The Neutrino Option

The minimal seesaw scenario can radiatively generate the Higgs potential to induce electroweak symmetry breaking while supplying an origin of the Higgs vacuum expectation value from an underlying Majorana scale. If the Higgs potential and (derived) electroweak scale have this origin, the heavy $\rm SU(3) \times SU(2) \times U(1)_Y$ singlet states are expected to reside at $m_N \sim 10-500 \, {\rm PeV}$ for couplings $|\omega| \sim 10^{-4.5}-10^{-6}$ between the Majorana sector and the Standard Model. In this framework, the challenge of the electroweak scale hierarchy problem is replaced with a need to generate or accommodate PeV Majorana mass scales in ultraviolet models; the usual hierarchy problem is absent as the electroweak scale is not a fundamental scale.Comment: 5 pages, 5 figures, one radiative potential. Updated version consistent with the one accepted for publication in PRL (title changed in the journal

Martingale Option Pricing

We show that our generalization of the Black-Scholes partial differential equation (pde) for nontrivial diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, this was proven for the case of the Gaussian logarithmic returns model by Harrison and Kreps, but we prove it for much a much larger class of returns models where the diffusion coefficient depends on both returns x and time t. That option prices blow up if fat tails in logarithmic returns x are included in the market dynamics is also explained

Examining the neutrino option

The neutrino option is a scenario where the electroweak scale, and thereby the Higgs mass, is generated simultaneously with neutrino masses in the seesaw model. This occurs via the leading one loop and tree level diagrams matching the seesaw model onto the Standard Model Effective Field Theory. We advance the study of this scenario by determining one loop corrections to the leading order matching results systematically, performing a detailed numerical analysis of the consistency of this approach with Neutrino data and the Standard Model particle masses, and by examining the embedding of this scenario into a more ultraviolet complete model. We find that the neutrino option remains a viable and intriguing scenario to explain the origin of observed particle masses.Comment: 26 pages, 6 figures v2, typo corrections and refs adde

Signaling an Outside Option

We consider the case of an upstream seller who works to improve an asset that has been specialized to a downstream buyer's needs. The buyer then makes a take it or leave it offer to the seller about how the future surplus should be split. We assume that the seller from the outset has private information about the fraction of the surplus that he can realize on his own, and show that this leads to higher investment compared to the complete information case. This positive effect on investment is countervailed by the occurrence of inefficient separations, which result when the buyer mistakenly tries to call the seller's bluff with a low offer

Option Investor Rationality Revisited

Do option investors rationally exercise their options? Numerous studies report evidence of irrational behavior. In this paper, we pay careful attention to intraday option quotes and reach the opposite conclusion. An exercise boundary violation (EBV) occurs when the best bid price for an American option is below the option’s intrinsic value. Far from being unusual, we show that EBVs occur very frequently. Under these conditions, the rational response of an investor liquidating an option is to exercise the option rather than sell it. Empirically, we find that the likelihood of early exercise is strongly influenced by the existence and duration of EBVs. Not only do these results reverse standard theory on American option valuation and optimal exercise strategy, but they also suggest that the ability to avoid selling at an EBV price creates an additional source of value for American options that is unrelated, and in addition to, dividend payments. This additional value may help explain why American options appear overpriced relative to European options