Smiles all around: FX joint calibration in a multi-Heston model

We introduce a novel multi-factor Heston-based stochastic volatility model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models and relying on a reasonable number of parameters. A successful joint calibration to real market data is presented together with various in- and out-of-sample calibration exercises to highlight the robustness of the parameters estimation. The proposed model preserves the natural inversion and triangulation symmetries of FX spot rates and its functional form, irrespective of choice of the risk-free currency. That is, all currencies are treated in the same way.Comment: Journal of Banking and Finance. Accepte

Pricing caps with HJM models: the benefits of humped volatility

In this paper we compare different multifactor HJM models with humped volatility structures, to each other and to models with strictly decreasing volatility. All the models are estimated on Euribor and swap rates panel data. We develop the analysis in two steps: first we study the in-sample properties of the estimated models, then we study the pricing performance on caps. We find the humped volatility specification to greatly improve the model estimation and to provide sufficiently accurate cap prices, although the models has been calibrated on interest rates data and not on cap prices. Moreover we find the two factor humped volatility model to outperform the three factor models in pricing capsFinance, interest rates, humped volatility, Kalman filter, cap and floor pricing

Nuevas Técnicas de Estimación en Modelos de Derivados de Materias Primas bajo la Medida Neutral al Riesgo

En la literatura es muy habitual utilizar modelos a fines para valorar derivados de materias primas, por su sencillez y adaptabilidad. Para poder obtener una forma cerrada del precio del derivado, se suelen considerar funciones paramétricas sencillas. De hecho, en la mayoría de los casos, los precios de riesgo del mercado se consideran constantes. Entonces, las funciones de los procesos bajo la medida neutral al riesgo se estiman a partir de las observaciones de los precios del derivado. Por ejemplo, Gibson y Schwartz [36], Schwartz [73] y Cortazar et al. [24] consideran modelos a fines con uno, dos o tres factores, y obtienen una forma cerrada de la solución para el precio del derivado. Sin embargo, estos autores no introducen saltos ni estacionalidad en sus modelos. Además, no hay ninguna evidencia empírica de que los modelos a fines sean mejores para valorar derivados de materias primas. Si consideramos otras dinámicas más realistas para las variables de estado, no se suele conocer una forma cerrada de la solución. Entonces, los precios de riesgo del mercado o las funciones de los procesos neutrales al riesgo no se pueden estimar, porque no son observables. De hecho, este problema es una de las cuestiones abiertas en la valoración de derivados de materias primas, y es el principal objetivo de esta tesis. Así pues, para resolver este problema, proponemos un nuevo enfoque para estimar las funciones de los procesos neutrales al riesgo del modelo a partir de los datos del mercado, incluso cuando no se conoce una expresión de la solución. Es decir, diseñamos nuevas técnicas de estimación para diferentes comportamientos del precio al contado de la materia prima en el mercado.Departamento de Economía AplicadaDoctorado en Economí

An Evaluation of Multi-Factor CIR Models Using LIBOR, Swap Rates, and Cap and Swaption Prices

We evaluate the classical Cox, Ingersoll and Ross (1985) (CIR) model using data on LIBOR, swap rates and caps and swaptions. With three factors the CIR model is able to fit the term structure of LIBOR and swap rates rather well. The model is able to match the hump shaped unconditional term structure of volatility in the LIBOR-swap market. However, statistical tests indicate that the model is misspecified. In particular the pricing errors are related to the slope of the swap yield curve. The economic importance of these shortcomings is highlighted when the model is confronted with data on cap and swaption prices. Pricing errors are large relative to the bid-ask spread in these markets. The model tends to overvalue shorter maturity caps and undervalue longer maturity caps. With only one or two factors, the model also tends to undervalue swaptions. Our findings point out the need for evaluating term structure models using data on derivative prices.

Leverage and Feedback Effects on Multifactor Wishart Stochastic Volatility for Option Pricing

The paper proposes a general asymmetric multifactor Wishart stochastic volatility (AMWSV) diffusion process which accommodates leverage, feedback effects and multifactor for the covariance process. The paper gives the closed-form solution for the conditional and unconditional Laplace transform of the AMWSV models. The paper also suggests estimating the AMWSV model by the generalized method of moments using information not only of stock prices but also of realized volatilities and co-volatilities. The empirical results for the bivariate data of the NASDAQ 100 and S&P 500 indices show that the general AMWSV model is preferred among several nested models

The CTMC-Heston model: calibration and exotic option pricing with SWIFT

This work presents an efficient computational framework for pricing a general class of exotic and vanilla options under a versatile stochastic volatility model. In particular, we propose the use of a finite state continuous time Markov chain (CTMC) model, which closely approximates the classic Heston model but enables a simplified approach for consistently pricing a wide variety of financial derivatives (...

Gas storage valuation under multifactor Lévy processes

A practical problem for energy companies is instituting a consistent framework across its supply and trading activities to deliver on all-important P&L and at-Risk reporting requirements. With a focus on storage assets and wider natural gas market exposures, we present a gas storage valuation methodology, which uniquely uses a flexible multifactor Lévy process setting that allows for consistent valuation and risk management reporting across a general derivative book. Our approach is capable of replicating the complex covariance structure of the natural gas forward curve and capturing time spread volatility, a key driver of extrinsic storage value, while being simultaneously capable of accurately calibrating to market traded options. We begin by extending a single factor Mean Reverting Variance Gamma process to an arbitrary number of dimensions and, by way of specific examples, show how the traditional Principal Component Analysis based view of gas forward curve dynamics can be incorporated into a primarily market based valuation. We develop in the process an innovative implied moments based calibration technique, which allows for efficient calibration of general multifactor forward curve models to delivery period options common in energy and commodity markets. Furthermore, to accommodate the forward curve and traded options market consistency, we propose an appropriate joint market based calibration and historical estimation methodology. Through a formal model specification analysis, we provide evidence that the multifactor Lévy models we propose provide a better joint fit to NBP natural gas options-forward market data, relative to comparative benchmark models. Finally, we develop a novel multidimensional fast Fourier transform based storage valuation algorithm and provide empirical evidence that the multifactor Lévy model suite is better specified to more accurately capture extrinsic value

Structural RFV: Recovery Form and Defaultable Debt Analysis

Receiving the same fractional recovery of par at default for bonds of the same issuer and seniority, regardless of remaining maturity, has been labelled in the academic literature as a Recovery of Face Value at Default (RFV).Such a recovery form results from language found in typical bond indentures and is supported by empirical evidence from defaulted bond values.We incorporate RFV into an exogenous boundary structural credit risk model and compare its e ect to more typical recovery forms found in such models.We find that the chosen recovery form can significantly a ect valuation and the sensitivities produced by these models, thus having important implications for empirical studies attempting to validate structural credit risk models.We show that some features of existing structural models are a result of the recovery form assumed in the model and do not necessarily hold under an RFV recovery form.Some of our results complement those found in the literature which examines the endogeneity of the default boundary.We find that some features that may have been solely attributed to modelling the boundary as an optimal decision by the firm can be obtained in an exogenous boundary framework with RFV.This has direct implications for studies which attempt to determine whether endogenous or exogenous models are better supported empirically.We extend our results to incorporate a multifactor default-free term structure model and examine the impact of the recovery form in estimating the cost of debt capital within a structural model framework.bonds;credit;risk;capital costs;debt