Multi-Asset Barrier Options Pricing by Collocation BEM (with Matlab® Code)

In this paper, we extend the SABO technique (Semi-Analytical method for Barrier Options), based on collocation Boundary Element Method (BEM), to the pricing of Barrier Options with payoff dependent on more than one asset. The efficiency and accuracy already revealed in the case of a single asset is confirmed by the presented numerical results.

Metode Enhanced Trinomial Pada Aproksimasi Numerik Pada Barrier Options Pricing

Barrier options pricing sering digunakan dalam jual beli saham karena memiliki harga yang lebih murah dari harga saham plain vanilla option. Dengan menggunakan metode trinomial, didapatkan tiga kemungkinan nilai pergerakan saham yaitu nilai saham naik, turun, dan tetap. Nilai parameter-parameter dari metode trinomial diperoleh dengan menentukan nilai peluang tetapnya . Selanjutnya dicari nilai peluang naik dan turunnya dengan menyamakan ekspektasi diskrit dengan kontinu dan menyamakan variansi diskrit dengan kontinu.Metode enhanced trinomial merupakan metode trinomial yang nilai sahamnya didekati menggunakan nilai upper dan lower barrier dengan rumus enhanced numerical. Sehingga didapatkan nilai opsi saham yang lebih kecil daripada metode trinomial standar. Oleh karena itu, dengan metode enhanced trinomial nilai opsi saham yang lebih cepat konvergen. hal ini dibuktikan dari simulasi yang telah dilakukan dalam penelitian ini

Detecting Jump Risk and Jump-Diffusion Model for Bitcoin Options Pricing and Hedging

In this paper, we conduct a fast calibration in the jump-diffusion model to capture the Bitcoin price dynamics, as well as the behavior of some components affecting the price itself, such as the risk of pitfalls and its ambiguous effect on the evolution of Bitcoin’s price. In addition, in our study of the Bitcoin option pricing, we find that the inclusion of jumps in returns and volatilities are significant in the historical time series of Bitcoin prices. The benefits of incorporating these jumps flow over into option pricing, as well as adequately capture the volatility smile in option prices. To the best of our knowledge, this is the first work to analyze the phenomenon of price jump risk and to interpret Bitcoin option valuation as “exceptionally ambiguous”. Crucially, using hedging options for the Bitcoin market, we also prove some important properties: Bitcoin options follow a convex, but not strictly convex function. This property provides adequate risk assessment for convex risk measure.

Critical Value-Based Power Options Pricing Problems in Uncertain Financial Markets

Compared with investing an ordinary options, investing the power options may possibly yield greater returns. On the one hand, the power option is the best choice for those who want to maximize the leverage of the underlying market movements. On the other hand, power options can also prevent the financial market changes caused by the sharp fluctuations of the underlying assets. In this paper, we investigate the power option pricing problem in which the price of the underlying asset follows the Ornstein–Uhlenbeck type of model involving an uncertain fractional differential equation. Based on critical value criterion, the pricing formulas of European power options are derived. Finally, some numerical experiments are performed to illustrate the results.