相关论文: On the valuation of Asian options: integral repres…

We provide results relating to the integrability, uniform integrability and local integrability of exponential MAPs, which are natural extensions of exponential Levy models. Then, we use Mellin transform and partial integro-differential…

In this paper, we introduce a novel semi-analytical method for solving a broad class of initial value problems involving differential, integro-differential, and delay equations, including those with fractional and variable-order…

We use Lie symmetry methods to price certain types of barrier options. Usually Lie symmetry methods cannot be used to solve the Black-Scholes equation for options because the function defining the maturity condition for an option is not…

We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all the terms by induction is also given. At…

In the paper written by Klibanov et al, it proposes a novel method to calculate implied volatility of a European stock options as a solution to ill-posed inverse problem for the Black-Scholes equation. In addition, it proposes a trading…

Options financial instruments designed to protect investors from the stock market randomness. In 1973, Fisher Black, Myron Scholes and Robert Merton proposed a very popular option pricing method using stochastic differential equations…

We provide a complete representation of the interest rate in the extended CIR model. Since it was proved in Maghsoodi (1996) that the representation of the CIR process as a sum of squares of independent Ornstein-Uhlenbeck processes is…

Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some…

In common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his…

We present a method derived from Laplace transform theory that enables the evaluation of fractional integrals. This method is adapted and extended in a variety of ways to demonstrate its utility in deriving alternative representations for…

We proposed classification models that utilize the result from the Quasi-Reversibility Method, which solves the Black-Scholes equation to forecast the option prices one day in advance. Combining the minimizer from QRM with our machine…

This paper examines the pricing issue of margin-call stock loans with finite maturities under the Black-Scholes-Merton framework. In particular, using a Fourier Sine transform method, we reduce the partial differential equation governing…

In this note, Black--Scholes implied volatility is expressed in terms of various optimisation problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries…

We consider a generalization of the variance-gamma (generalized asymmetric Laplace) distribution, defined as a normal mean - variance mixture with a gamma mixing distribution. While this model is typically studied in the univariate setting,…

We discuss several aspects of Mellin transform, including distributional Mellin transform and inversion of multiple Mellin-Barnes integrals in $\mathbb{C}^n$ and its connection to residue expansion or evaluation of Laplace integrals. These…

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…

Extracting implied information, like volatility and/or dividend, from observed option prices is a challenging task when dealing with American options, because of the computational costs needed to solve the corresponding mathematical problem…

Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and…

A master equation approach to the numerical solution of option pricing models is developed. The basic idea of the approach is to consider the Black--Scholes equation as the macroscopic equation of an underlying mesoscopic stochastic option…

We classify valuations on lattice polygons with values in the ring of formal power series that commute with the action of the affine unimodular group. A typical example of such valuations is induced by the Laplace transform, but as it turns…