Related papers: Calculating the Greeks by Cubature formulas
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
Expectiles are statistical parameters which also provide a class of sublinear risk measures in finance. They are solutions of continuous optimization problems. The corresponding first order condition provides two different fixed point…
In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…
The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their…
This paper investigates the pricing of financial derivatives and the calculation of their delta Greek when the underlying asset is a jump-diffusion process in which the stochastic intensity component follows the CIR process. Utilizing…
The pricing of options, warrants and other derivative securities is one of the great success of financial economics. These financial products can be modeled and simulated using quantum mechanical instruments based on a Hamiltonian…
There is a vast literature on numerical valuation of exotic options using Monte Carlo, binomial and trinomial trees, and finite difference methods. When transition density of the underlying asset or its moments are known in closed form, it…
In financial mathematics, the calculation of the Greeks, especially the delta, is emphasized due to its role in risk management. In this article, we employ Malliavin calculus to determine the delta of European and Asian options, where the…
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique…
In this paper we provide a valuation formula for different classes of actuarial and financial contracts which depend on a general loss process, by using the Malliavin calculus. In analogy with the celebrated Black-Scholes formula, we aim at…
We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra process dynamics. Such a price dynamics is particularly relevant in energy markets, modelling for example the spot price of…
We develop a model for indifference pricing in derivatives markets where price quotes have bid-ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investor's beliefs, risk…
We investigate the problem of pricing derivatives under a fractional stochastic volatility model. We obtain an approximate expression of the derivative price where the stochastic volatility can be composed of deterministic functions of time…
In previous works Avellaneda et al. pioneered the pricing and hedging of index options - products highly sensitive to implied volatility and correlation assumptions - with large deviations methods, assuming local volatility dynamics for all…
Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative…
Continuous time models in the theory of real options give explicit formulas for optimal exercise strategies when options are simple and the price of an underlying asset follows a geometric Brownian motion. This paper suggests a general,…
Main results and techniques of the fractional calculus of variations are surveyed. We consider variational problems containing Caputo derivatives and study them using both indirect and direct methods. In particular, we provide necessary…
In this paper, it is shown that Bermudan option pricing based on either the r\'eduite (in a one-dimensional setting: piecewise harmonic interpolation) or cubature -- is sensible from an economic vantage point: Any sequence of thus-computed…
In a market with transaction costs, the price of a derivative can be expressed in terms of (preconsistent) price systems (after Kusuoka (1995)). In this paper, we consider a market with binomial model for stock price and discuss how to…
In a rather general setting of multivariate stochastic volatility market models we derive global iterative probabilistic schemes for computing the free boundary and its Greeks for a generic class of American derivative models using…