BTC Inverse Call and the Standard FX Framework

Crypto quanto and inverse options

“…Anyway, we can write the payoff to a USD‐denominated trader as $$$$\begin{equation} V^{^{_{\mathbb {\$}}}}_{_T} = \bar{S}_{_T}^{^{_{\$}}} V^{^{_{\mathbb {B}}}}_{_T} =\bar{S}_{_T}^{^{_{\$}}} \frac{{\left(S_{_T}^{^{_{\$}}} - K ^{^{_{\$}}}\right)}^+}{S_{_T}^{^{_{\$}}}}\approx {\left(S_{_T}^{^{_{\$}}} - K^{^{_{\$}}} \right)}^+. \end{equation}$$$$This shows that one can think of the inverse option payoff as equivalent to a standard FX option, except that the payoff is denominated in the foreign currency as remarked by Lucic (2022). There is a large body of academic research on FX options, their pricing, hedging, volatility dynamics, and so forth, see Levy (1992), Carr and Wu (2007), Demeterfi (1998), and many others.…”

“…This shows that one can think of the inverse option payoff as equivalent to a standard FX option, except that the payoff is denominated in the foreign currency as remarked by Lucic (2022). There is a large body of academic research on FX options, their pricing, hedging, volatility dynamics, and so forth, see Levy (1992), Carr and Wu (2007), Demeterfi (1998), and many others.…”

“…(2000) with the GARCH‐filtered kernel density of McNeil and Frey (2000). Four other papers focus exclusively on inverse options, including the pricing of such options under the standard FX framework (Lucic, 2022); pricing within a SV jump model framework (Sepp & Rakhmonov, 2022; Teng & Härdle, 2022); and their empirical dynamic delta hedging performance relative to the BS delta (Alexander & Imeraj, 2023; Teng & Härdle, 2022).…”

“…Matic et al (2023) use the daily implied volatilities quoted by the Deribit exchange to calibrate a stochastic-volatility (SV) inspired surface and simulate the underlying through the SV process introduced by Duffie et al (2000) with the GARCH-filtered kernel density of McNeil and Frey (2000). Four other papers focus exclusively on inverse options, including the pricing of such options under the standard FX framework (Lucic, 2022); pricing within a SV jump model framework (Sepp & Rakhmonov, 2022;Teng & Härdle, 2022); and their empirical dynamic delta hedging performance relative to the BS delta (Alexander & Imeraj, 2023;Teng & Härdle, 2022).…”