Deep learning for quadratic hedging in incomplete jump market

Agram, Nacira (avtor), Øksendal, Bernt Karsten (avtor), Rems, Jan (avtor)

We propose a deep learning approach to study the minimal variance pricing and hedging problem in an incomplete jump diffusion market. It is based on a rigorous stochastic calculus derivation of the optimal hedging portfolio, optimal option price, and the corresponding equivalent martingale measure through the means of the Stackelberg game approach. A deep learning algorithm based on the combination of the feed-forward and LSTM neural networks is tested on three different market models, two of which are incomplete. In contrast, the complete market Black–Scholes model serves as a benchmark for the algorithm’s performance. The results that indicate the algorithm’s good performance are presented and discussed. In particular, we apply our results to the special incomplete market model studied by Merton and give a detailed comparison between our results based on the minimal variance principle and the results obtained by Merton based on a different pricing principle. Using deep learning, we find that the minimal variance principle leads to typically higher option prices than those deduced from the Merton principle. On the other hand, the minimal variance principle leads to lower losses than the Merton principle.

• Jezik: Angleški jezik
• Ključne besede: option pricing, incomplete market, equivalent martingale measure, Merton model, deep learning, LSTM
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2024
• Št. strani: Str. 463-499
• Številčenje: Vol. 6, iss. 3
• PID: 20.500.12556/RUL-162188
• UDK: 519.2:004.8
• ISSN pri članku: 2524-6984
• DOI: 10.1007/s42521-024-00112-5
• COBISS.SI-ID: 208122627
• Datum objave v RUL: 19.09.2024

Gradivo je del revije

• Naslov: Digital finance
• Skrajšan naslov: Digit. finance
• Založnik: Springer Nature
• ISSN: 2524-6984
• COBISS.SI-ID: 114564611

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Projekti

• Financer: Drugi - Drug financer ali več financerjev
• Program financ.: Swedish Research Council
• Številka projekta: 2020-04697

• Financer: ARIS - Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
• Številka projekta: P1-0448
• Naslov: Stohastične metode in njihova uporaba