European and Asian Greeks for Exponential Lévy Processes

نویسندگان

چکیده

In this paper we give easy-to-implement closed-form expressions for European and Asian Greeks general L2-payoff functions underlying assets in an exponential L\'evy process model with nonvanishing Brownian motion part. The results are based on Hilbert space valued Malliavin Calculus extend previous from the literature. Numerical experiments suggest, that case of a continuous payoff function, combination Monte Carlo finite difference method has better convergence behavior, whereas discontinuous functions, clearly is superior compared to approach, first- second order Greeks. Reduction arguments literature measure change imply also hold true generalized options particular fixed floating strike options.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Efficient Pricing of European-Style Asian Options under Exponential Lévy Processes Based on Fourier Cosine Expansions

We propose an efficient pricing method for arithmetic and geometric Asian options under exponential Lévy processes based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European-style and American-style Asian options and for discretely and continuously monitored versions. In the present paper we focus on the European-style Asian options. The...

متن کامل

Optimal portfolios for exponential Lévy processes

We consider the problem of maximizing the expected utility from consumption or terminal wealth in a market where logarithmic securities prices follow a Lévy process. More specifically, we give explicit solutions for power, logarithmic and exponential utility in terms of the Lévy-Chinchine triplet. In the first two cases, a constant fraction of current wealth should be invested in each of the se...

متن کامل

Asian options and meromorphic Lévy processes

One method to compute the price of an arithmetic Asian option in a Lévy driven model is based on the exponential functional of the underlying Lévy process: If we know the distribution of the exponential functional, we can calculate the price of the Asian option via the inverse Laplace transform. In this paper we consider pricing Asian options in a model driven by a general meromorphic Lévy proc...

متن کامل

Minimal F Q - Martingale Measures for Exponential Lévy Processes

Let L be a multidimensional Lévy process under P in its own filtration. The f-minimal martingale measure Qq is defined as that equivalent local martingale measure for E(L) which minimizes the f-divergence E [ (dQ/dP ) ] for fixed q ∈ (−∞, 0) ∪ (1,∞). We give necessary and sufficient conditions for the existence of Qq and an explicit formula for its density. For q = 2, we relate the sufficient c...

متن کامل

Distributional properties of exponential functionals of Lévy processes ∗

We study the distribution of the exponential functional I(ξ, η) = ∫∞ 0 exp(ξt−)dηt, where ξ and η are independent Lévy processes. In the general setting, using the theory of Markov processes and Schwartz distributions, we prove that the law of this exponential functional satisfies an integral equation, which generalizes Proposition 2.1 in [9]. In the special case when η is a Brownian motion wit...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Methodology and Computing in Applied Probability

سال: 2023

ISSN: ['1387-5841', '1573-7713']

DOI: https://doi.org/10.1007/s11009-023-10014-5