Related papers: Calculating the Greeks by Cubature formulas
Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…
We investigate a machine learning approach to option Greeks approximation based on Gaussian process (GP) surrogates. The method takes in noisily observed option prices, fits a nonparametric input-output map and then analytically…
We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of…
In this paper we derive an effective equation for derivative pricing which accounts for the presence of virtual arbitrage opportunities and their elimination by the market. We model the arbitrage return by a stochastic process and find an…
A unified explicit form for difference formulas to approximate the fractional and classical derivatives is presented. The formula gives finite difference approximations for any classical derivatives with a desired order of accuracy at nodal…
We derive the implied volatility estimation formula in European power call options pricing, where the payoff functions are in the form of $V=(S^{\alpha}_T-K)^{+}$ and $V=(S^{\alpha}_T-K^{\alpha})^{+}$ ($\alpha>0$)respectively. Using…
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…
Option written on several foreign exchange rates (FXRs) depends on correlation between the rates. To evaluate the option, historical estimates for correlations can be used but usually they are not stable. More significantly, pricing of the…
Hedging strategies in bond markets are computed by martingale representation and the Clark-Ocone formula under the choice of a suitable of numeraire, in a model driven by the dynamics of bond prices. Applications are given to the hedging of…
Many modern numerical methods in computational science and engineering rely on derivatives of mathematical models for the phenomena under investigation. The computation of these derivatives often represents the bottleneck in terms of…
We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied…
Managing exotic derivatives requires accurate mark-to-market pricing and stable Greeks for reliable hedging. The Local Volatility (LV) model distinguishes itself from other pricing models by its ability to match observable market prices…
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…
This article provides an accessible introduction to fractional derivatives, a concept that extends classical calculus by allowing derivatives of non-integer order. It explores both the fundamental definitions and some of the most relevant…
We address the information content of European option prices about volatility in terms of the Fisher information matrix. We assume that observed option prices are centred on the theoretical price provided by Heston's model disturbed by…
We derive new formulas for the high dimensional biharmonic potential acting on Gaussians or Gaussians times special polynomials. These formulas can be used to construct accurate cubature formulas of an arbitrary high order which are fast…
In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to…
We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is…
This paper is concerned with the study of insurance related derivatives on financial markets that are based on non-tradable underlyings, but are correlated with tradable assets. We calculate exponential utility-based indifference prices,…
We describe the pricing and hedging of financial options without the use of probability using rough paths. By encoding the volatility of assets in an enhancement of the price trajectory, we give a pathwise presentation of the replication of…