Novel no-arbitrage conditions for options written on defaultable assets

Abstract

is currently an assistant professor in the Department of Mathematics and Statistics at 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, Office: Nab 254, PO Box 26666, Sharjah, UAE E-mail: gorosi@ucalgary.ca ABSTRACT In this work, we derive an improved lower bound for European-style put options written on defaultable assets. Furthermore, we establish two additional no-arbitrage conditions, one for European-style puts and one for calls, which are tighter than the ones commonly reported in current literature. All of our results are based on static arbitrage arguments and have important implications for constructing arbitrage-free call or put option surfaces. In particular, we point out that the commonly stated conditions required for a call option surface are not always sufficient to generate an arbitrage-free call option surface.

Equity Option Implied Probability of Default and Equity Recovery Rate

“…Our methodology is based on new static arbitrage‐free lower bounds for European call and put option prices when the expected default probability and equity recovery are known. We derive these lower bounds by generalizing the results of Orosi ().…”

“…The lower bounds for European call and put prices derived in Merton () (referred to hereafter as Merton's lower bounds) are based on the assumption that the underlying asset price follows a strictly positive price process, which is not the case when there is a positive probability of default. Orosi () proposes improved lower bounds under the assumption that the underlying asset can default and the price of the asset at default is zero. In the case of equity options, this means a zero equity recovery at default.…”

“…In practice, however, Orosi's lower bounds are often violated for equity options. In this section, we first present an alternative derivation of the lower bounds proposed in Orosi (), then show that relaxing the assumption of zero equity recovery can explain the presence of violations of Orosi's bounds in practice.…”