Abstract
This paper deals with the European option-valuation problem under a prediction model for the underlying asset prices with an external impact. We suggest an alternative model for risky asset prices in which the parameters are dependent on a non-Markovian process. This generalizes the regime-switching models with continuous-time Markov-chain processes. A notable problem of this model is that the process embedded in the parameter of the stock price is non-Markovian; in addition, the market is incomplete. The change from the historical probability to a risk-neutral one is investigated, and the set of equivalent martingale measures is determined. In addition, an infinitesimal generator is obtained, which allows numerical simulations of the non-Markovian and the stock-price processes to be conducted. Several illustrations are provided.
| Original language | English |
|---|---|
| Pages (from-to) | 15-23 |
| Number of pages | 9 |
| Journal | Advances in the Theory of Nonlinear Analysis and its Applications |
| Volume | 7 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2023 |
Keywords
- Quadratic stochastic process Brownian motion Non-Markov Options pricing Regime switching models
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
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