The Zeeman Effect in Finance: Libor Spectroscopy and Basis Risk Management

Once upon a time there was a classical financial world in which all the Libors were equal. Standard textbooks taught that simple relations held, such that, for example, a 6 months Libor Deposit was replicable with a 3 months Libor Deposits plus a 3x6 months Forward Rate Agreement (FRA), and that Libor was a good proxy of the risk free rate required as basic building block of no-arbitrage pricing theory. Nowadays, in the modern financial world after the credit crunch, some Libors are more equal than others, depending on their rate tenor, and classical formulas are history. Banks are not anymore too "big to fail", Libors are fixed by panels of risky banks, and they are risky rates themselves. These simple empirical facts carry very important consequences in derivative's trading and risk management, such as, for example, basis risk, collateralization and regulatory pressure in favour of Central Counterparties. Something that should be carefully considered by anyone managing even a single plain vanilla Swap. In this qualitative note we review the problem trying to shed some light on this modern animal farm, recurring to an analogy with quantum physics, the Zeeman effect

Two Curves, One Price :Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves

We revisit the problem of pricing and hedging plain vanilla single-currency interest rate derivatives using multiple distinct yield curves for market coherent estimation of discount factors and forward rates with dierent underlying rate tenors. Within such double-curve-single-currency framework, adopted by the market after the credit-crunch crisis started in summer 2007, standard single-curve no-arbitrage relations are no longer valid, and can be recovered by taking properly into account the forward basis bootstrapped from market basis swaps. Numerical results show that the resulting forward basis curves may display a richer micro-term structure that may induce appreciable effects on the price of interest rate instruments. By recurring to the foreign-currency analogy we also derive generalised no-arbitrage double-curve market-like formulas for basic plain vanilla interest rate derivatives, FRAs, swaps, caps/floors and swaptions in particular. These expressions include a quanto adjustment typical of cross-currency derivatives, naturally originated by the change between the numeraires associated to the two yield curves, that carries on a volatility and correlation dependence. Numerical scenarios confirm that such correction can be non negligible, thus making unadjusted double-curve prices, in principle, not arbitrage free. Both the forward basis and the quanto adjustment find a natural financial explanation in terms of counterparty risk.liquidity, crisis, counterparty risk, yield curve, forward curve, discount curve, pricing, hedging, interest rate derivatives, FRAs, swaps, basis swaps, caps, floors, swaptions, basis adjustment, quanto adjustment, measure changes, no arbitrage, QuantLib

Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and Global Sensitivity Analysis

We review and apply Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques to pricing and risk management (greeks) of representative financial instruments of increasing complexity. We compare QMC vs standard Monte Carlo (MC) results in great detail, using high-dimensional Sobol' low discrepancy sequences, different discretization methods, and specific analyses of convergence, performance, speed up, stability, and error optimization for finite differences greeks. We find that our QMC outperforms MC in most cases, including the highest-dimensional simulations and greeks calculations, showing faster and more stable convergence to exact or almost exact results. Using GSA, we are able to fully explain our findings in terms of reduced effective dimension of our QMC simulation, allowed in most cases, but not always, by Brownian bridge discretization. We conclude that, beyond pricing, QMC is a very promising technique also for computing risk figures, greeks in particular, as it allows to reduce the computational effort of high-dimensional Monte Carlo simulations typical of modern risk management.Comment: 43 pages, 21 figures, 6 table

Brexit or Bremain ? Evidence from bubble analysis

We applied the Johansen-Ledoit-Sornette (JLS) model to detect possible bubbles and crashes related to the Brexit/Bremain referendum scheduled for 23rd June 2016. Our implementation includes an enhanced model calibration using Genetic Algorithms. We selected a few historical financial series sensitive to the Brexit/Bremain scenario, representative of multiple asset classes. We found that equity and currency asset classes show no bubble signals, while rates, credit and real estate show super-exponential behaviour and instabilities typical of bubble regime. Our study suggests that, under the JLS model, equity and currency markets do not expect crashes or sharp rises following the referendum results. Instead, rates and credit markets consider the referendum a risky event, expecting either a Bremain scenario or a Brexit scenario edulcorated by central banks intervention. In the case of real estate, a crash is expected, but its relationship with the referendum results is unclear

