Related papers: Pricing Parisian down-and-in options
Nowadays many financial derivatives, such as American or Bermudan options, are of early exercise type. Often the pricing of early exercise options gives rise to high-dimensional optimal stopping problems, since the dimension corresponds to…
An accurate valuation of American call options is critical in most financial decision making environments. However, traditional models like the Barone-Adesi Whaley (B-AW) and Binomial Option Pricing (BOP) methods fall short in handling the…
Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct…
American options in a multi-asset market model with proportional transaction costs are studied in the case when the holder of an option is able to exercise it gradually at a so-called mixed (randomised) stopping time. The introduction of…
This paper concerns the numerical valuation of swing options with discrete action times under a linear two-factor mean-reverting model with jumps. The resulting sequence of two-dimensional partial integro-differential equations (PIDEs) are…
This study investigates the application of machine learning algorithms, particularly in the context of pricing American options using Monte Carlo simulations. Traditional models, such as the Black-Scholes-Merton framework, often fail to…
We establish an explicit approximation formula for European put option prices within a general stochastic volatility model with time-dependent parameters. Our methodology is based on expansions of the mixing representation of the put option…
The main purpose of this article is to give a general overview and understanding of the first widely used option-pricing model, the Black-Scholes model. The history and context are presented, with the usefulness and implications in the…
We present a new numerical method to price vanilla options quickly in time-changed Brownian motion models. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a…
In this paper, we study a game with positive or plus infinite expectation and determine the optimal proportion of investment for maximizing the limit expectation of growth rate per attempt. With this objective, we introduce a new pricing…
When the underlying asset displays oscillations, spikes or heavy-tailed distributions, the lognormal diffusion process (for which Black and Scholes developed their momentous option pricing formula) is inadequate: in order to overcome these…
In this paper we study pricing of American put options on the Black and Scholes market with a stochastic interest rate and finite-time maturity. We prove that the option value is a $C^1$ function of the initial time, interest rate and stock…
An analytic method for pricing American call options is provided; followed by an empirical method for pricing Asian call options. The methodology is the pricing theory presented in "A Modern Theory of Random Variation", by Patrick…
We develop a novel deep learning approach for pricing European basket options written on assets that follow jump-diffusion dynamics. The option pricing problem is formulated as a partial integro-differential equation, which is approximated…
Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here we model the price…
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…
A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…
In this paper, we study a version of the perpetual American call/put option where exercise opportunities arrive only periodically. Focusing on the exponential L\'evy models with i.i.d. exponentially-distributed exercise intervals, we show…
The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a…
The purpose of this paper is to analyze and compute the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility which can be a function of the second derivative of the option price itself. A…