ACTA UNIVERSITATIS APULENSIS No 19/2009 A COMBINED MONTE CARLO AND QUASI-MONTE CARLO METHOD WITH APPLICATIONS TO OPTION PRICING
نویسنده
چکیده
In this paper, we apply a combined Monte Carlo and Quasi-Monte Carlo method, which we proposed in an earlier paper [32], to the evaluation of an European Call option and of an Asian Call option. We assume that the stock price of the underlying asset S = S(t) is driven by a Lévy process Z(t), with independent increments distributed according to a NIG distribution. We compare our method with the Monte Carlo and Quasi-Monte Carlo methods. The numerical results indicate that our method provides significant error reduction over these methods. 2000 Mathematics Subject Classification: 11K36, 11K38, 11K45, 62P05, 65C05, 91B24, 91B28.
منابع مشابه
ACTA UNIVERSITATIS APULENSIS No 16/2008 RISK MANAGEMENT USING VAR SIMULATION WITH APPLICATIONS TO BUCHAREST STOCK EXCHANGE
In a recent paper, we have proposed and analyzed, from a theoretical point of view, a multidimensional stock market model (see [?]). In this paper, we construct a portfolio of stocks for a particular case of this market model. We introduce the Value at Risk, as a powerful tool for managing risks, which follow from holding such a portfolio. We present a mathematical calculation of Value at Risk ...
متن کاملACTA UNIVERSITATIS APULENSIS No 14/2007 A MIXED MONTE CARLO AND QUASI-MONTE CARLO SEQUENCE FOR MULTIDIMENSIONAL INTEGRAL ESTIMATION
In this paper, we propose a method for estimating an sdimensional integral I. We define a new hybrid sequence that we call the H-mixed sequence. We obtain a probabilistic bound for the H-discrepancy of this sequence. We define a new estimator for a multidimensional integral using the H-mixed sequence. We prove a central limit theorem for this estimator. We show that by using our estimator, we o...
متن کاملACTA UNIVERSITATIS APULENSIS No 18/2009 ON G-DISCREPANCY AND MIXED MONTE CARLO AND QUASI-MONTE CARLO SEQUENCES
The G-star and the G-discrepancy are generalizations of the well known star and the extreme discrepancy; thereby G denotes a given continuous distribution function on the d-dimensional unit cube [0, 1]. We list and prove some results that describe the behavior of the G-star and the Gdiscrepancy in terms of the dimension d and the number of sample points N . Our main focus is on so-called mixed ...
متن کاملApplications of Monte Carlo/Quasi-Monte Carlo Methods in Finance: Option Pricing
The pricing of options is a very important problem encountered in nancial markets today. The famous Black-Scholes model provides explicit closed form solutions for the values of certain (European style) call and put options. But for many other options, either there are no closed form solutions, or if such closed form solutions exist, the formulas exhibiting them are complicated and diicult to e...
متن کاملComparisons of alternative quasi-Monte Carlo sequences for American option pricing
Quasi-Monte Carlo sequences have been shown to provide accurate option price approximations for a variety of options. In this paper, we apply quasi-Monte Carlo sequences in a duality approach to value American options. We compare the results using different low discrepancy sequences and estimate error bounds and computational effort. The results demonstrate the value of sequences using expansio...
متن کامل