Pricing vulnerable European options with stochastic default barriers

CF Lo and KC Ku Institute of Theoretical Physics and Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China Email: cho-hoi_hui{at}hkma.gov.hk Received on 31 July 2006. Accepted on 15 March 2007. This paper develops a valuation model of European options incorporatinga stochastic default barrier, which extends a constant defaultbarrier proposed in the Hull–White model. The defaultbarrier is considered as an option writer's liability. Closed-formsolutions of vulnerable European option values based on themodel are derived to study the impact of the stochastic defaultbarriers on option values. The numerical results show that negativecorrelation between the firm values and the stochastic defaultbarriers of option writers gives material reductions in optionvalues where the options are written by firms with leverageratios corresponding to BBB or BB ratings.     

Galactose-derived phosphonate analogues as potential inhibitors of phosphatidylinositol biosynthesis in mycobacteria

Galactose-based phosphonate analogues of myo-inositol-1-phosphate and phosphatidylinositol have been synthesized from methyl beta-d-galactopyranoside. Michaelis-Arbuzov reaction of isopropyl diphenyl phosphite or triisopropyl phosphite with a 6-iodo-3,4-isopropylidene galactoside afforded the corresponding phosphonates. Deprotection of the diphenyl phosphonate afforded methyl beta-d-galactoside 6-phosphonate, an analogue of myo-inositol-1-phosphate. The diisopropyl esters of the diisopropyl phosphonate were selectively deprotected and the corresponding anion was coupled with 1,2-dipalmitoyl-sn-glycerol using dicyclohexylcarbodiimide. Deprotection afforded a methyl beta-d-galactoside-derived analogue of phosphatidylinositol. The galactose-derived analogues of phosphatidylinositol and myo-inositol-1-phosphate were not substrates for mycobacterial mannosyltransferases (at concentrations up to 1 mM) involved in phosphatidylinositol mannoside biosynthesis in a cell-free extract of Mycobacterium smegmatis. The galactose-derived phosphonate analogue of phosphatidylinositol was shown to be an inhibitor at 0.01 mM of PimA mannosyltransferase involved in the synthesis of phosphatidylinositol mannoside from phosphatidylinositol, and a weaker inhibitor of the next mannosyltransferase(s), which catalyzes the mannosylation of phosphatidylinositol mannoside.