Related papers: Path Dependent Option Pricing: the path integral p…
This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed…
We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a…
The objective of this paper is to introduce the theory of option pricing for markets with informed traders within the framework of dynamic asset pricing theory. We introduce new models for option pricing for informed traders in complete…
In this paper we reformulate the problem of pricing options in a quantum setting. Our proposed algorithm involves preparing an initial state, representing the option price, and then evolving it using existing imaginary time simulation…
Hamiltonian approach in quantum mechanics provides a new thinking for barrier option pricing. For proportional floating barrier step options, the option price changing process is similar to the one dimensional trapezoid potential barrier…
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…
In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent…
We introduce a path sampling method for the computation of rate constants for systems with a highly diffusive character. Based on the recently developed algorithm of transition interface sampling (TIS) this procedure increases the…
Our goal is to analyze the system of Hamilton-Jacobi-Bellman equations arising in derivative securities pricing models. The European style of an option price is constructed as a difference of the certainty equivalents to the value functions…
We develop a tractable framework for valuing Asian options when trading the underlying generates market impact and execution costs. Starting from a discrete-time, quote-level model, we construct a reference midpoint suitable for Asian…
Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one,…
We provide a lean, non-technical exposition on the pricing of path-dependent and European-style derivatives in the Cox-Ross-Rubinstein (CRR) pricing model. The main tool used in the paper for cleaning up the reasoning is applying static…
In the paper, the pricing of Quanto options is studied, where the underlying foreign asset and the exchange rate are correlated with each other. Firstly, we adopt Bayesian methods to estimate unknown parameters entering the pricing formula…
We consider call option prices in diffusion models close to expiry, in an asymptotic regime ("moderately out of the money") that interpolates between the well-studied cases of at-the-money options and out-of-the-money fixed-strike options.…
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…
The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic…
Importance sampling is a promising variance reduction technique for Monte Carlo simulation based derivative pricing. Existing importance sampling methods are based on a parametric choice of the proposal. This article proposes an algorithm…
The aim of this paper is to provide a mathematical contribution on the semi-static hedge of timing risk associated to positions in American-style options under a multi-dimensional market model. Barrier options are considered in the paper…
We propose an innovative data-driven option pricing methodology that relies exclusively on the dataset of historical underlying asset prices. While the dataset is rooted in the objective world, option prices are commonly expressed as…
We generalize a semi-classical path integral approach originally introduced by Giachetti and Tognetti [Phys. Rev. Lett. 55, 912 (1985)] and Feynman and Kleinert [Phys. Rev. A 34, 5080 (1986)] to time-dependent Hamiltonians, thus extending…