Weak time-derivatives and no-arbitrage pricing

Massimo Marinacci and Federico Severino ()
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Federico Severino: Università della Svizzera Italiana (USI)

Finance and Stochastics, 2018, vol. 22, issue 4, No 7, 1007-1036

Abstract: Abstract We prove a risk-neutral pricing formula for a large class of semimartingale processes through a novel notion of weak time-differentiability that permits to differentiate adapted processes. In particular, the weak time-derivative isolates drifts of semimartingales and is null for martingales. Weak time-differentiability enables us to characterize no-arbitrage prices as solutions of differential equations, where interest rates play a key role. Finally, we reformulate the eigenvalue problem of Hansen and Scheinkman (Econometrica 77:177–234, 2009) by employing weak time-derivatives.

Keywords: No-arbitrage pricing; Weak time-derivative; Martingale component; Special semimartingales; Stochastic interest rates; 60G07; 91G80; 49J40 (search for similar items in EconPapers)
JEL-codes: C02 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00780-018-0371-9

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