Improved lower bounds of call options written on defaultable assets

Abstract

is currently an Assistant Professor in the Department of Mathematics and Statistics at the American University of Sharjah. He holds a PhD in Applied Mathematics with a specialization in mathematical finance from the University of Calgary. His research areas include computational finance and applications, numerical methods applied to derivative pricing, empirical performance of option pricing models and non-parametric modeling.Correspondence: Greg Orosi, Department of Mathematics and Statistics, American University of Sharjah, Nab 254, PO Box 26666, Sharjah, UAE E-mail: gorosi@ucalgary.ca ABSTRACT This article provides an improvedmodel-independent lower bound of European call options written on defaultable assets. On the basis of static arbitrage arguments, improved lower bounds are established, which also depend on the probability of option-implied default. The results are also extended to dividend-paying stocks. Moreover, our findings imply that it is never optimal to exercise certain American call options. Finally, we discuss the implications of our results for constructing an arbitrage-free volatility surface and extracting risk-neutral densities from option prices.

Novel no-arbitrage conditions for options written on defaultable assets

“…Proof Orosi (2014b) shows that the lower bound of a European call option written on a defaultable asset is…”

“…Hence, if conditions (8), (9), (10) and (11) are ignored when fitting an arbitrage-free option surface to certain market quotes, which imply a positive probability of default, arbitrage violations can occur even if the commonly stated arbitrage conditions are not violated. The implications of condition (9) have been discussed in Orosi (2014b), therefore we will direct our attention to the other three conditions. First of all, it should be noted that, assuming PD > 0, (8) is higher for strike prices for which K Á e -rT -S 0 + D<0 than Merton's lower bound of PðK; T Þ⩾maxðK Á e -rT -S 0 + D; 0Þ:…”