Download or read book On Cross Currency Models with Stochastic Volatility and Correlated Interest Rates written by Lech A. Grzelak and published by . This book was released on 2014 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of Hull-White [HW96]. We then extend the framework by modeling the interest rate by a stochastic volatility displaced-diffusion Libor Market Model [AA02], which can model an interest rate smile. We provide semi-closed form approximations which lead to efficient calibration of the multi-currency models. Finally, we add a correlated stock to the framework and discuss the construction, model calibration and pricing of equity-FX-interest rate hybrid payoffs.

Download or read book On Cross currency Models with Stochastic Volatility and Correlated Interest Rates written by Lech Aleksander Grzelak and published by . This book was released on 2010 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Affine Multi Currency Model with Stochastic Volatility and Stochastic Interest Rates written by Alessandro Gnoatto and published by . This book was released on 2014 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX rates can be performed efficiently through the FFT methodology thanks to the affinity of the model. A joint calibration exercise of the implied volatility surfaces of a triangle of FX rates shows the flexibility of our framework in dealing with the typical symmetries that characterize the FX market. Our framework is also able to describe many non trivial links between FX rates and interest rates: a second calibration exercise highlights the ability of the model to fi t simultaneously FX implied volatilities while being coherent with interest rate products.

Download or read book A study of cross currency models with correlated interest rates written by and published by . This book was released on 2012 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Currency Derivative and International Term Structure Pricing in a Stochastic Interest Rate Stochastic Volatility and Stochastic Jump Intensity World written by Shijun Liu and published by . This book was released on 2007 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We first derive closed form solutions for currency options, currency futures, future options and the term structures of interest rates in a diffusion-jump model of stochastic interest rate, stochastic volatility and time varying jump intensity in currency price. We demonstrate that the introduction of constant jump intensity in the nominal stochastic discount factor shifts the whole term structure of interest rates vertically but has no influence on its shape. However, when the jump intensity is endogenous (time varying) the shape of the term structure is influenced through the factor sensitivity of interest rates. We also document considerable improvement in currency option pricing precision over alternative models if the true model is diffusion-jump with endogenous intensity in a simulation experiment. We conclude that allowing for multidimensional interaction is of significant qualitative and quantitative importance for the pricing of currency options and for understanding the shape of the term structure.

Download or read book Stochastic Interest Rate and Stochastic Volatility Models of Currency Futures Options written by Thadavillil Jithendranathan and published by . This book was released on 1993 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A General Stochastic Volatility Model for the Pricing and Forecasting of Interest Rate Derivatives written by Anders B. Trolle and published by . This book was released on 2006 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a tractable and flexible stochastic volatility multi-factor model of the term structure of interest rates. It features correlations between innovations to forward rates and volatilities, quasi-analytical prices of zero-coupon bond options and dynamics of the forward rate curve, under both the actual and risk-neutral measure, in terms of a finite-dimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities. The model also performs well in forecasting interest rates and derivatives.

Download or read book From Moving Average Local and Stochastic Volatility Models to 2 Factor Stochastic Volatility Models written by Oleg Kovrizhkin and published by . This book was released on 2008 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the following models:1. Generalization of a local volatility model rolled with a moving average of the spot: dS = mu Sdt + sigma(S/A)SdW$ where A(t) is a moving average of spot S.2. Generalization of Heston pure stochastic volatility model rolled with a moving average of the stochastic volatility: dS = mu Sdt + sigma SdW, dsigma^2 = k(theta - sigma^2)dt + gamma sigma dZ where theta(t) is a moving average of variance sigma^2.3. Generalization of a full stochastic volatility with the process for volatility depending on both sigma and S and rolled with a moving average of S: dS = mu Sdt + sigma SdW, dsigma = a(sigma, S/A)dt + b(sigma, S/A)dZ,corr(dW, dZ) = rho(sigma, S/A)$, where A(t) is a moving average of the spot S. We will generalize these and other ideas further and show that they lead to a 2-factor pure stochastic volatility model: dS = mu Sdt + sigma SdW$, sigma = sigma(v_1, v_2), dv_1 = a_1(v_1, v_2)dt + b_1(v_1, v_2)dZ_1,dv_2 = a_2(v_1, v_2)dt + b_2(v_1, v_2)dZ_2, corr(dW, dZ_1) = rho_1(v_1, v_2), corr(dW, dZ_2) = rho_2(v_1, v_2), corr(dZ_1, dZ_2) = rho_3(v_1, v_2) and give examples of analytically solvable models, applicable for multicurrency models consistent with cross currency pairs dynamics in FX. We also consider jumps and stochastic interest rates.

