Stochastic Skew in Currency Options

We document the behavior of over-the-counter currency option prices across moneyness, maturity, and calendar time on two of the most actively traded currency pairs over the past eight years. We find that the risk-neutral distribution of currency returns is relatively symmetric on average. However, on any given date, the conditional currency return distribution can show strong asymmetry. This asymmetry varies greatly over time and often switch directions. We design and estimate a class of models that capture these unique features of the currency options prices and perform much better than traditional jump- diffusion stochastic volatility models.currency options, stochastic skew, time-changed Levy processes

The Finite Moment Log Stable Process and Option Pricing

We document a surprising pattern in market prices of S&P 500 index options. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharply with the implications of many pricing models and with the asymptotic behavior implied by the central limit theorem (CLT). We develop a parsimonious model which deliberately violates the CLT assumptions and thus captures the observed behavior of the volatility smirk over the maturity horizon. Calibration exercises demonstrate its superior performance against several widely used alternatives.Volatility smirk; central limit theorem; Levy a­lpha-stable motion; self­similarity; option pricing.

Variance Risk Premia

We propose a direct and robust method for quantifying the variance risk premium on financial assets. We theoretically and numerically show that the risk-neutral expected value of the return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. Ignoring the small approximation error, the difference between the realized variance and this synthetic variance swap rate quantifies the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premia on five stock indexes and 35 individual stocks.Stochastic volatility, variance risk premia, variance swap, volatility swap, option pricing, expectation hypothesis

On the Hedging of Options On Exploding Exchange Rates

We study a novel pricing operator for complete, local martingale models. The new pricing operator guarantees put-call parity to hold for model prices and the value of a forward contract to match the buy-and-hold strategy, even if the underlying follows strict local martingale dynamics. More precisely, we discuss a change of num\'eraire (change of currency) technique when the underlying is only a local martingale modelling for example an exchange rate. The new pricing operator assigns prices to contingent claims according to the minimal cost for superreplication strategies that succeed with probability one for both currencies as num\'eraire. Within this context, we interpret the lack of the martingale property of an exchange-rate as a reflection of the possibility that the num\'eraire currency may devalue completely against the asset currency (hyperinflation).Comment: Major revision. Accepted by Finance and Stochastics. The original publication is available at http://link.springer.co

What Type of Process Underlies Options? A Simple Robust Test

We develop a simple robust test for the presence of continuous and discontinuous (jump) com­ponents in the price of an asset underlying an option. Our test examines the prices of at­the­money and out­of­the­money options as the option maturity approaches zero. We show that these prices converge to zero at speeds which depend upon whether the sample path of the underlying asset price process is purely continuous, purely discontinuous, or a mixture of both. By applying the test to S&P 500 index options data, we conclude that the sample path behavior of this index contains both a continuous component and a jump component. In particular, we find that while the pres­ence of the jump component varies strongly over time, the presence of the continuous component is constantly felt. We investigate the implications of the evidence for parametric model specifications.Jumps; continuous martingale; option pricing; Levy density; double tails; local time.

Non-traditional students in tertiary education: inter-disciplinary collaboration in curriculum and pedagogy in community services education in Australia

Education policy in Australia has accelerated its aim to increase participation of under-represented groups in tertiary education including students who are culturally and linguistically diverse and have low socio-economic status. These students generally have not had prior access to privileged academic discourse, which can further disadvantage them in their participation and progress in tertiary education. In this article, we outline a cross-discipline curriculum initiative and pedagogy that draws on critical literacy and the metaphor of discourse community to integrate language and academic skills into community services qualifications. We argue that this – supports the genuine participation of under-represented (non-traditional) students. It aspires to not only support students’ entry into the new academic terrain, but to enable students to adopt a critical stance to the discourses in which they are learning to participate. This we argue is crucial, when expertise is not just a way of meeting its ostensible purposes, but is also a way of exercising power. Although we report on the application of this initiative to entry level curricula (Diploma), we suggest that it has relevance and application to Bachelor levels in a range of disciplines, both in supporting pedagogy and for transition to Bachelor level study