Related papers: Path Integral Method for Pricing Proportional Step…
Path integral method in quantum mechanics provides a new thinking for barrier option pricing. For proportional step options, the option price changing process is similar to the one dimensional trapezoid potential barrier scattering problem…
Hamiltonian approach in quantum mechanics provides a new thinking for barrier option pricing. For proportional floating barrier step options, the option price changing process is similar to the one dimensional trapezoid potential barrier…
In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the…
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and…
We continue a series of papers devoted to construction of semi-analytic solutions for barrier options. These options are written on underlying following some simple one-factor diffusion model, but all the parameters of the model as well as…
Recent progress in the development of efficient computational algorithms to price financial derivatives is summarized. A first algorithm is based on a path integral approach to option pricing, while a second algorithm makes use of a neural…
We use a path integral approach for solving the stochastic equations underlying the financial markets, and we show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the…
We present the method of moments approach to pricing barrier-type options when the underlying is modelled by a general class of jump diffusions. By general principles the option prices are linked to certain infinite dimensional linear…
We develop the general integral transforms (GIT) method for pricing barrier options in the time-dependent Heston model (also with a time-dependent barrier) where the option price is represented in a semi-analytical form as a two-dimensional…
We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is…
This paper deals with a high-order accurate implicit finite-difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on…
In this paper, a time substitution as used by Duru and Kleinert in their treatment of the hydrogen atom with path integrals is performed to price timer options under stochastic volatility models. We present general pricing formulas for both…
We provided an analytical representation of the price of a barrier option with one type of special moving barrier. We consider the case that risk free rate, dividend rate and stock volatility are time dependent. We get a pricing formula and…
A time-dependent double-barrier option is a derivative security that delivers the terminal value $\phi(S_T)$ at expiry $T$ if neither of the continuous time-dependent barriers $b_\pm:[0,T]\to \RR_+$ have been hit during the time interval…
In this work we develop an alternative approach for solution of Quantum Trajectories using the Path Integral method. The state-of-the-art technique in the field is to solve a set of non-linear, coupled partial differential equations (PDEs)…
We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we…
In this paper, we study option pricing under Vasicek Model by a Hamiltonian approach. Since the interest rate changes with time, we split the time to maturity into infinite steps, and the matrix element during each step could be calculated…
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…
We derive a closed-form solution for the price of an average price as well as an average strike geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also…