相关论文: Calculating the Greeks by Cubature formulas
In this article we furnish a new simple proof of a hard identity from the theory of cubature formulas via the method of coefficients.
We investigate upper and lower hedging prices of multivariate contingent claims from the viewpoint of game-theoretic probability and submodularity. By considering a game between "Market" and "Investor" in discrete time, the pricing problem…
The paper contains a generalization of known properties of Chebyshev polynomials of the second kind in one variable to polynomials of $n$ variables based on the root lattices of compact simple Lie groups $G$ of any type and of rank $n$. The…
The approach that allows find European option price on the assumption of hedging at discrete times is proposed. The routine allows find the option price not for lognormal distribution functions of underlying asset only but for wide enough…
In this paper we study the pricing of exchange options under a dynamic described by stochastic correlation with random jumps. In particular, we consider a Ornstein-Uhlenbeck covariance model with Levy Background Noise Process driven by…
We construct cubature formulas on spheres supported by homothetic images of shells in some Euclidian lattices. Our analysis of these cubature formulas uses results from the theory of modular forms. Examples are worked out on the sphere of…
We study Vanna-Volga methods which are used to price first generation exotic options in the Foreign Exchange market. They are based on a rescaling of the correction to the Black-Scholes price through the so-called `probability of survival'…
We consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follows a multidimensional exponential Levy model. We carefully examine the relation between the option prices, related partial…
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and…
The pricing, hedging, optimal exercise and optimal cancellation of game or Israeli options are considered in a multi-currency model with proportional transaction costs. Efficient constructions for optimal hedging, cancellation and exercise…
Using both fractional derivatives, defined in the Riemann-Liouville and Caputo senses, and classical derivatives of the integer order we examine different numerical approaches to ordinary differential equations. Generally we formulate some…
Affine processes play an important role in mathematical finance and other applied areas due to their tractable structure. In the present article, we derive probabilistic representations and integration by parts (IBP) formulas for…
In this paper, we introduce a new generalized derivative, which we term the specular derivative. We establish the Quasi-Rolles' Theorem, the Quasi-Mean Value Theorem, and the Fundamental Theorem of Calculus in light of the specular…
The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.
The natural forms of the Leibniz rule for the $k$th derivative of a product and of Fa\`a di Bruno's formula for the $k$th derivative of a composition involve the differential operator $\partial^k/\partial x_1 ... \partial x_k$ rather than…
In the present paper we study high-order cubature formulas for the computation of advection-diffusion potentials over boxes. By using the basis functions introduced in the theory of approximate approximations, the cubature of a potential is…
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…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.
The quanto option is a cross-currency derivative in which the pay-off is given in foreign currency and then converted to domestic currency, through a constant exchange rate, used for the conversion and determined at contract inception.…
Although many methods for computing the Greeks of discrete-time Asian options are proposed, few methods to calculate the Greeks of continuous-time Asian options are known. In this paper, we develop an integration by parts formula in the…