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Charting the Unknown: First Passage Time Probabilities for Pearson Diffusion Process and Application to Options Risk Management

Author

Listed:
  • Patra, Saswat

    (University of Luxembourg, Esch-sur-Alzette, Luxembourg and SP Jain Institute of Management & Research (SPJIMR), Mumbai, India)

  • Bhattacharyya, Malay

    (Indian Institute of Management-Udaipur, Udaipur, India)

Abstract

The first passage time probabilities have applications in many fields, including Finance, Marketing, Economics, Physics, and Statistics. In this paper, we study the first passage time probabilities for a Pearson diffusion process and obtain the lower and upper bounds of the first passage time density. We show that the density may be approximated by the upper bound with an error of approximately five percent. We present an application by modelling the profit and loss function of the S&P 500, FTSE 100 and DAX 40 index options using a Pearson diffusion process. Further, we establish the relation between first passage time probabilities and MaxVaR, i.e., the intra-horizon risk and obtain the MaxVaR for various index options based on first passage time probabilities. This is important as MaxVaR can capture the risk and potential losses incurred at any time of the trading horizon. In addition, we conduct a sensitivity analysis on the parameters for the purpose of robustness.

Suggested Citation

  • Patra, Saswat & Bhattacharyya, Malay, 2024. "Charting the Unknown: First Passage Time Probabilities for Pearson Diffusion Process and Application to Options Risk Management," American Business Review, Pompea College of Business, University of New Haven, vol. 27(2), pages 623-639, November.
    • Handle: RePEc:ris:ambsrv:0117
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    More about this item

    Keywords

    First Passage Time Density; Pearson Diffusion Process; MaxVaR; Risk Management;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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