Related papers: Quantile hedging for basket derivatives
The risk minimizing problem $\mathbf{E}[l((H-X_T^{x,\pi})^{+})]\overset{\pi}{\longrightarrow}\min$ in the multidimensional Black-Scholes framework is studied. Specific formulas for the minimal risk function and the cost reduction function…
In the paper a problem of risk measures on a discrete-time market model with transaction costs is studied. Strategy effectiveness and shortfall risk is introduced. This paper is a generalization of quantile hedging presented in [4].
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…
The state price density of a basket, even under uncorrelated Black-Scholes dynamics, does not allow for a closed from density. (This may be rephrased as statement on the sum of lognormals and is especially annoying for such are used most…
We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a…
In this paper we propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model, based on Taylor expansions and the calculation of mixed exponential-power moments of a Gaussian distribution. Our…
A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for…
In this paper we use Bernstein and Chebyshev polynomials to approximate the price of some basket options under a bivariate Black-Scholes model. The method consists in expanding the price of a univariate related contract after conditioning…
Pricing a multi-asset derivative is an important problem in financial engineering, both theoretically and practically. Although it is suitable to numerically solve partial differential equations to calculate the prices of certain types of…
This paper studies equity basket options -- i.e., multi-dimensional derivatives whose payoffs depend on the value of a weighted sum of the underlying stocks -- and develops a new and innovative approach to ensure consistency between options…
An investor faced with a contingent claim may eliminate risk by perfect hedging, but as it is often quite expensive, he seeks partial hedging (quantile hedging or efficient hedging) that requires less capital and reduces the risk. Efficient…
With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the agent minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time,…
Quantum Stochastic Calculus can be used as a means by which randomness can be introduced to observables acting on a Hilbert space. In this article we show how the mechanisms of Quantum Stochastic Calculus can be used to extend the classical…
In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by…
We investigate the problem of pricing and hedging derivatives of Electricity Futures contract when the underlying asset is not available. We propose to use a cross hedging strategy based on the Futures contract covering the larger delivery…
The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a…
We present closed analytical approximations for the pricing of basket options, also applicable to Asian options with discrete averaging under the Black-Scholes model with time-dependent parameters. The formulae are obtained by using a…
The paper introduces and studies hedging for game (Israeli) style extension of swing options considered as multiple exercise derivatives. Assuming that the underlying security can be traded without restrictions we derive a formula for…
The pricing of derivatives tied to baskets of assets demands a sophisticated framework that aligns with the available market information to capture the intricate non-linear dependency structure among the assets. We describe the dynamics of…
We propose a hybrid quantum-classical algorithm, originated from quantum chemistry, to price European and Asian options in the Black-Scholes model. Our approach is based on the equivalence between the pricing partial differential equation…