Sains Malaysiana 53(9)(2024): 3197-3213

http://doi.org/10.17576/jsm-2024-5309-23

Credible Delta Gamma (Theta) Normal Value at Risk for Assessing European Call Option Risk

(Nilai Normal Delta-Gamma (Theta) Berisiko Boleh Percaya untuk Menilai Risiko Pilihan Panggilan Eropah)

EVY SULISTIANINGSIH¹, DEDI ROSADI^2,* & MAHARANI ABU BAKAR³

¹Department of Mathematics, Universitas Tanjungpura. Jl. Prof. Dr. H. Hadari Nawawi, Pontianak, 78124 Indonesia 

²Department of Mathematics, Universitas Gadjah Mada, Yogyakarta 55281, Indonesia

³Department of Applied Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia

Received: 19 November 2023/Accepted: 9 July 2024

Abstract

The current research introduces a novel risk metric called credible delta-gamma (theta)-normal Value-at-Risk (CredDGTN VaR) for the purpose of the option risk assessment. CredDGTN VaR represents an extension of the credible Value-at-Risk (CredVaR) framework, whereby risk assessment is conducted through the integration of CredVaR with delta-gamma(theta)-normal VaR. The present study introduces a novel approach that is deemed suitable for evaluating the risk of a portfolio of European call options. The proposed method takes into account the nonlinear interdependence of the market risk factors determining the value of a European call option, according to the Formula of Black-Scholes. The present methodology is employed to assess simulated financial data that portrays the return of multiple assets throughout ten investment periods. The novel approach is additionally employed to assess the level of risk associated with a portfolio comprised of actively traded stock options. According to Kupiec's backtesting, CredDGTN's efficacy in gauging the risk of an option portfolio is noteworthy, as it accurately measures the risk at 80%, 90%, and 95% confidence levels, even in cases where the profit/loss (P/L) exhibits non-normal distribution. Furthermore, the performance of CredDGTN VaR empirically outperforms credible delta-normal VaR (CredDN VaR) and credible delta-gamma-normal VaR (CredDGN VaR) in similar cases. Moreover, CredDN VaR, CredDGN VaR, and CredDGTN VaR will provide equal VaR when delta and gamma are zero.

Keywords: Greek; mixed-assets; portfolio

Abstrak

Penyelidikan ini memperkenalkan metriks risiko baharu yang dipanggil nilai normal delta-gamma (theta) berisiko boleh percaya (CredDGTN VaR) untuk tujuan penilaian risiko pilihan. CredDGTN VaR mewakili lanjutan daripada rangka kerja Nilai Berisiko (CredVaR) boleh percaya yang mana penilaian risiko dijalankan melalui penyepaduan CredVaR dengan delta-gamma(theta)-normal VaR. Kajian ini memperkenalkan pendekatan baharu yang dianggap sesuai untuk menilai risiko portfolio pilihan panggilan Eropah. Kaedah yang dicadangkan mengambil kira kebergantungan tidak linear faktor risiko pasaran yang menentukan nilai pilihan panggilan Eropah, menurut Formula Black-Scholes. Metodologi sedia ada digunakan untuk menilai simulasi data kewangan yang menggambarkan pulangan berbilang aset sepanjang sepuluh tempoh pelaburan. Pendekatan baharu ini digunakan untuk menilai tahap risiko yang berkaitan dengan portfolio yang terdiri daripada pilihan saham yang didagangkan secara aktif. Menurut pengiraan ke belakang Kupiec, keberkesanan CredDGTN dalam mengukur risiko portfolio pilihan patut diberi perhatian, kerana ia mengukur risiko dengan tepat pada tahap keyakinan 80%, 90% dan 95%, walaupun dalam kes keuntungan/kerugian (P/L) menunjukkan taburan bukan normal. Tambahan pula, prestasi CredDGTN VaR secara empirik mengatasi VaR delta-normal boleh percaya (CredDN VaR) dan VaR delta-gamma-normal boleh percaya (CredDGN VaR) dalam kes yang serupa. Selain itu, CredDN VaR, CredDGN VaR dan CredDGTN VaR akan memberikan VaR yang sama apabila delta dan gamma adalah sifar.

Kata kunci: Aset gabungan; Greek; portfolio

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*Corresponding author; email: dedirosadi@gadjahmada.edu