Showing 1 - 10 of 24
Given a geometric Brownian motion S=(St)t[set membership, variant][0,T] and a Borel measurable function such that g(ST)[set membership, variant]L2, we approximate bywhere 0=[tau]0[less-than-or-equals, slant]...[less-than-or-equals, slant][tau]n=T is an increasing sequence of stopping times and...
Persistent link: https://www.econbiz.de/10008874256
This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in...
Persistent link: https://www.econbiz.de/10008622232
This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in...
Persistent link: https://www.econbiz.de/10008790635
In a complete market with a constant interest rate and a risky asset, which is a linear diffusion process, we are interested in the discrete time hedging of a European vanilla option with payoff function f. As regards the perfect continuous hedging, this discrete time strategy induces, for the...
Persistent link: https://www.econbiz.de/10005390703
We give a broad overview of approximation methods to derive analytical formulas for accurate and quick evaluation of option prices. We compare different approaches, from the theoretical point of view regarding the tools they require, and also from the numerical point of view regarding their...
Persistent link: https://www.econbiz.de/10010898714
For general time-dependent local volatility models, we propose new approximation formulas for the price of call options. This extends previous results of [BGM10b] where stochastic expansions combined with Malliavin calculus were performed to obtain approximation formulas based on the local...
Persistent link: https://www.econbiz.de/10010898787
In the context of an asset paying affine-type discrete dividends, we present closed analytical approximations for the pricing of European vanilla options in the Black-Scholes model with time-dependent parameters. They are obtained using a stochastic Taylor expansion around a shifted lognormal...
Persistent link: https://www.econbiz.de/10010899076
A wide class of hybrid products are evaluated with a model where one of the underlying price follows a local volatility diffusion and the other asset value a log-normal process. Because of the generality for the local volatility function, the numerical pricing is usually much time consuming....
Persistent link: https://www.econbiz.de/10010883196
We study the problem of estimating the coefficients of a diffusion (Xl, t 2:: 0); the estimation is based on discrete data Xn . . n = 0, 1, ... ,N. The sampling frequency delta t is constant , and asymptotics arc taken at the number of observations tends to infinity. We prove that the problem of...
Persistent link: https://www.econbiz.de/10010983786
In the context of an asset paying affine-type discrete dividends, we present closed analytical approximations for the pricing of European vanilla options in the Black--Scholes model with time-dependent parameters. They are obtained using a stochastic Taylor expansion around a shifted lognormal...
Persistent link: https://www.econbiz.de/10010973374