This paper introduces a design of asymmetric compensation filters based on stochastic computation for auditory signal processing. Asymmetric compensation filters are used to model gammachirp filters, which well express the performance of human auditory peripheral mechanism and can be used for hearing assisting devices and noise robust speech recognition systems. Using stochastic computation, the asymmetric compensation filters are simply designed using cascaded IIR filters, thanks to a low-complexity implementation of a multiplication. However, the maximum gain of stochastic filters is limited to 1, causing undesirable filter responses. To address the issue, the proposed flexible gain adjusting (FGA) technique normalizes the gain at each IIR filter in stochastic domain while adjusting the total gain in binary domain. For hardware implementation, stochastic asymmetric compensation filters are designed using TSMC 65 nm CMOS technology and the performance is evaluated with the chip layout generated using a standard cell design flow.