Abstarct: This thesis aims to price call options with Islamic treasury bills as underlying assets and baxsed on the Heath-Jarrow-Merton model replace the Levy process with the Brownian process. For this purpose, the data of three cases of Islamic treasury bills have been used and option pricing of transactions whose basic assets are treasury bills has been done. Three methods of fast Fourier transformation, fractional Fourier transformation, and cosine transformation have been used for this pricing. Studies show that the cosine transform method performs poorly in short-term maturities. To set the price, the default options are applied and the obtained results are shown in the diagram.