Control of Brokerage Margins * * This work was supported in part by Directa Sim, a leading Italian online brokerage company. The access to financial data provided by Directa Sim is also gratefully acknowledged.

摘要

In this paper we analyze financial risk from the point of view of a brokerage company, who exposes itself to risk by lending assets or money to its clients for allowing short-selling or leveraged operations (firm-wise risk). We develop analytical models for control of firm-wise risk, by defining both specific margin factors for single assets and a global margin factor that takes into account the overall riskiness of a complex portfolio. In the first part of this work we derive a model to evaluate leverage factors, by linking them with the probability for the client’s portfolio value to go below a certain safety threshold, using Value-at-Risk and Expected Shortfall approaches. Further, we present optimization models based on these two approaches in order to determine the optimal leverage factors. In the second part, we present a model for margin control based on the concept of marginal availability. A global margin factor considering the overall riskiness of a complex portfolio is derived, and we show the effectiveness of the approach also when dealing with portfolios containing options.