document: Valuing corporate debt : the effect of cross-holdings of stock and debt We have developed a simple approach to valuing risky corporate debt when corporations own securities issued by other corporations . We assume that corporate debt can be valued as an option on corporate business asset value , and derive payoff functions when there exist cross-holdings of stock or debt between two firms . Next we show that payoff functions with multiple cross-holdings can be solved by the contraction principle . The payoff functions which we derive provide a number of insights about the risk structure of company cross-holdings . First , the Modigliani-Miller theorem can obtain when there exist cross-holdings between firms . Second , by establishing cross-shareholdings each of stock holders distributes a part of its payoff values to the bond holder of the other 's firm , so that both firms can decrease credit risks by cross-shareholdings . In the numerical examples , we show that the correlation in firms can be a critical condition for reducing credit risk by cross-holdings of stock using Monte Carlo simulation . Moreover , we show we can calculate the default spread easily when complicated cross-holdings exist , and find which shares are beneficial or disadvantageous
doc_bio_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O B I I I O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: securities option corporate business asset value payoff functions bond holder credit risks correlation monte carlo simulation
abstractive_keyphrases: risky corporate debt valuation stock holdings debt holdings multiple cross-holdings modigliani-miller theorem cross-shareholdings