MENENTUKAN HARGA OPSI DENGAN METODE MONTE CARLO BERSYARAT MENGGUNAKAN BARISAN KUASI ACAK FAURE

An option contract is a contract that gives the owner the right to sell or even to buy an asset at the predetermined price and period time. The conditional Monte Carlo is one of the several methods that is used to determine the option price which in the process uses random numbers with normal standard distribution. At the same time, the random number generator can be substituted by using a quasi-random sequence, as in Faure's quasi-random sequence. The aim of this study is to determine the contract price of the call option with the European type by applying the conditional Monte Carlo method. This method used the Faure quasi-random sequence and compared it with the method of Monte Carlo standard, Monte Carlo standard in using the quasi-random sequence of Faure, and conditional Monte Carlo. The results of this study showed that the call option calculated using the conditional Monte Carlo method using the quasi-random Faure sequence began to stabilize at the 5000th simulation for K = 32575 and K = 34725 and in the 10000th simulation for K = 33000 and K = 33950. Research also show that with the conditional Monte Carlo in using the quasi-random sequence of Faure is more stable. Therefore, it is obtained its real value faster than the Monte Carlo standard, Monte Carlo standard in using the quasi-random sequence of Faure, and conditional Monte Carlo. The MAPE value of conditional Monte Carlo in using the quasi-random sequences of Faure and the Monte Carlo standard is smaller than the Monte Carlo standard in using the quasi-random sequence of Faure, and conditional Monte Carlo. Therefore, it can be said to be more accurate when calculating the European type call option price at BBCA.JK stocks.

CONDITIONAL MONTE CARLO SCHEME FOR STABLE GREEKS OF WORST-OF AUTOCALLABLE NOTES

It is well known that the application of Monte Carlo method in pricing of products with early termination feature results in a high Monte Carlo error and unstable greeks; see Fries & Joshi (2011). We develop a Monte Carlo scheme that utilizes a special structure of worst-of autocallable notes and produces stable greeks. This scheme clearly demonstrates the variance reduction in Monte Carlo scheme and can be used in pricing of multi-asset worst-of autocallable notes with any number of underlying assets. We suggest an algorithm and analyze its performance for an autocallable note on four assets. The suggested algorithm allows one to calculate stable greeks (delta, gamma, vega and others) and substantially reduce the computational effort to achieve the desired accuracy in comparison to standard Monte Carlo algorithm.

Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities

Pricing multi-asset options has always been one of the key problems in financial engineering because of their high dimensionality and the low convergence rates of pricing algorithms. This paper studies a method to accelerate Monte Carlo (MC) simulations for pricing multi-asset options with stochastic volatilities. First, a conditional Monte Carlo (CMC) pricing formula is constructed to reduce the dimension and variance of the MC simulation. Then, an efficient martingale control variate (CV), based on the martingale representation theorem, is designed by selecting volatility parameters in the approximated option price for further variance reduction. Numerical tests illustrated the sensitivity of the CMC method to correlation coefficients and the effectiveness and robustness of our martingale CV method. The idea in this paper is also applicable for the valuation of other derivatives with stochastic volatility.