Paper: Oct 07,2024
q-fin.MF
ID:2410.04748
Hedging via Perpetual Derivatives: Trinomial Option Pricing and Implied Parameter Surface Analysis
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.
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Paper Author: Jagdish Gnawali,W. Brent Lindquist,Svetlozar T. Rachev
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