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    https://quant.stackexchange.com/a/58720 – Daneel Olivaw Mar 24 '22 at 12:27

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