Estimation of risk-neutral density surfaces

2014

J Deriv Hedge Funds

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.

Section: Proposition 3 Early Exercise Of An Americanmentioning

confidence: 99%

Improved lower bounds of call options written on defaultable assets

2014

J Deriv Hedge Funds

“…A popular technique to do this task is to fit implied volatility-based models. Such techniques have excellent empirical performance, but Fengler (2009) and Monteiro et al (2011) pointed out that it is difficult to guarantee the absence of static arbitrage due to the non-linearity of the constraints in the related optimization problem. The resulting RND can take negative values and lead to mispricings.…”

Section: Introductionmentioning

confidence: 99%

A robust method to retrieve option implied risk neutral densities for defaultable assets

Leduc

2016

IJFMD

Risk neutral densities recovered from option prices can be used to infer market participants' expectations of future stock returns and are a vital tool for pricing illiquid exotic options. Although there is a broad literature on the subject, most studies do not address the likelihood of default. To fill this gap, in this paper we develop a novel method to retrieve the risk neutral probability density function from call options written on a defaultable asset. The primary advantage of the method is that default probabilities inferred by the model can be analytically expressed and, if available, can be incorporated as an input in a flexible, robust and easily implementable manner.

“…For example, using the implied risk-neutral density, Monteiro et al (2011) accurately price Europeanstyle binary options, Benaim et al (2008) calculate the convexity correction for constant maturity swaps, and Cherubini and Luciano (2002) price bivariate equity options. Moreover, although interpolation performed in the implied volatility space has several advantages (see for example Figlewski (2009) andOrosi (2012)), the resulting call option surface is not arbitrage-free.…”

Section: Introductionmentioning

confidence: 99%

Novel no-arbitrage conditions for options written on defaultable assets

2014

J Deriv Hedge Funds

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.