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A Mathematical Model for the Pricing of Derivative Financial Products: the Role of the Banking Supervision and of the Model Risk

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  • Rosa Ferrentino
  • Luca Vota

Abstract

This paper aims to identify an innovative procedure to assess the model risk of a derivative financial product. More precisely, the authors, after briefly discussing the role of banking supervision, present a framework to estimate the model risk at the current time of a bond and they distinguish its systematic component. This model, consisting of two different expressions of the security price, is based on the hypothesis that the underlying interest rate is a swap rate that may be represented also as an AR(1)-GARCH(1,1) process. Moreover, the authors show that their model can be used for forecasting purposes. In reality, the aim of this study is to investigate the link between pricing models of financial derivatives and model risk and to highlight that this latter depends on the volatility of the security and on the price distribution. Â JEL classification numbers: C02, C60, G17, G20.

Suggested Citation

  • Rosa Ferrentino & Luca Vota, 2022. "A Mathematical Model for the Pricing of Derivative Financial Products: the Role of the Banking Supervision and of the Model Risk," Journal of Finance and Investment Analysis, SCIENPRESS Ltd, vol. 11(1), pages 1-2.
    • Handle: RePEc:spt:fininv:v:11:y:2022:i:1:f:11_1_2
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    References listed on IDEAS

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    1. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(4), pages 419-440, December.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Merton, Robert C & Scholes, Myron S & Gladstein, Mathew L, 1978. "The Returns and Risk of Alternative Call Option Portfolio Investment Strategies," The Journal of Business, University of Chicago Press, vol. 51(2), pages 183-242, April.
    5. Danielsson, Jon & James, Kevin R. & Valenzuela, Marcela & Zer, Ilknur, 2016. "Model risk of risk models," Journal of Financial Stability, Elsevier, vol. 23(C), pages 79-91.
    6. Merton, Robert C & Scholes, Myron S & Gladstein, Mathew L, 1982. "The Returns and Risks of Alternative Put-Option Portfolio Investment Strategies," The Journal of Business, University of Chicago Press, vol. 55(1), pages 1-55, January.
    7. Black, Fischer & Scholes, Myron S, 1972. "The Valuation of Option Contracts and a Test of Market Efficiency," Journal of Finance, American Finance Association, vol. 27(2), pages 399-417, May.
    8. Nelson, Daniel B & Ramaswamy, Krishna, 1990. "Simple Binomial Processes as Diffusion Approximations in Financial Models," The Review of Financial Studies, Society for Financial Studies, vol. 3(3), pages 393-430.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    10. Robert Engle, 2001. "GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 157-168, Fall.
    11. Jean-Philippe Bouchaud & Didier Sornette, 1994. "The Black-Scholes option pricing problem in mathematical finance: generalization and extensions for a large class of stochastic processes," Science & Finance (CFM) working paper archive 500040, Science & Finance, Capital Fund Management.
    12. Filippo Curti & Ibrahim Ergen & Minh Le & Marco Migueis & Rob T. Stewart, 2016. "Benchmarking Operational Risk Models," Finance and Economics Discussion Series 2016-070, Board of Governors of the Federal Reserve System (U.S.).
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    More about this item

    Keywords

    Model risk; Pricing model; Reverse Floater; Financial derivatives; Banking supervision.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

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