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We consider conditional-mean hedging in a fractional Black-Scholes pricing model in the presence of proportional transaction costs. We develop an explicit formula for the conditional-mean hedging portfolio in terms of the recently…

Pricing of Securities · Quantitative Finance 2017-09-20 Foad Shokrollahi , Tommi Sottinen

In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We derive the governing fractional…

Computational Engineering, Finance, and Science · Computer Science 2021-04-19 Grzegorz Krzyżanowski , Marcin Magdziarz , Łukasz Płociniczak

The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the…

Physics and Society · Physics 2009-11-11 L. Moriconi

A classical inventory problem is studied from the perspective of embedded options, reducing inventory-management to the design of optimal contracts for forward delivery of stock (commodity). Financial option techniques \`{a} la…

Optimization and Control · Mathematics 2019-04-10 Roy O. Davies , A. J. Ostaszewski

We develop an expansion approach for the pricing of European quanto options written on LIBOR rates (of a foreign currency). We derive the dynamics of the system of foreign LIBOR rates under the domestic forward measure and then consider the…

Pricing of Securities · Quantitative Finance 2018-04-04 Julien Hok , Philip Ngare , Antonis Papapantoleon

We consider the discretized Bachelier model where hedging is done on an equidistant set of times. Exponential utility indifference prices are studied for path-dependent European options and we compute their non-trivial scaling limit for a…

Probability · Mathematics 2022-03-03 Asaf Cohen , Yan Dolinsky

We present a unified, market-complete model that integrates both the Bachelier and Black-Scholes-Merton frameworks for asset pricing. The model allows for the study, within a unified framework, of asset pricing in a natural world that…

Mathematical Finance · Quantitative Finance 2024-06-11 W. Brent Lindquist , Svetlozar T. Rachev , Jagdish Gnawali , Frank J. Fabozzi

This paper presents a novel way to predict options price for one day in advance, utilizing the method of Quasi-Reversibility for solving the Black-Scholes equation. The Black-Scholes equation solved forwards in time with Tikhonov…

Analysis of PDEs · Mathematics 2022-03-21 Mikhail V. Klibanov , Kirill V. Golubnichiy , Andrey V. Nikitin

This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a…

Analysis of PDEs · Mathematics 2016-09-27 Anindya Goswami , Jeeten Patel , Poorva Shevgaonkar

In the framework of bilateral Gamma stock models we seek for adequate option pricing measures, which have an economic interpretation and allow numerical calculations of option prices. Our investigations encompass Esscher transforms, minimal…

Mathematical Finance · Quantitative Finance 2025-11-21 Uwe Küchler , Stefan Tappe

We show that our generalization of the Black-Scholes partial differential equation (pde) for nontrivial diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, this was proven for the…

Physics and Society · Physics 2009-11-11 J. L. McCauley , G. H. Gunaratne , K. E. Bassler

In this paper we discuss backward stochastic differential equations with Markov chain noise, having continuous drivers. We obtain the existence of a solution which is possibly not unique. Moreover, we show there is a minimal solution for…

Probability · Mathematics 2014-12-01 Dimbinirina Ramarimbahoaka , Zhe Yang , Robert J. Elliott

Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can…

Risk Management · Quantitative Finance 2026-01-05 Pengpeng Li , Shi-Dong Liang

We obtain option pricing formulas for stock price models in which the drift and volatility terms are functionals of a continuous history of the stock prices. That is, the stock dynamics follows a nonlinear stochastic functional differential…

Pricing of Securities · Quantitative Finance 2020-11-17 Flavia Sancier , Salah Mohammed

We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient…

Mathematical Finance · Quantitative Finance 2016-09-19 Ben Hambly , Matthieu Mariapragassam , Christoph Reisinger

We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a…

Optimization and Control · Mathematics 2008-12-02 Erhan Bayraktar , Virginia R. Young

Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the…

Pricing of Securities · Quantitative Finance 2013-04-18 Youssef El-Khatib , Abdulnasser Hatemi-J

No--arbitrage property provides a simple method for pricing financial derivatives. However, arbitrage opportunities exist among different markets in various fields, even for a very short time. By knowing that an arbitrage property exists,…

Computational Finance · Quantitative Finance 2022-05-24 Yasushi Ota , Yu Jiang , Daiki Maki

This paper investigates the necessary optimality conditions for uniformly overtaking optimal control on infinite horizon in the free end case. %with free right endpoint. In the papers of S.M.Aseev, A.V.Kryazhimskii, V.M.Veliov, K.O.Besov…

Optimization and Control · Mathematics 2012-07-24 Dmitry Khlopin

Prices of European call options in a regime-switching local volatility model can be computed by solving a parabolic system which generalises the classical Black and Scholes equation, giving these prices as functionals of the local…

Analysis of PDEs · Mathematics 2017-10-10 Mourad Bellassoued , Raymond Brummelhuis , Michel Cristofol , Eric Soccorsi