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Random Time Forward-Starting Options

Author

Listed:
  • F. ANTONELLI

    (Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, via Vetoio, Coppito, L'Aquila 67100, Italy)

  • A. RAMPONI

    (#x2020;Department of Economics and Finance, University of Roma – Tor Vergata, via Columbia 2, Roma 00133, Italy)

  • S. SCARLATTI

    (#x2020;Department of Economics and Finance, University of Roma – Tor Vergata, via Columbia 2, Roma 00133, Italy)

Abstract

We introduce a natural generalization of the forward-starting options. 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 and in absence of simultaneous jumps between the random time and the assets' prices. Practical implementations of the pricing methodologies are also provided. Finally, a credit value adjustment (CVA) formula for these over the counter (OTC) options is computed for the unilateral counterparty credit risk.

Suggested Citation

  • F. Antonelli & A. Ramponi & S. Scarlatti, 2016. "Random Time Forward-Starting Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-25, December.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:08:n:s0219024916500503
    DOI: 10.1142/S0219024916500503
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    Cited by:

    1. Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2020. "Approximate XVA for European claims," Papers 2007.07701, arXiv.org.
    2. F. Antonelli & A. Ramponi & S. Scarlatti, 2021. "CVA and vulnerable options pricing by correlation expansions," Annals of Operations Research, Springer, vol. 299(1), pages 401-427, April.
    3. E. Alòs & F. Antonelli & A. Ramponi & S. Scarlatti, 2021. "Cva And Vulnerable Options In Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 1-34, March.

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