Pricing Exotic Options Using Some Lattice Procedures

In this work, we discuss some very simple and extremely efficient lattice models, namely, Binomial tree model (BTM) and Trinomial tree model (TTM) for valuing some types of exotic barrier options in details. For both these models, we consider the concept of random walks in the simulation of the path which is followed by the underlying stock price. Our main objective is to estimate the value of barrier options by using BTM and TTM for different time steps and compare these with the exact values obtained by the benchmark Black-Scholes model (BSM). Moreover, we analyze the convergence of these lattice models for these exotic options. All the results have been shown numerically as well as graphically. GANITJ. Bangladesh Math. Soc.41.1 (2021) 26-40

Prediksi Harga Saham Perusahaan Operator Telekomunikasi Selular pada Masa Pandemi Menggunakan Metode Binomial

The corona virus causes all activities to be carried out online so that all activities require Internet access which makes mobile telecommunications operator companies one of the promising investments in this pandemic. Stock investing allows investors to get profits in a relatively short time. Investments in stocks are currently unstable, as the whole world has been in difficult times since the coronavirus. Capital market players can feel the loss, which causes share prices to tend to decline. The impact of the corona virus is to paralyze all areas, especially the economy, so that an investor must be able to predict an increase or decrease in stock prices. The binomial method helps investors to predict the possibility of a stock price that will occur and is clarified by using a binomial tree that can be predicted in the form of stock prices by having the possibility of four predictions, two predictions describing an increase in shares and two other predictions describing the possibility of a falling stock price. Abstrak. Virus korona menyebabkan semua kegiatan dilakukan melalui daring (online) sehingga semua kegiatan memerlukan akses Internet yang membuat perusahaan operator telekomunikasi seluler menjadi salah satu investasi yang menjanjikan dimasa pandemi ini Investasi ialah komitmen menempatkan sejumlah dana dalam waktu yang cukup lama untuk memperoleh keuntungan di masa datang. Investasi saham memungkinkan investor mendapatkan keuntungan dalam waktu yang relatif singkat. Investasi dalam bentuk saham pada saat ini tidaklah stabil, karena seluruh dunia dalam masa sulit semenjak adanya virus korona. Kerugianpun dapat dirasakan oleh pelaku pasar modal yang menyebabkan harga saham cenderung menurun. Dampak virus korona adalah melumpuhkan segala bidang terutama perekonomian sehingga sebagai seorang investor harus bisa memprediksi peningkatan atau penurunan harga saham. Metode binomial membantu investor untuk memprediksi kemungkinan harga saham yang akan terjadi dan diperjelas dengan menggunakan pohon binomial hasil prediksi yang di dapat berupa harga saham dengan memiliki kemungkinan empat prediksi dua prediksi menggambarkan kenaikan saham dan dua prediksi lain menggambarkan kemungkinan harga saham turun.

Binomial tree method for option pricing: Discrete Carr and Madan formula approach

This paper suggests a new Fourier analysis approach to evaluate the option prices and its sensitivities (Greeks) using the binomial tree model. In the last half of this paper, we show that option prices are efficiently and effectively evaluated using a semi-closed form formula for European option prices. We can compute option prices in a broad class of jump-diffusion models because we calculate the characteristic function for an underlying asset price numerically. Furthermore, we also compute the price of European options in the exp-Levy model. This numerical experiment gives new insights into option pricing in the nonparametric Levy model. The option prices and sensitivities can be computed very accurately and efficiently, even in binomial tree models with jumps.

Joshi’s Split Tree for Option Pricing

In a thorough study of binomial trees, Joshi introduced the split tree as a two-phase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American put options. Here we introduce a “flexible” version of Joshi’s tree, and develop the corresponding convergence theory in the European case: we find a closed form formula for the coefficients of 1/n and 1/n3/2 in the expansion of the error. Then we define several optimized versions of the tree, and find closed form formulae for the parameters of these optimal variants. In a numerical study, we found that in the American case, an optimized variant of the tree significantly improved the performance of Joshi’s original split tree.

An Adaptive Neuro-Based Fuzzy Inference System (ANFIS) for the Prediction of Option Price

Option price prediction has been an important issue in the finance literature within recent years. Affected by numerous factors, option price forecasting remains a challenging problem. In this study, a novel hybrid model for forecasting option price consisting of parametric and non-parametric methods is presented. This method is composed of three stages. First, the conventional option pricing methods such as Binomial Tree, Monte Carlo, and Finite Difference are used to primarily calculate the option prices. Next, the author employs an Adaptive Neuro-Fuzzy Inference System (ANFIS) in which the parameters are trained with particle swarm optimization to minimize the prediction errors associated with parametric methods. To select the best input data for the ANFIS structure, which has high mutual information associated with the future option price, the proposed method uses an entropy approach. Experimental examples with data from the Australian options market demonstrate the effectivity of the proposed hybrid model in enhancing the prediction accuracy compared to another method.