Aluminium transformer vs copper transformer: A technical and economic comparison

The possible applications for dry-type transformers are multiple and versatile. Together with the choice of the correct technology and execution, it is quite often under discussion which one can be the best solution for a conductor if using aluminium or copper to have the best result in terms of performances. The analysis must be carried on considering different topics we are deepening here

Interest Rates After The Credit Crunch: Multiple-Curve Vanilla Derivatives and SABR

We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of collateral agreements and CSA-discounting, in terms of credit and liquidity effects. We also review the new modern pricing approach prevailing among practitioners, based on multiple yield curves reflecting the different credit and liquidity risk of Libor rates with different tenors and the overnight discounting of cash flows originated by derivative transactions under collateral with daily margination. We report the classical and modern no-arbitrage pricing formulas for plain vanilla interest rate derivatives, and the multiple-curve generalization of the market standard SABR model with stochastic volatility. We then report the results of an empirical analysis on recent market data comparing pre- and post-credit crunch pricing methodologies and showing the transition of the market practice from the classical to the modern framework. In particular, we prove that the market of Interest Rate Swaps has abandoned since March 2010 the classical Single-Curve pricing approach, typical of the pre-credit crunch interest rate world, and has adopted the modern Multiple-Curve CSA approach, thus incorporating credit and liquidity effects into market prices. The same analysis is applied to European Caps/Floors, finding that the full transition to the modern Multiple-Curve CSA approach has retarded up to August 2010. Finally, we show the robustness of the SABR model to calibrate the market volatility smile coherently with the new market evidences.Comment: 26 pages, 13 color figures, 6 tables; revised typo

Application of Quasi Monte Carlo and Global Sensitivity Analysis to Option Pricing and Greeks

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Two Curves, One Price :Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves

We revisit the problem of pricing and hedging plain vanilla single-currency interest rate derivatives using multiple distinct yield curves for market coherent estimation of discount factors and forward rates with dierent underlying rate tenors. Within such double-curve-single-currency framework, adopted by the market after the credit-crunch crisis started in summer 2007, standard single-curve no-arbitrage relations are no longer valid, and can be recovered by taking properly into account the forward basis bootstrapped from market basis swaps. Numerical results show that the resulting forward basis curves may display a richer micro-term structure that may induce appreciable effects on the price of interest rate instruments. By recurring to the foreign-currency analogy we also derive generalised no-arbitrage double-curve market-like formulas for basic plain vanilla interest rate derivatives, FRAs, swaps, caps/floors and swaptions in particular. These expressions include a quanto adjustment typical of cross-currency derivatives, naturally originated by the change between the numeraires associated to the two yield curves, that carries on a volatility and correlation dependence. Numerical scenarios confirm that such correction can be non negligible, thus making unadjusted double-curve prices, in principle, not arbitrage free. Both the forward basis and the quanto adjustment find a natural financial explanation in terms of counterparty risk

Cognitive reserve in granulin-related frontotemporal dementia: from preclinical to clinical stages

OBJECTIVE Consistent with the cognitive reserve hypothesis, higher education and occupation attainments may help persons with neurodegenerative dementias to better withstand neuropathology before developing cognitive impairment. We tested here the cognitive reserve hypothesis in patients with frontotemporal dementia (FTD), with or without pathogenetic granulin mutations (GRN+ and GRN-), and in presymptomatic GRN mutation carriers (aGRN+). METHODS Education and occupation attainments were assessed and combined to define Reserve Index (RI) in 32 FTD patients, i.e. 12 GRN+ and 20 GRN-, and in 17 aGRN+. Changes in functional connectivity were estimated by resting state fMRI, focusing on the salience network (SN), executive network (EN) and bilateral frontoparietal networks (FPNs). Cognitive status was measured by FTD-modified Clinical Dementia Rating Scale. RESULTS In FTD patients higher level of premorbid cognitive reserve was associated with reduced connectivity within the SN and the EN. EN was more involved in FTD patients without GRN mutations, while SN was more affected in GRN pathology. In aGRN+, cognitive reserve was associated with reduced SN. CONCLUSIONS This study suggests that cognitive reserve modulates functional connectivity in patients with FTD, even in monogenic disease. In GRN inherited FTD, cognitive reserve mechanisms operate even in presymptomatic to clinical stages