Random Time Forward Starting Options

19 Pages Posted: 1 Apr 2015

See all articles by Fabio Antonelli

Fabio Antonelli

Sapienza University of Rome

Alessandro Ramponi

Dept. Economics and Finance, University of Rome Tor Vergata

Sergio Scarlatti

University of Rome Tor Vergata

Date Written: March 31, 2015

Abstract

We introduce a natural generalization of the forward-starting options, first discussed by M. Rubinstein [Rubin]. The main feature of the contract presented here is that the strike-determination time is not fixed ex-ante, but allowed to be random, usually related to the occurrence of some event, either of financial nature or not. We will call these options Random Time Forward Starting (RTFS).

We show that, under an appropriate "martingale preserving" hypothesis, we can exhibit arbitrage free prices, which can be explicitly computed in many classical market models, at least under independence between the random time and the assets' prices. Practical implementations of the pricing methodologies are also provided. Finally a credit value adjustment formula for these OTC options is computed for the unilateral counterparty credit risk.

Keywords: Random times, forward-starting options, CVA

JEL Classification: G13

Suggested Citation

Antonelli, Fabio and Ramponi, Alessandro and Scarlatti, Sergio, Random Time Forward Starting Options (March 31, 2015). Available at SSRN: https://ssrn.com/abstract=2587711 or http://dx.doi.org/10.2139/ssrn.2587711

Fabio Antonelli

Sapienza University of Rome ( email )

Piazzale Aldo Moro 5
Roma, Rome 00185
Italy

Alessandro Ramponi

Dept. Economics and Finance, University of Rome Tor Vergata ( email )

Via Columbia, 2
Rome, Lazio 00133
Italy

Sergio Scarlatti (Contact Author)

University of Rome Tor Vergata ( email )

Via di Tor Vergata
Rome, Lazio 00133
Italy

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