Study on the Valuation Method for Overseas Oil and Gas Extraction Based on the Modified Trinomial Tree Option Pricing Model

Wandering of oil prices at lower values and the bitter reality have forced people to look for a more accurate valuation method for overseas oil and gas extraction of China. However, the currently available resource classification method, discount cash flow (DCF) method, and real option method all suffer from their own disadvantages. This paper identifies multiple uncertainty factors such as oil prices and reserves. It then investigates the transmission mechanism of how each uncertainty factor impacts the oil and gas extraction value and quantifies the transmission efficiency. The probability distribution patterns of each uncertainty factor have been determined; the trinomial tree option pricing model is modified, with consideration upon the nonstandardness of the probability distribution. Decision points and strategies space are designed in accordance with the practical oil and gas production; and the Bermuda option is adopted to replace the conventional decision-based tree model with the probability-based tree. Finally, a backward algorithm is developed to calculate the probability at each decision point, which avoids difficulties in determining the asset volatility ratio; and a case study is presented to demonstrate application of the proposed method. Results show that decision rights for overseas investment are valuable. The value of extraction does not yet necessarily grow with higher uncertainty, and instead, it is under joint effects of the cash flow and strategy space. So, valuation should incorporate the composite value of future cash flow and decision rights. Volatility of the value of extraction is not solely dependent on the oil price, but affected by multiple factors. Similar to the Bermuda option, the decision-making behavior for oil and gas extraction occurs only at finite decision points, to which the trinomial tree option pricing model is applicable. The adoption of probability distribution can to a great extent exploit the uncertain information. Replacement of the decision-based tree with the probability-based tree provides more accurate probability distribution of the calculated value of extraction, and moreover the disperse degree of the probability can reflect how high risks are, which is conducive to decision-making for investment.

Non-recombining trinomial tree pricing model and calibration for the volatility smile

In this paper, we consider the non-recombining trinomial tree pricing model under the volatility, which is a function of time, establish the option pricing model and give the convergence rates of the non-recombining trinomial tree method. In addition, we research the calibration problem of volatility and adopt an exterior penalty method to transform this problem into a nonlinear unconstrained optimization problem. For the optimization problem, we use the quasi-Newton algorithm. Finally, we test our model by numerical examples and options data on the S&P 500 index. The results show the effectiveness of the non-recombining trinomial tree pricing model.

PENENTUAN HARGA OPSI CALL WINDOW RESET MENGGUNAKAN METODE BINOMIAL TREE DAN TRINOMIAL TREE

Opsi window reset merupakan salah satu jenis opsi yang bersifat path-dependent sehingga nilai opsi tersebut tidak mempunyai rumus eksak. Oleh karena itu, dibutuhkan metode numerik untuk menentukan nilainya. Penelitian ini membahas tentang penentuan harga opsi call window reset dengan menggunakan salah satu metode numerik. Jenis metode numerik tersebut, yakni metode tree yang terdiri dari binomial tree dan trinomial tree. Jika harga saham semakin kecil dan menyentuh reset strike, harga strike akan di-reset ke harga yang baru sehingga nilai opsi pun menjadi semakin meningkat. Sebaliknya jika harga saham tidak menyentuh reset strike maka harga strike tidak akan berubah sampai masa jatuh tempo opsi. Setelah dilakukan simulasi numerik, harga opsi call window reset cenderung sama pada kedua metode tree tersebut dan harga opsi call window reset cenderung lebih tinggi dibandingkan dengan harga opsi call Eropa standar.