Interest Rate Caps “Smile” Too! But Can the LIBOR Market Models Capture the Smile?

Jarrow, Robert A.; Li, Haitao; Zhao, Feng

doi:10.1111/j.1540-6261.2007.01209.x

Cited by 112 publications

(93 citation statements)

References 46 publications

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“…However, they are contrary to the findings of Canina and Figlewske (1993) in equity market also where the choice of wider at-the-money band may lead to the bias in their research. The implied volatility bias in Figure 1 especially for short maturity options is also consistent with Jarrow, Li and Zhao (2007) and Deuskar, Gupta and Subrahmanyam (2008) which examine the patterns of volatility smile in long-term over-the-counter interest rate derivatives markets.…”

Section: ⅳ Gmm Regression Test Correcting For Autocorrelation and Hementioning

confidence: 50%

“…For long-term interest rate option markets, Jarrow, Li and Zhao (2007) examine the volatility smile in interest rate caps and floors, and find that even a multifactor term structure models augmented with stochastic volatility and jumps do not fully capture the volatility smile. Deuskar, Gupta and Subrahmanyam (2008) investigate the economic determinants of interest rate volatility bias for the over-the-counter interest rate caps and floors which have up to 10-year maturity.…”

Section: ⅰ Introductionmentioning

confidence: 99%

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Informational Content of Volatility Forecasts in Eurodollar Markets

Kim¹

2016

Glob Bus Financ Rev

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A B S T R A C TThe volatility of asset prices as a measure of risk in the financial market has motivated many financial economists and industry professionals, and induced the innovation in the financial markets. The paper studies how expectations of future volatility are formed, and whether or not historical or implied volatilities measures for different maturity and moneyness of options have any information to explain ex post actual volatility over the life of the options in Eurodollar futures and futures options markets. Employing the autocorrelation and heteroscedasticity consistent GMM regression test, we find that the volatilities implied in the at-the-money options tend to outperform the in-the-money or out-of-the-money implied volatilities and different definitions of historical volatilities. Keywords: Implied Volatility; Volatility Bias; Eurodollar Futures Options; GMM Regression Ⅰ. IntroductionGlobal financial markets have been growing rapidly for the past several decades and financial assets evolve to be more complicated as investors and market participants become more sophisticated. Futures and options contracts are the instruments that allow investors to capitalize the available information in the market while limiting risk to a predetermined level. Financial futures markets began in the late 1970's, about 150 years after commodity futures trading began. In spite of their late start, financial futures trading exceeded the trading of the sum of all other futures contracts combined after † Kwanho Kim Department of Economics, Chungbuk National University, 1 Chungdae-Ro Seowon-Gu, Cheongju, Republic of Korea Tel.: +82-43-261-3015; https://sites.google.com/site/financekkim/ E-mail: kimk@chungbuk.ac.kr the first decade. The Eurodollar futures are by far the most liquid of all financial futures contracts. This paper studies how expectations of future volatility are formed and whether or not historical or implied volatility have any information relevant to explain future realized volatility over the life of each option. The option pricing model is inverted to calculate the implied volatilities where it assumes that the volatility process is stationary and at most a deterministic function of time. Option valuation models were first developed by Black and Scholes (1973) and Merton (1973) for the European option, and the early exercise problem and stochastic volatility problem have been investigated by many researchers. Among others, Geske (1979) examines the valuation of options where stocks are considered as options on the value of a firm and the stock price follows a nonstationary random walk process. Thus, the volatility of the stock price is expected to fluctuate

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Section: ⅳ Gmm Regression Test Correcting For Autocorrelation and Hementioning

confidence: 50%

Section: ⅰ Introductionmentioning

confidence: 99%

Informational Content of Volatility Forecasts in Eurodollar Markets

Kim¹

2016

Glob Bus Financ Rev

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“…Unlike Gupta and Subrahmanyam (2005) [21], they find no advantage in moving beyond a one-factor model. Using 3 years of interest rate caps price data accross strikes, Jarrow, Li, and Zhao (2007) [37] show that even a three-factor model with stochastic volatility and jumps cannot completely capture the smile/skew patterns observed in this market.…”

Section: Previous Studiesmentioning

confidence: 99%

Choice of Interest Rate Term Structure Models for Assets and Liability Management

et al. 2008

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The working papers are produced by The University of Manchester -Manchester Business School and are to be circulated for discussion purposes only. Their contents should be considered to be preliminary. The papers are expected to be published in due course, in a revised form and should not be quoted without the authors' permission. Author(s) and affiliation AbstractThis paper compares the pricing and hedging performance of the LMM model against two spot-rate models, namely Hull-White and Black-Karasinski, and the more recent Swap Market Model from an Asset-Liability-Management (ALM) perspective. In contrast to previous studies in the literature, our emphasis here is on ALM and we use hedging performance on Bermudan swaptions to proxy risk management outcome of long-term mortgage loans. Our tests involve calibrating the four interest rate models to European swaption prices for EURO and USD over the period February 2005 to September 2007. The calibrated models are then used to price and hedge a constant 11-year Bermudan swaption portfolio using a series of interest rate swaps and a 1-year holding-revision period. Our empirical results show that, the calibrated parameters of all four models are stable and their pricing errors are small and comparable. No single model dominates in the pricing exercise. The hedging performance of all four models is similar for the Euro market. For the USD market, the short rate models perform marginally better than SMM and LMM. The HW model is marginally better than BK model in terms of model parameter stability and smaller pricing and hedging errors. The hedging performance of all four models is similar for the Euro market. For the USD market, the short rate models perform marginally better than SMM and LMM. The HW model is marginally better than BK model in terms of model parameter stability and smaller pricing and hedging errors. How to quote or cite this document

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“…Many studies, such as Han (2002), Jarrow, Li, and Zhao (2007), and Trolle and Schwartz (2007), also have documented the importance of stochastic volatility for pricing interest rate caps. While the level factor is automatically incorporated in existing methods, our new extension of A• t-Sahalia and Duarte (2003) is needed to incorporate the slope and volatility factors in our nonparametric estimation.…”

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confidence: 99%

“…For example, the standard LIBOR market models of Brace, Gatarek, and Musiela (1997) and Miltersen, Sandmann, and Sondermann (1997) assume that L k (t) follows a log-normal distribution and price caplet using the Black formula. The models of Jarrow, Li, and Zhao (2007) assume that L k (t) follows a ne jump-di usions of Du e, Pan, and Singleton (2000).…”

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confidence: 99%