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In this paper we introduce a deep learning method for pricing and hedging American-style options. It first computes a candidate optimal stopping policy. From there it derives a lower bound for the price. Then it calculates an upper bound, a…
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…
The literature on volatility modelling and option pricing is a large and diverse area due to its importance and applications. This paper provides a review of the most significant volatility models and option pricing methods, beginning with…
This paper studies four trading algorithms of a professional trader at a multilateral trading facility, observing a realistic two-sided limit order book whose dynamics are driven by the order book events. The identity of the trader can be…
In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the…
In this paper, a new numerical method based on adaptive gradient descent optimizers is provided for computing the implied volatility from the Black-Scholes (B-S) option pricing model. It is shown that the new method is more accurate than…
In this article, we study the rate of convergence of prices when a model is approximated by some simplified model. We also provide a method how explicit error formula for more general options can be obtained if such formula is available for…
This research investigates pricing financial options based on the traditional martingale theory of arbitrage pricing applied to neural SDEs. We treat neural SDEs as universal It\^o process approximators. In this way we can lift all…
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…
Utility based methods provide a very general theoretically consistent approach to pricing and hedging of securities in incomplete financial markets. Solving problems in the utility based framework typically involves dynamic programming,…
The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic…
Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can…
In this paper we present two parallel Monte Carlo based algorithms for pricing multi--dimensional Bermudan/American options. First approach relies on computation of the optimal exercise boundary while the second relies on classification of…
In this work, we propose an algorithm to price American options by directly solving the dual minimization problem introduced by Rogers. Our approach relies on approximating the set of uniformly square integrable martingales by a finite…
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…
The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as \begin{equation*}…
After a brief review of option pricing theory, we introduce various methods proposed for extracting the statistical information implicit in options prices. We discuss the advantages and drawbacks of each method, the interpretation of their…
Option pricing models, essential in financial mathematics and risk management, have been extensively studied and recently advanced by AI methodologies. However, American option pricing remains challenging due to the complexity of…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…
Subdiffusion is a well established phenomenon in physics. In this paper we apply the subdiffusive dynamics to analyze financial markets. We focus on the financial aspect of time fractional diffusion model with moving boundary i.e. American…