A multicurrency extension of the lognormal interest rate Market Models

Schlögl, Erik

doi:10.1007/s007800100054

Cited by 65 publications

(51 citation statements)

References 17 publications

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“…The literature on market models has grown substantially in recent years, and it is impossible to give a full list. Apart from the standard references (Miltersen / Sandmann / Sondermann (1997), Brace / Gatarek / Musiela (1997) and Jamshidian (1997)), the mathematical methods in E. Schlögl's (1999) multicurrency extension of the Libor market model are related to the methods in this paper. Schlögl also analyses the problems that arise when several numeraires and martingale measures have to be used in parallel.…”

Section: Introductionmentioning

confidence: 99%

A Libor Market Model with Default Risk

Schönbucher

2001

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. ABSTRACT. In this paper a new credit risk model for credit derivatives is presented. The model is based upon the 'Libor market' modelling framework for default-free interest rates. We model effective default-free forward rates and effective forward credit spreads as lognormal diffusion processes, and recovery is modelled as a fraction of the par value of the defaulted claim. The newly introduced survival-based pricing measures are a valuable tool in the pricing of defaultable payoffs and allow a straightforward derivation of the no-arbitrage dynamics of forward rates and forward credit spreads. The model can be calibrated to the prices of defaultable coupon bonds, asset swap rates and default swap rates for which closed-form solutions are given. For options on default swaps and caps on credit spreads, approximate solutions of high accuracy exist. This pricing formula for options on default swaps is made exact in a modified modelling framework using an analogy to the swap measure, the default swap measure. Terms of use: Documents in

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Section: Introductionmentioning

confidence: 99%

A Libor Market Model with Default Risk

Schönbucher

2001

SSRN Journal

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“…To define continuous time dynamics for a zero-coupon bond, interpolation techniques are available (see, for example, [Schlögl(a), 2002;Piterbarg, 2004;Davis and Mataix-Pastor, 2009;Beveridge and Joshi, 2009] We consider here the linear interpolation scheme, proposed in [Schlögl(a), 2002], which reads:…”

Section: Multi-currency Model With Interest Rate Smilementioning

confidence: 99%

On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates

Grzelak

Oosterlee

2012

Applied Mathematical Finance

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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 HullWhite [Hull and White, 1990]. We then extend the framework by modeling the interest rate by a stochastic volatility displaced-diffusion Libor Market Model [Andersen and Andreasen, 2002], 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.

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“…In Section 3.2, the optimal foreign currency value, x t , was presented as the solution to Equation (13).…”

Section: A Currency Call Option Distribution For Currencies With Uncomentioning

confidence: 99%

“…Secondly, the paper views foreign currency rates as being dependent on macroeconomic variables. Many existing models overlook macroeconomic variables preferring to be market-based ( [12] [13]), or jump diffusion-based ( [14] [15] [16]). Thirdly, this paper recognizes that options have higher volatility than the foreign currency.…”

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confidence: 99%

Pricing Currency Call Options

Abraham¹

2018

TEL

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This paper presents a theoretical model to price foreign currency call options. Currency options are employed in international trade to reduce the risk of loss due to the reduction of revenues obtained in depreciating foreign currency for an exporter, or the escalation of expense from appreciating foreign currency for an importer. Other users include banks and hedge funds who engage in currency speculation. Given the fluctuation of option prices over time, the model describes the distribution of foreign currency as a Weiner process for macroeconomically constrained foreign currencies followed by a Laplace distribution for unconstrained currencies. In a departure from existing currency option models, this model expresses foreign currencies as dependent upon the change in macroeconomic variables, such as inflation, interest rates, and government deficits. The distribution of currency calls is described as a Levy process in the context of an option trader's risk preferences to account for the multiple discontinuities of a jump process. The paper concludes with three models of price functions of the Weiner process for Euro-related currency options, a Weiner process for stable currency options, and a Levy-Khintchine process for volatile currency calls.

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A multicurrency extension of the lognormal interest rate Market Models

Cited by 65 publications

References 17 publications

A Libor Market Model with Default Risk

A Libor Market Model with Default Risk

On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates

Pricing Currency Call Options

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