Insurance Premium Formulation for Agricultural Commodity Prices
Abstract
This research develops the appropriate formula to determine insurance premiums on agricultural commodity prices that provide coverage to policyholders for losses caused by falling prices. The price component is assumed to follow the Brownian Geometric motion in determining the insurance premiums for agricultural commodity prices. So, through the Ito process, a target price can be selected and is used as a reference to determine whether a claim can be made or not at harvest time. The approach of the Black-Scholes model is used to construct an appropriate model to determine insurance premiums of agricultural commodity prices due to a decrease in prices from the expected price. A simulation study is carried out using daily price data for red chili commodities in the Jambi province in 2020 with several assumptions made based on literature studies and farmers’ common habits in Jambi. The simulation results indicate that the average return is -0.001069649, and the standard deviation is 0.07297269. Thus, the expected estimated value of the profit rate is -0.001069649, and the estimated volatility value is 0.07297269. Furthermore, using the target price value, the red chili price insurance premium for a one-planting period with an area of one hectare is Rp. 1,527,088.
Keywords: agriculture insurance; Black-Scholes model; European option; Ito process.
Abstrak
Penelitian ini mengembangkan formula yang sesuai untuk menetapkan harga premi asuransi harga komoditas hasil pertanian yang memberikan pertanggungan kepada nasabah atas kerugian yang disebabkan oleh turunnya harga. Dalam menentukan premi asuransi harga komoditas hasil pertanian, komponen harga diasumsikan bergerak mengikuti Gerak Brownian Geometrik. Sehingga melalui proses Ito dapat ditentukan target harga yang akan dijadikan acuan untuk menentukan klaim atau tidaknya nasabah pada saat panen. Pendekatan model Black-Scholes digunakan untuk mengkonstruksi model yang sesuai untuk menentukan premi asuransi harga komoditas hasil pertanian yang disebabkan karena turunnya harga komoditas dari harga yang diharapkan. Simulasi dilakukan menggunakan data harga harian komoditas cabe merah di Provinsi Jambi tahun 2020 dengan beberapa asumsi yang dibangun berdasarkan kajian literatur dan kebiasaan umum petani di Provinsi Jambi. Hasil simulasi menunjukkan bahwa rata-rata return adalah -0,001069649 dan standar deviasi 0,07297269. Sehingga diperoleh nilai estimasi tingkat keuntungan yang diinginkan sebesar -0,001069649, dan nilai estimasi volatilitas sebesar 0,07297269 . Selanjutnya, menggunakan nilai target harga diperoleh premi asuransi harga cabe merah untuk 1 periode tanam dengan luas lahan 1 hektar sebesar Rp. 1.527.088.
Kata Kunci: asuransi pertanian; model Black-Scholes; opsi eropa; proses Ito.
2020MSC: 62P05
Keywords
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DOI: 10.15408/inprime.v4i2.26238
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