Related papers: Path-dependent option pricing with two-dimensional…
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic…
This paper develops a deep learning-based framework for pricing convertible bonds with path-dependent contractual features, namely downward conversion price reset and issuer call clauses under rolling-window trigger rules, which are…
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…
We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average…
Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are usually of high dimensionality and discontinuities. The two factors may significantly deteriorate the…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and…
We consider the problem of finding model-independent bounds on the price of an Asian option, when the call prices at the maturity date of the option are known. Our methods differ from most approaches to model-independent pricing in that we…
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…
We introduce a new deep-learning based algorithm to evaluate options in affine rough stochastic volatility models. Viewing the pricing function as the solution to a curve-dependent PDE (CPDE), depending on forward curves rather than the…
This paper presents a new model for options pricing. The Black-Scholes-Merton (BSM) model plays an important role in financial options pricing. However, the BSM model assumes that the risk-free interest rate, volatility, and equity premium…
Under the assumption of no-arbitrage, the pricing of American and Bermudan options can be casted into optimal stopping problems. We propose a new adaptive simulation based algorithm for the numerical solution of optimal stopping problems in…
This paper develops three polynomial-time pricing techniques for European Asian options with provably small errors, where the stock prices follow binomial trees or trees of higher-degree. The first technique is the first known Monte Carlo…
The pricing of financial derivatives, which requires massive calculations and close-to-real-time operations under many trading and arbitrage scenarios, were largely infeasible in the past. However, with the advancement of modern computing,…
We develop a mixed least squares Monte Carlo-partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets whose volatility is stochastic. The algorithm is formulated for an arbitrary number of assets and…
Pricing financial derivatives, in particular European-style options at different time-maturities and strikes, means a relevant problem in finance. The dynamics describing the price of vanilla options when constant volatilities and interest…
We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…
This paper reconsiders the ODMTS Design with Adoptions problem (ODMTS-DA) to capture the latent demand in on-demand multimodal transit systems. The ODMTS-DA is a bilevel optimization problem, for which Basciftci and Van Hentenryck (2022)…
Credit value adjustment (CVA) is the charge applied by financial institutions to the counterparty to cover the risk of losses on a counterpart default event. In this paper we estimate such a premium under the Bates stochastic model (Bates…
We develop a quantum algorithm to price discretely monitored lookback options in the Black-Scholes framework using imaginary time evolution. By rewriting the pricing PDE as a Schrodinger-type equation, the problem becomes the imaginary time…