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Margin system for margin loans using cash and stock as collateral isconsidered in this paper, which is the line of defence for brokers against riskassociated with margin trading. The conditional probability of negative returnis used as risk measure, and a recursive algorithm is proposed to realize thismeasure under a Markov chain model. Optimal margin system is chosen from thosesystems which satisfy the constraint of the risk measure. The resulted marginsystem is able to adjust actively with respect to the changes of stock prices.The margin system required by the Shanghai Stock Exchange is compared with theproposed system, where 25,200 margin loans of 126 stocks listed on the SSE areinvestigated. It is found that the number of margin calls under the proposedmargin system is significantly less than its counterpart under the requiredsystem for the same level of risk, and the average costs of the loans aresimilar under the two types of margin systems.

Active margin system for margin loans using cash and stock as collateral and its application in Chinese market