Related papers: Beyond Black-Scholes: A Computational Framework fo…
Deep hedging is a framework for hedging derivatives in the presence of market frictions. In this study, we focus on the problem of hedging a given target option by using multiple options. To extend the deep hedging framework to this…
A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of…
The Heston stochastic volatility model is a widely used tool in financial mathematics for pricing European options. However, its calibration remains computationally intensive and sensitive to local minima due to the model's nonlinear…
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…
Model risk arises from the misspecification of probabilistic models used for pricing and hedging derivatives. While model risk for European-style claims has been widely studied, much less attention has been given to American-style…
One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This assumption can be fulfilled only in perfectly liquid markets.…
We propose a deep learning approach to study the minimal variance pricing and hedging problem in an incomplete jump diffusion market. It is based upon a rigorous stochastic calculus derivation of the optimal hedging portfolio, optimal…
Motivated by the work of Segal and Segal on the Black-Scholes pricing formula in the quantum context, we study a quantum extension of the Black-Scholes equation within the context of Hudson-Parthasarathy quantum stochastic calculus. Our…
Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…
We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for…
We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift,…
Black-Scholes implied volatility is a quantile. The insight follows from the normalized option price being a probability on the variance scale, with the inverse Gaussian distribution providing the link. It enables analytically exact and…
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American…
Contrary to the common view that exact pricing is prohibitive owing to the curse of dimensionality, this study proposes an efficient and unified method for pricing options under multivariate Black-Scholes-Merton (BSM) models, such as the…
Jump stochastic volatility models are central to financial econometrics for volatility forecasting, portfolio risk management, and derivatives pricing. Markov Chain Monte Carlo (MCMC) algorithms are computationally unfeasible for the…
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…
We test various volatility models using the Bitcoin spot price series. Our models include HIST, EMA ARCH, GARCH, and EGARCH, models. Both of our in-sample-fit and out-of-sample-forecast results suggest that GARCH and EGARCH models perform…
In this paper we analyze a nonlinear Black--Scholes model for option pricing under variable transaction costs. The diffusion coefficient of the nonlinear parabolic equation for the price $V$ is assumed to be a function of the underlying…
We consider the problem of pricing basket options in a multivariate Black Scholes or Variance Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high dimensional numerical integration problems with…
In common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his…