• Considertwo-datebinomialmodel.companyhasbothdebtandequityinitscapitalstructure.Thevalueofthecompanyis100atDate0.Date1,itisequallylikethatthevalueofthecompanyincreasesby20%ordecreasesby10%.Thetotalpromisedamounttothedebtholdersis100atDate1.Theriskfreeinterestrate,10%.
• 1.Whatarethepossiblepayoffstotheequityholdersatdate1?Whatkindoffinancialproducthasthesamepayoffs?Pleasedescribethedetailedcharacteristicsofthefinancialproduct.
• 2.Whatarethepossiblepayoffstothebondholdersatdate1?Aretheyriskfree?Whatkindoffinancialproduct/portfoliohasthesamepayoffs?Pleasedescribethedetailedcharacteristicsofthefinancialproduct/portfolio.
• 3.WhatisthevalueofthedebtatDate0?WhatisthevalueoftheequityatDate0?
• 4.Supposethegovernmentannouncesthatitguaranteesthecompanyspaymenttothedebtholders.Howmuchisthegovernmentguaranteeworth?
• 5.Now we extend the model to a three-date setting. At both Date 1 and Date 2, it is equally likely that the value of the company increases by 20% or decreases by 10%, as depicted in the graph below. Suppose there is an American put option written on the entire firm with strike price 100. What is the value of this American put at Date 0?