Related papers: Nonparametric estimates of pricing functionals
This thesis provides an overview of the recent advances in reinforcement learning in pricing and hedging financial instruments, with a primary focus on a detailed explanation of the Q-Learning Black Scholes approach, introduced by Halperin…
We develop series expansions in powers of $q^{-1}$ and $q^{-1/2}$ of solutions of the equation $\psi(z) = q$, where $\psi(z)$ is the Laplace exponent of a hyperexponential L\'{e}vy process. As a direct consequence we derive analytic…
We study the pricing and hedging of European spread options on correlated assets when, in contrast to the standard framework and consistent with imperfect liquidity markets, the trading in the stock market has a direct impact on stocks…
This study deals with the problem of pricing European currency options in discrete time setting, whose prices follow the fractional Black Scholes model with transaction costs. Both the pricing formula and the fractional partial differential…
We study the Heston model for pricing European options on stocks with stochastic volatility. This is a Black\--Scholes\--type equation whose spatial domain for the logarithmic stock price $x\in \RR$ and the variance $v\in (0,\infty)$ is the…
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…
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…
In this paper, a rapid and high accurate numerical method for pricing discrete single and double barrier knock-out call options is presented. According to the well-known Black-Scholes framework, the price of option in each monitoring date…
A nonlinear wave alternative for the standard Black-Scholes option-pricing model is presented. The adaptive-wave model, representing 'controlled Brownian behavior' of financial markets, is formally defined by adaptive nonlinear…
We study the problem of reconstruction of special special time dependent local volatility from market prices of options with different strikes at two expiration times. For a general diffusion process we apply the linearization technique and…
Recent literature seek to forecast implied volatility derived from equity, index, foreign exchange, and interest rate options using latent factor and parametric frameworks. Motivated by increased public attention borne out of the…
We use the expectation of the range of an arithmetic Brownian motion and the method of moments on the daily high, low, opening and closing prices to estimate the volatility of the stock price. The daily price jump at the opening is…
Exponential L\'evy processes can be used to model the evolution of various financial variables such as FX rates, stock prices, etc. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such…
The true probability of a European call option to achieve positive return is investigated under the Black-Scholes model. It is found that the probability is determined by those market factors appearing in the BS formula, besides the growth…
The aim of this paper is to investigate the use of close formula approximation for pricing European mortgage options. Under the assumption of logistic duration and normal mortgage rates the underlying price at the option expiry is…
We consider a non-Gaussian option pricing model, into which the underlying log-price is assumed to be driven by an $\alpha$-stable distribution. We remove the a priori divergence of the model by introducing a Mellin regularization for the…
We develop a numerical method for pricing multidimensional vanilla options in the Black-Scholes framework. In low dimensions, we improve an adaptive integration algorithm proposed by two of the authors by introducing a new splitting…
We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures,…
In this paper we develop numerical pricing methodologies for European style Exchange Options written on a pair of correlated assets, in a market with finite liquidity. In contrast to the standard multi-asset Black-Scholes framework, trading…
The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a…