How can we price options in markets with extreme price jumps? This paper introduces a general class of truncated Lévy processes and explores ways to fit these models to market data. The study focuses on the pricing of options in markets where asset prices exhibit sudden, discontinuous jumps. For a market with a riskless bond and a stock whose log-price follows a truncated Lévy process, the paper derives TLP-analogs of the Black–Scholes equation and formula. It also constructs a locally risk-minimizing portfolio and computes an optimal exercise price for a perpetual American put. These theoretical developments provide valuable tools for financial engineers and researchers working with option pricing models. They offer a way to better capture the impact of extreme events and price jumps in financial markets.
This theoretical work, published in the International Journal of Theoretical and Applied Finance, aligns with the journal's scope of providing cutting-edge research in financial modeling. By introducing a new approach to option pricing using truncated Lévy processes, the paper contributes to the ongoing development of sophisticated tools for financial analysis and risk management.
| Category | Category Repetition |
|---|---|
| Science: Mathematics | 1 |
| Science: Physics | 1 |