اختیار فروش آمریکایی تصادفی - بی ثباتی تعهدات خط اعتباری بانک ها :: ارزش گذاری و الزامات سیاستگذاری

This paper investigates commitment credit risk and valuation in connection with their risk-adjusted balance used in computing the bank's capital requirement mandated by the Bank for International Settlements (BIS). In a two-factor model of the marked-to-market value of the credit line (CL), x, and its mean-reverting volatility, V, the value of the American commitment put is obtained as the sum of a Fourier-based solution for the European put and a quadratic approximation for the early-exercise premium. Once computed, the put value is combined with the line fees and a conditional exercise-cum-takedown proportion to determine the commitment net value and the bank's exposure to commitment credit risk. A comparison between the stochastic and constant volatility option models reveals that correlation rather than stochastic volatility forms the greater source of bias: the impact of the correlation-generated skewness on the distribution of the CL marked-to-market value is more significant than that of the σ-generated kurtosis. The random-volatility model is next used to ascertain how commitment credit risk affects banks' capital requirement. According to the BIS accounting-based procedure, the risk-adjusted balance of short-term commitments is nil; this is not the case when the same risk-adjusted balance is computed by way of the option-based procedure. Beyond capital sufficiency, the approach also determines the impact of commitment credit risk on the bank's future profits.