On pricing risky loans and collateralized fund obligations

Loan spreads are analyzed for two types of loans. The first type takes losses at maturity only; the second follows the formulation of collateralized fund obligations, with losses registered over the lifetime of the contract. In both cases, the implementation requires the choice of a process for the underlying asset value and the identification of the parameters. The parameters of the process are inferred from the option volatility surface by treating equity options as compound options with equity itself being viewed as an option on the asset value with a strike set at the debt level following Merton. Using data on the stock of General Motors during 2002-3, we show that the use of spectrally negative Lévy processes is capable of delivering realistic spreads without inflating debt levels, deflating debt maturities or deviating from the estimated probability laws

Options on realized variance and convex orders

Realized variance option and options on quadratic variation normalized to unit expectation are analysed for the property of monotonicity in maturity for call options at a fixed strike. When this condition holds the risk-neutral densities are said to be increasing in the convex order. For Leacutevy processes, such prices decrease with maturity. A time series analysis of squared log returns on the S&P 500 index also reveals such a decrease. If options are priced to a slightly increasing level of acceptability, then the resulting risk-neutral densities can be increasing in the convex order. Calibrated stochastic volatility models yield possibilities in both directions. Finally, we consider modeling strategies guaranteeing an increase in convex order for the normalized quadratic variation. These strategies model instantaneous variance as a normalized exponential of a Leacutevy process. Simulation studies suggest that other transformations may also deliver an increase in the convex order

The fine structure of asset returns: an empirical investigation

We investigate the importance of diffusion and jumps in a new model for asset returns. In contrast to standard models, we allow for jump components displaying finite or infinite activity and variation. Empirical investigations of time series indicate that index dynamics are devoid of a diffusion component, which may be present in the dynamics of individual stocks. This leads to the conjecture, confirmed on options data, that the risk-neutral process should be free of a diffusion component. We conclude that the statistical and risk-neutral processes for equity prices are pure jump processes of infinite activity and finite variation

Tenor specific pricing

Observing that pure discount curves are now based on a variety of tenors giving rise to tenor specific zero coupon bond prices, the question is raised on how to construct tenor specific prices for all financial contracts. Noting that in conic finance one has the law of two prices, bid and ask, that are nonlinear functions of the random variables being priced, we model dynamically consistent sequences of such prices using the theory of nonlinear expectations. The latter theory is closely connected to solutions of backward stochastic difference equations. The drivers for these stochastic di¤erence equations are here constructed using concave distortions that implement risk charges for local tenor specific risks. It is then observed that tenor specific prices given by the mid quotes of bid and ask converge to the risk neutral price as the tenor is decreased and liquidity increased when risk charges are scaled by the tenor. Square root tenor scaling can halt the convergence to risk neutral pricing, preserving bid ask spreads in the limit. The greater liquidity of lower tenors may lead to an increase or decrease in prices depending on whether the lower liquidity of a higher tenor has a mid quote above or below the risk neutral value. Generally for contracts with a large upside and a bounded downside the prices fall with liquidity while the opposite is the case for contracts subject to a large downside and a bounded upside

Conic coconuts : the pricing of contingent capital notes using conic finance

In this paper we introduce a fundamental model under which we will price contingent capital notes using conic finance techniques. The model is based on more realistic balance-sheet models recognizing the fact that asset and liabilities are both risky and have been treated differently taking into account bid and ask prices in a prudent fashion. The underlying theory makes use of the concept of acceptability and distorted expectations, which we briefly discuss. We overview some potential funded and unfunded contingent capital notes. We argue that the traditional core tier one ration is maybe not optimal, certainly when taking into account the presence of risky liabilities; we as an alternative introduce triggers based on capital shortfall. The pricing of 7 variations of funded as well as unfunded notes is overviewed. We further investigate the effect of the dilution factor and the grace factor. In an appendix we show conic balance sheets including contingent capital instruments

Chaotic memristor

We suggest and experimentally demonstrate a chaotic memory resistor (memristor). The core of our approach is to use a resistive system whose equations of motion for its internal state variables are similar to those describing a particle in a multi-well potential. Using a memristor emulator, the chaotic memristor is realized and its chaotic properties are measured. A Poincar\'{e} plot showing chaos is presented for a simple nonautonomous circuit involving only a voltage source directly connected in series to a memristor and a standard resistor. We also explore theoretically some details of this system, plotting the attractor and calculating Lyapunov exponents. The multi-well potential used resembles that of many nanoscale memristive devices, suggesting the possibility of chaotic dynamics in other existing memristive systems.Comment: Applied Physics A (in press