A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Random neural nets learn Black-Scholes PDEs without dimensionality issues.
Derives Black-Scholes model without stochastic calculus or PDEs.
The paper presents a PDE method for xVA incorporation in financial derivatives.
Enhanced Black-Scholes model for option pricing with stochastic volatility and interest rate variability.
New quantum algorithm simplifies complex financial derivatives pricing.
When the underlying stock price is a strict local martingale process under an equivalent local martingale measure, Black-Scholes PDE associated with an European option may have multiple solutions. In this paper, we study an approximation for the smallest hedging price of such an European option. Our results show that a…
Artificial neural networks (ANNs) have very successfully been used in numerical simulations for a series of computational problems ranging from image classification/image recognition, speech recognition, time series analysis, game intelligence, and computational advertising to numerical approximations of partial differ…
This research analyzes deep PDE solvers for option pricing accuracy.
Deep neural network approximates multivariate option pricing.
A contour integral method recently proposed by Weideman [IMA J. Numer. Anal., to appear] for integrating semi-discrete advection-diffusion PDEs, is extended for application to some of the important equations of mathematical finance. Using estimates for the numerical range of the spatial operator, optimal contour parame…
New method uses tensor networks to price multi-asset options efficiently.
In this paper, we study the asymptotic behavior of Asian option prices in the worst case scenario under an uncertain volatility model. We give a procedure to approximate the Asian option prices with a small volatility interval. By imposing additional conditions on the boundary condition and cutting the obtained Black-S…
We apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation. First, for a generic market dynamics given by a multidimensional Itô's process we specify and prove the equivalence between (NFLVR) and expected utility maximization. A…
Quantum Monte Carlo speeds up option pricing for complex payoff functions.
Market illiquidity, feedback effects, presence of transaction costs, risk from unprotected portfolio and other nonlinear effects in PDE based option pricing models can be described by solutions to the generalized Black-Scholes parabolic equation with a diffusion term nonlinearly depending on the option price itself. Di…
Quantum algorithm for multi-asset option pricing under different volatility models.
Deep learning solves high-dimensional PDEs efficiently.
A neural network solves Black-Scholes PDE for option pricing with uncertainty quantification.
The usual derivation of the Fokker-Planck partial differential eqn. assumes the Chapman-Kolmogorov equation for a Markov process. Starting instead with an Ito stochastic differential equation we argue that finitely many states of memory are allowed in Kolmogorov's two pdes, K1 (the backward time pde) and K2 (the Fokker…
Quantum algorithm speeds up option pricing in finance.
Stochastic differential equations (SDEs) and the Kolmogorov partial differential equations (PDEs) associated to them have been widely used in models from engineering, finance, and the natural sciences. In particular, SDEs and Kolmogorov PDEs, respectively, are highly employed in models for the approximative pricing of …
Differential equations can be used to construct predictive models of a diverse set of real-world phenomena like heat transfer, predator-prey interactions, and missile tracking. In our work, we explore one particular application of stochastic differential equations, the Black-Scholes-Merton model, which can be used to p…
Deep learning model solves high-dimensional PDEs using Actor-Critic approach.
Develops a new option pricing model under G-expectation framework.
New model for options pricing accounting for time-varying interest rates, volatility, and equity premium.
Quantum machine learning solves high-dimensional PDEs with lower variance and improved accuracy.
Paper proposes an analytical pricing model for puttable bonds with credit risk.
The vast majority of works on option pricing operate on the assumption of risk neutral valuation, and consequently focus on the expected value of option returns, and do not consider risk parameters, such as variance. We show that it is possible to give explicit formulae for the variance of European option returns (vani…
Paper uses IGA for efficient pricing of financial derivatives, comparing it to FDM and FEM.
In this article we present new results for the pricing of arithmetic Asian options within a Black-Scholes context. To derive these results we make extensive use of the local scale invariance that exists in the theory of contingent claim pricing. This allows us to derive, in a natural way, a simple PDE for the price of …
Efficiently values and computes sensitivities of Bermudan options using Method of Lines.
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number …
Study liquidity impact on spread option pricing.
We take the holistic approach of computing an OTC claim value that incorporates credit and funding liquidity risks and their interplays, instead of forcing individual price adjustments: CVA, DVA, FVA, KVA. The resulting nonlinear mathematical problem features semilinear PDEs and FBSDEs. We show that for the benchmark v…
An option market maker incurs funding costs when carrying and hedging inventory. To hedge a net long delta inventory, for example, she pays a fee to borrow stock from the securities lending market. Because of haircuts, she posts additional cash margin to the lender which needs to be financed at her unsecured debt rate.…
We analyse derivative securities whose value is NOT a deterministic function of an underlying which means presence of a basis risk at any time. The key object of our analysis is conditional probability distribution at a given underlying value and moment of time. We consider time evolution of this probability distributi…
We show that our generalization of the Black-Scholes partial differential equation (pde) for nontrivial diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, this was proven for the case of the Gaussian logarithmic returns model by Harrison and Kreps, but we prove …
In this paper, the valuation of European and path-dependent options in foreign exchange (FX) markets is considered when the currency exchange rate evolves according to the Heston model combined with the Cox-Ingersoll-Ross dynamics for the stochastic domestic and foreign short interest rates. The mixed Monte Carlo/PDE m…
The change of numeraire gives very important computational simplification in option pricing. This technique reduces the number of sources of risks that need to be accounted for and so it is useful in pricing complicated derivatives that have several sources of risks. In this article, we considered the underlying mathem…
Quantum algorithms speed up derivative pricing beyond Black-Scholes models.
Deriving option prices from operational-time Markov lattices
Neural networks improve financial derivative pricing accuracy.
ANNs solve financial option valuation problems without numerical methods.
The main result of this paper is a probabilistic proof of the penalty method for approximating the price of an American put in the Black-Scholes market. The method gives a parametrized family of partial differential equations, and by varying the parameter the corresponding solutions converge to the price of an American…
We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamical programming approach leads to an investigation of t…
The paper challenges the notion that asset return doesn't affect Black-Scholes-Merton model.
The paper proposes a different method of solving a simplified version of the Black-Scholes equation. This paper will discuss the importance of the Black-Scholes equation and its applications in finance.
Modeling stochastic arbitrage bubbles in Black-Scholes framework.