1,720,996 research outputs found
Back-of-the-envelope Swaptions in a Very Parsimonious Multi-Curve Interest Rate Model
No full textWe propose an elementary model in multi-curve setting that allows to price with simple exact closed formulas European swaptions. Swaptions can be both physical delivery and cash-settled ones. The proposed model is very parsimonious: it is a three-parameter multi-curve extension of the two-parameter J. Hull & A. White (1990) [Pricing interest-rate-derivative securities. Review of Financial Studies 3(4), 573-592] model. The model allows also to obtain simple formulas for all other plain vanilla Interest Rate derivatives and convexity adjustments. Calibration issues are discussed in detail
Additive normal tempered stable processes for equity derivatives and power-law scaling
Full text linkWe introduce a simple additive process for equity index derivatives. The model generalizes Lévy Normal Tempered Stable processes (e.g. NIG and VG) with time-dependent parameters. It accurately fits the equity index volatility surfaces in the whole time range of quoted instruments, including options with small time-horizon (days) and long time-horizon (years). We introduce the model via its characteristic function. This allows using classical Fourier pricing techniques. We discuss the calibration issues in detail and we show that, in terms of mean squared error, calibration is on average two orders of magnitude better than both Lévy and Sato processes alternatives. We show that even if the model loses the classical stationarity property of Lévy processes, it presents interesting scaling properties for the calibrated parameters
Model risk in mean-variance portfolio selection: an analytic solution to the worst-case approach
Full text linkIn this paper we consider the worst-case model risk approach described in Glasserman and Xu (Quant Finance 14(1):29–58, 2014). Portfolio selection with model risk can be a challenging operational research problem. In particular, it presents an additional optimisation compared to the classical one. We find the analytical solution for the optimal mean-variance portfolio selection in the worst-case scenario approach and for the special case with the additional constraint of a constant mean vector considered in Glasserman and Xu (Quant Finance 14(1):29–58, 2014). Moreover, we prove in two relevant cases—the minimum-variance case and the symmetric case, i.e. when all assets have the same mean—that the analytical solutions in the alternative model and in the nominal one are equal; we show that this corresponds to the situation when model risk reduces to estimation risk
Synthetic forwards and cost of funding in the equity derivative market
Full text linkThis study introduces a new technique to recover the implicit discount factor in the derivative market using only European put and call prices: this discount is grounded in actual transactions in active markets. Moreover, this study identifies the implied cost of funding, over OIS, of major market players. Does a liquid equity market allow arbitrage? The key idea is that the (unique) forward contract -built using the put-call parity relation- contains information about the market discount factor: by no-arbitrage conditions we identify the implicit interest rate such that the forward contract value does not depend on the strike. The procedure is applied to options on S&P 500 and EURO STOXX 50 indices. There is statistical evidence that, in the EURO STOXX 50 market, the implicit interest rate curve coincides with the EUR OIS one, while, in the S&P 500 market, a cost of funding of, on average, 34 basis points is added on top of the USD OIS curve
Cluster approximation for Ising spin glasses
No full textWe report about a new variational method [9] which approximates in a hierarchical way the random Ising spin glass on lattice in d dimensions. At the lon est level our approximation coincides with the Sherrington-Kirkpatrick model, while at the highest level it coincides with the true d-dimensional system. The attention is focused on finite size clusters of spins where the action of the rest of the system is taken into account by a coupling field, which is the variational parameter of the problem
A variational approach to Ising spin glasses in finite dimensions
No full textWe introduce a hierarchical class of approximations of the random Ising spin glass in d dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the lowest level (cluster of a single spin) our approximation coincides with the SK model while at the highest level it coincides with the true d-dimensional system. The method is variational and it uses the replica approach to spin glasses and the Parisi ansatz for the order parameter. As a result we have rigorous bounds for the quenched free energy which become more and more precise when larger and larger clusters are considered
A closed formula for illiquid corporate bonds and an application to the European market
Full text linkHow to price illiquid corporate bonds when their prices are not available for several days in the marketplace, but other bonds of the same issuer trade frequently? This situation appears to be quite common in the fixed income market: it is rather usual to find issuers that, besides liquid benchmark bonds, issue some other debt instruments that either are placed to a small number of investors in private placements or have a limited issue size. To answer to this question we propose an option approach for pricing bond illiquidity that is reminiscent of the celebrated work of Longstaff (1995) on the non-marketability of some non-dividend-paying shares in IPOs. Our approach models interest rate and credit risks via a convenient reduced-form approach. We deduce a simple closed formula for illiquid corporate coupon bond prices when liquid bonds with similar characteristics (e.g. maturity) are present in the market for the same issuer. The key model parameter is the time-to-liquidate a position, i.e. the time that an experienced bond trader takes to liquidate a given position on a corporate coupon bond. We show that illiquid bonds present an additional liquidity spread that depends on the time-to-liquidate aside from bond volatility. We provide a detailed application for two financial issuers in the European market
Moving averages and price dynamics
No full textWe introduce a stochastic price model where, together with a random component, a moving average of logarithmic prices contributes to the price formation. The future price is linearly influenced by the difference between the moving average and the current price, together with a noise component. Our model is tested against financial datasets, showing an extremely good agreement with them
Forecast in foreign exchange markets
No full textWe perform a statistical study of weak efficiency in Deutschemark/US dollar exchange rates using high frequency data. The presence of correlations in the returns sequence implies the possibility of a statistical forecast of market behavior. We show the existence of correlations and how information theory can be relevant in this context
Antipersistent Markov behavior in foreign exchange markets
No full textA quantitative check of efficiency in US dollar/Deutsche mark exchange rates is developed using high-frequency (tick by tick) data. The antipersistent Markov behavior of log-price fluctuations of given size implies, in principle, the possibility of a statistical forecast. We introduce and measure the available information of the quote sequence, and we show how it can be profitable following a particular trading rule. (C) 2002 Elsevier Science B.V. All rights reserved
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