A New Computational Scheme for Computing Greeks by the Asymptotic Expansion Approach
نویسندگان
چکیده
We developed a new scheme for computing ”Greeks” of derivatives by an asymptotic expansion approach. In particular, we derived analytical approximation formulae for Deltas and Vegas of plain vanilla and average European call options under general Markovian processes of underlying asset prices. Moreover, we introduced a new variance reduction method of Monte Carlo simulations based on the asymptotic expansion scheme. Finally, several numerical examples under CEV processes confirmed the validity of our method.
منابع مشابه
Numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type
In this paper, we have proposed a numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided in...
متن کاملA Deterministic Multiple Key Space Scheme for Wireless Sensor Networks via Combinatorial Designs
The establishing of a pairwise key between two nodes for encryption in a wireless sensor network is a challenging issue. To do this, we propose a new deterministic key pre-distribution scheme which has modified the multiple key space scheme (MKSS). In the MKSS, the authors define two random parameters to make better resilience than existing schemes. Instead of a random selection of these parame...
متن کاملAsymptotic algorithm for computing the sample variance of interval data
The problem of the sample variance computation for epistemic inter-val-valued data is, in general, NP-hard. Therefore, known efficient algorithms for computing variance require strong restrictions on admissible intervals like the no-subset property or heavy limitations on the number of possible intersections between intervals. A new asymptotic algorithm for computing the upper bound of the samp...
متن کاملSESOS: A Verifiable Searchable Outsourcing Scheme for Ordered Structured Data in Cloud Computing
While cloud computing is growing at a remarkable speed, privacy issues are far from being solved. One way to diminish privacy concerns is to store data on the cloud in encrypted form. However, encryption often hinders useful computation cloud services. A theoretical approach is to employ the so-called fully homomorphic encryption, yet the overhead is so high that it is not considered a viable s...
متن کاملA Hybrid Asymptotic Expansion Scheme: an Application to Long-term Currency Options
This paper develops a general approximation scheme, henceforth called a hybrid asymptotic expansion scheme for valuation of multi-factor European path-independent derivatives. Specifically, we apply it to pricing long-term currency options under a market model of interest rates and a general diffusion stochastic volatility model with jumps of spot exchange rates. Our scheme is very effective fo...
متن کامل