Download or read book Extension of Stochastic Volatility Equity Models with Hull White Interest Rate Process written by Lech A. Grzelak and published by . This book was released on 2014 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an extension of stochastic volatility equity models by a stochastic Hull-White interest rate component while assuming non-zero correlations between the underlying processes. We place these systems of stochastic differential equations in the class of affine jump diffusion - linear quadratic jump-diffusion processes (Duffie, Pan and Singleton, Cheng and Scaillet) so that the pricing of European products can be efficiently done within the Fourier cosine expansion pricing framework. We compare the new stochastic volatility Schobel-Zhu-Hull-White hybrid model with a Heston-Hull-White model, and also apply the models to price some hybrid structured derivatives that combine the equity and interest rate asset classes.

Download or read book Modern Pricing of Interest Rate Derivatives written by Riccardo Rebonato and published by Princeton University Press. This book was released on 2012-01-16 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, interest-rate modeling has developed rapidly in terms of both practice and theory. The academic and practitioners' communities, however, have not always communicated as productively as would have been desirable. As a result, their research programs have often developed with little constructive interference. In this book, Riccardo Rebonato draws on his academic and professional experience, straddling both sides of the divide to bring together and build on what theory and trading have to offer. Rebonato begins by presenting the conceptual foundations for the application of the LIBOR market model to the pricing of interest-rate derivatives. Next he treats in great detail the calibration of this model to market prices, asking how possible and advisable it is to enforce a simultaneous fitting to several market observables. He does so with an eye not only to mathematical feasibility but also to financial justification, while devoting special scrutiny to the implications of market incompleteness. Much of the book concerns an original extension of the LIBOR market model, devised to account for implied volatility smiles. This is done by introducing a stochastic-volatility, displaced-diffusion version of the model. The emphasis again is on the financial justification and on the computational feasibility of the proposed solution to the smile problem. This book is must reading for quantitative researchers in financial houses, sophisticated practitioners in the derivatives area, and students of finance.

Download or read book A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives written by Anders B. Trolle and published by . This book was released on 2016 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a tractable and flexible stochastic volatility multi-factor model of the term structure of interest rates. It features unspanned stochastic volatility factors, correlation between innovations to forward rates and their volatilities, quasi-analytical prices of zero-coupon bond options, and dynamics of the forward rate curve, under both the actual and risk-neutral measure, in terms of a finitedimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities.

Download or read book Consistency Problems for Heath Jarrow Morton Interest Rate Models written by Damir Filipovic and published by Springer. This book was released on 2004-11-02 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bond markets differ in one fundamental aspect from standard stock markets. While the latter are built up to a finite number of trade assets, the underlying basis of a bond market is the entire term structure of interest rates: an infinite-dimensional variable which is not directly observable. On the empirical side, this necessitates curve-fitting methods for the daily estimation of the term structure. Pricing models, on the other hand, are usually built upon stochastic factors representing the term structure in a finite-dimensional state space. Written for readers with knowledge in mathematical finance (in particular interest rate theory) and elementary stochastic analysis, this research monograph has threefold aims: to bring together estimation methods and factor models for interest rates, to provide appropriate consistency conditions and to explore some important examples.

Download or read book XVA written by Andrew Green and published by John Wiley & Sons. This book was released on 2015-10-08 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thorough, accessible coverage of the key issues in XVA XVA – Credit, Funding and Capital Valuation Adjustments provides specialists and non-specialists alike with an up-to-date and comprehensive treatment of Credit, Debit, Funding, Capital and Margin Valuation Adjustment (CVA, DVA, FVA, KVA and MVA), including modelling frameworks as well as broader IT engineering challenges. Written by an industry expert, this book navigates you through the complexities of XVA, discussing in detail the very latest developments in valuation adjustments including the impact of regulatory capital and margin requirements arising from CCPs and bilateral initial margin. The book presents a unified approach to modelling valuation adjustments including credit risk, funding and regulatory effects. The practical implementation of XVA models using Monte Carlo techniques is also central to the book. You'll also find thorough coverage of how XVA sensitivities can be accurately measured, the technological challenges presented by XVA, the use of grid computing on CPU and GPU platforms, the management of data, and how the regulatory framework introduced under Basel III presents massive implications for the finance industry. Explores how XVA models have developed in the aftermath of the credit crisis The only text to focus on the XVA adjustments rather than the broader topic of counterparty risk. Covers regulatory change since the credit crisis including Basel III and the impact regulation has had on the pricing of derivatives. Covers the very latest valuation adjustments, KVA and MVA. The author is a regular speaker and trainer at industry events, including WBS training, Marcus Evans, ICBI, Infoline and RISK If you're a quantitative analyst, trader, banking manager, risk manager, finance and audit professional, academic or student looking to expand your knowledge of XVA, this book has you covered.

