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Tenor Specific Pricing

Author

Listed:
  • DILIP B. MADAN

    (Robert H. Smith School of Business, University of Maryland, College Park, MD 20742, USA)

  • WIM SCHOUTENS

    (Department of Mathematics, K.U. Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium)

Abstract

Observing that pure discount projection curves are now based on a variety of tenors leads us to enquire into the possibility of theoretically deriving tenor specific zero coupon bond prices. The question then also arises on how to construct tenor specific prices for all financial contracts. Noting that in conic finance one has the law of two prices, bid and ask, that are nonlinear functions of the random variables being priced, we model dynamically consistent sequences of such prices using the theory of nonlinear expectations. The latter theory is closely connected to solutions of backward stochastic difference equations. The drivers for these stochastic difference equations are here constructed using concave distortions that implement risk charges for local tenor specific risks. It is then observed that tenor specific prices given by the mid quotes of bid and ask converge to the risk neutral price as the tenor is decreased and liquidity increased when risk charges are scaled by the tenor. Square root tenor scaling can halt the convergence to risk neutral pricing, preserving bid ask spreads in the limit. The greater liquidity of lower tenors may lead to an increase or decrease in prices depending on whether the lower liquidity of a higher tenor has a mid quote above or below the risk neutral value. Generally for contracts with a large upside and a bounded downside the prices fall with liquidity while the opposite is the case for contracts subject to a large downside and a bounded upside.

Suggested Citation

  • Dilip B. Madan & Wim Schoutens, 2012. "Tenor Specific Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1-21.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:06:n:s0219024912500434
    DOI: 10.1142/S0219024912500434
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    Citations

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    Cited by:

    1. Dilip B. Madan, 2016. "Benchmarking in two price financial markets," Annals of Finance, Springer, vol. 12(2), pages 201-219, May.
    2. Madan, Dilip B., 2014. "Modeling and monitoring risk acceptability in markets: The case of the credit default swap market," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 63-73.
    3. Dilip Madan, 2015. "Asset pricing theory for two price economies," Annals of Finance, Springer, vol. 11(1), pages 1-35, February.
    4. Dilip B. Madan & Wim Schoutens & King Wang, 2020. "Bilateral multiple gamma returns: Their risks and rewards," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-27, March.
    5. Dilip B. Madan & Martijn Pistorius & Wim Schoutens, 2017. "Conic Trading In A Markovian Steady State," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-22, March.
    6. Lin-Yee Hin & Nikolai Dokuchaev, 2016. "Short Rate Forecasting Based On The Inference From The Cir Model For Multiple Yield Curve Dynamics," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-33, March.

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