Related papers: Pricing of barrier options by marginal functional …
In this paper we present a very simple way to price a class of barrier options when the underlying process is driven by a huge class of L\'evy processes. To achieve our goal we assume that our market satisfies a symmetry property. In case…
We propose a quasi-Monte Carlo algorithm for pricing knock-out and knock-in barrier options under the Heston (1993) stochastic volatility model. This is done by modifying the LT method from Imai and Tan (2006) for the Heston model such that…
This article addresses the problem of approximating the price of options on discrete and continuous arithmetic average of the underlying, i.e. discretely and continuously monitored Asian options, in local volatility models. A…
We develop quantum algorithms for pricing Asian and barrier options under the Heston model, a popular stochastic volatility model, and estimate their costs, in terms of T-count, T-depth and number of logical qubits, on instances under…
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…
Quadratic hedging of option payoffs generates the variance optimal martingale measure. When an option features an exercise policy and its cash flows are hedged according to this approach, it may be tempting to optimize such a policy under…
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…
Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…
The present paper describes a practical example in which the probability distribution of the prices of a stock market blue chip is calculated as the wave function of a quantum particle confined in a potential well. This model may naturally…
We present a simple, fast, and accurate method for pricing a variety of discretely monitored options in the Black-Scholes framework, including autocallable structured products, single and double barrier options, and Bermudan options. The…
Semi-analytical pricing of American options in a time-dependent Ornstein-Uhlenbeck model was presented in [Carr, Itkin, 2020]. It was shown that to obtain these prices one needs to solve (numerically) a nonlinear Volterra integral equation…
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…
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…
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…
This paper presents a multinomial method for option pricing when the underlying asset follows an exponential Variance Gamma process. The continuous time Variance Gamma process is approximated by a discrete time Markov chain with the same…
Pricing of financial derivatives, in particular early exercisable options such as Bermudan options, is an important but heavy numerical task in financial institutions, and its speed-up will provide a large business impact. Recently,…
Diffusion processes driven by Fractional Brownian motion (FBM) have often been considered in modeling stock price dynamics in order to capture the long range dependence of stock price observed in reality. Option prices for such models had…
Based on empirical market data, a stochastic volatility model is proposed with volatility driven by fractional noise. The model is used to obtain a risk-neutrality option pricing formula and an option pricing equation.
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…
In this work, we present a quantum algorithm designed to solve the differential equation used in the pricing of Asian options, in the framework of the Black-Scholes model. Our approach modifies an existing quantum pre-conditioning method…