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Random Time Forward Starting Options

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Listed:
  • Fabio Antonelli
  • Alessandro Ramponi
  • Sergio Scarlatti

Abstract

We introduce a natural generalization of the forward-starting options, first discussed by M. Rubinstein. 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 {\bf 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.

Suggested Citation

  • Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2015. "Random Time Forward Starting Options," Papers 1504.03552, arXiv.org.
    • Handle: RePEc:arx:papers:1504.03552
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    1. 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.
    2. Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2020. "Approximate XVA for European claims," Papers 2007.07701, arXiv.org.
    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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