Hedging via Perpetual Derivatives: Trinomial Option Pricing and Implied Parameter Surface Analysis

Jagdish Gnawali (), W. Brent Lindquist and Svetlozar T. Rachev
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Jagdish Gnawali: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA
W. Brent Lindquist: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA
Svetlozar T. Rachev: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA

JRFM, 2025, vol. 18, issue 4, 1-32

Abstract: We introduce a fairly general, recombining trinomial tree model in the natural world. Market completeness is ensured by considering a market consisting of two risky assets, a riskless asset and a European option. The two risky assets consist of a stock and a perpetual derivative of that stock. The option has the stock and its derivative as its underlying. Using a replicating portfolio, we develop prices for European options and generate the unique relationships between the risk-neutral and real-world parameters of the model. We discuss calibration of the model to empirical data in the cases in which the risky asset returns are treated as either arithmetic or logarithmic. From historical price and call option data for select large cap stocks, we develop implied parameter surfaces for the real-world parameters in the model.

Keywords: trinomial tree; option pricing; perpetual derivative; implied parameter value (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2025
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