Download or read book Stochastic Volatility and Jumps in Interest Rates written by Ren-Raw Chen and published by . This book was released on 2010 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we examine possible stochastic volatility and jumps in short-term interest rates for four major countries: US, UK, Germany and Japan. An econometric model with stochastic volatility and jumps in both rates and volatility is derived and fit to the daily data for futures interest rates in four major currencies and the model provides a better fit for the empirical distributions. The distributions for changes in Eurocurrency interest rate futures are leptokurtic with fat tails and an unusually large percentage of observations concentrated at zero. The implied volatilities for at-the-money options on interest rate futures reveal evidence of stochastic volatility, as well as jumps in volatility.

Download or read book A Class of Stochastic Volatility Models for the Term Structure of Interest Rates written by Elisa Nicolato and published by . This book was released on 1999 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multi Currency Local Volatility Model written by Daniel Alexandre Bloch and published by . This book was released on 2008 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We establish the need for local volatility coupled with domestic and foreign stochastic interest rates to properly manage some exotic hybrid options. We then compute such a local volatility and identify a bias with respect to the local volatility with deterministic rates. Performing variance-covariance analysis on the logarithm of the underlying price together with the domestic and foreign spot rates we estimate that bias by calculating the variances of the logarithm of the underlying price with and without stochastic rates at fixed points in time and in space. Equating the resulting variances we express the local volatility with stochastic rates in terms of the one with deterministic rates plus a bias obtaining an exact, fast and robust way of calibrating any local volatility with stochastic rates to market prices. We calculate it by using a bootstrapping method requiring solving a quadratic equation at each maturity and strike and present results on the Japanese market.

Download or read book Notes On Stochastic Rates Dividends Volatilities in an Equity Framework written by Lionel Viet and published by . This book was released on 2012 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part 1 - Black-Scholes formulas are consistent with a diffusion in the respective forward neutral probability.Part 2 - Mixing Forward Neutral Probabilities for different maturities, we construct a probability more natural for non european payoffs, different from the Risk Neutral measure, that we call the Pricing Probability.Part 3 - Writing the Radon-Nikodym derivative for changing measure to the Pricing Probability, and the modified HJM relationship.Part 4 - We use a simple Ho amp; Lee model to get a sense of how the path-dependent hybrid terms impact the Stock diffusions. Due to hybrid effects, BS vols term structure is usually increasing.Part 5 - The Pricing Probability seems to be the natural Probability to be used to price Equity-Linked Structures with any kind of Hybrid Risks - ie all non Strictly European Structures. The alternative - working in the Risk Neutral Probability - would necessitate to recalibrate all volatility, correlation parameters from the Black / Black Scholes world (Forward Neutral Probabilities) to the Risk Neutral world.Part 6 - Some examples of Interest Rate models.Part 7 - Stochastic Dividends diffusions. Ho amp; Lee example.Part 8 - Cross-Currency framework. Ho amp; Lee example.Part 9 - Risky Curve Diffusions in the Survival Neutral Probabilities.Analogy with the Currency Quanto World.A quick look at Counterparty Risk and CVA adjustments.Part 10 - Multi-Underlying Framework. Ho amp; Lee example. Due to hybrid effects, BS correlations term structure is usually increasing.Part 11 - Stochastic Volatility Framework.A statistical bias between vol of realized vols and vol of implied vols.Variance Swaps on Spots, Variances Swaps on Forwards, European Options.Part 12 - Natural parametrizations of volsurfaces coherent with vol dynamics and risks, based on vol, volvol and correl spot/vol breakevens.Historical backtests of implied vs realized breakevens.Generalization with 6 parameters per Maturity.Part 13 - Correlation Skew and Stochastic Volatility.We show that we can calibrate a basket skew independently of individual skews without introducing a spot-dependent correlation: this is typically the case when individual vols move more with the basket spot than with individual spots.