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499
Empirical performance of alternative option pricing models
 Journal of Finance
, 1997
"... reserved. Readers may make verbatim copies of this document for noncommercial purposes by any means, provided that this copyright notice appears on all such copies. ..."
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Cited by 622 (18 self)
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reserved. Readers may make verbatim copies of this document for noncommercial purposes by any means, provided that this copyright notice appears on all such copies.
Efficient analytic approximation of American option values
 Journal of Finance
, 1987
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New Techniques to Extract Market Expectations from Financial Instruments
 Journal of Monetary Economics
, 1997
"... Central banks have several reasons for extracting information from asset prices. Asset prices may embody more accurate and more uptodate macroeconomic data than what is currently published or directly available to policy makers. Aberrations in some asset prices may indicate ..."
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Cited by 127 (4 self)
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Central banks have several reasons for extracting information from asset prices. Asset prices may embody more accurate and more uptodate macroeconomic data than what is currently published or directly available to policy makers. Aberrations in some asset prices may indicate
Closed Form Solutions for Term structure Derivatives with Log Normal Interest Rates
 Journal of Finance
, 1997
"... Abstract. We derive a unified term structure of interest rates model which gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zerocoupon bonds. The crucial assumption is that the simple interest rate over a fixed finite period that matches ..."
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Cited by 124 (1 self)
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Abstract. We derive a unified term structure of interest rates model which gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zerocoupon bonds. The crucial assumption is that the simple interest rate over a fixed finite period that matches the contract, which we want to price, is lognormally distributed. Moreover, this assumption is shown to be consistent with the HeathJarrowMorton model for a specific choice of volatility. 1.
Default and recovery implicit in the term structure of sovereign cds spreads. working paper
 of Sovereign CDS Spreads. Working Paper, MIT Sloan School of Management and Stanford Graduate School of Business
, 2005
"... This paper explores the nature of default arrival and recovery implicit in the term structures of sovereign CDS spreads. We argue that term structures of spreads reveal not only the arrival rates of credit events (λ Q), but also the loss rates given credit events. Applying our framework to Mexico, T ..."
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Cited by 116 (1 self)
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This paper explores the nature of default arrival and recovery implicit in the term structures of sovereign CDS spreads. We argue that term structures of spreads reveal not only the arrival rates of credit events (λ Q), but also the loss rates given credit events. Applying our framework to Mexico, Turkey, and Korea, we show that a singlefactor model with λ Q following a lognormal process captures most of the variation in the term structures of spreads. The risk premiums associated with unpredictable variation in λ Q are found to be economically significant and covary importantly with several economic measures of global event risk, financial market volatility, and macroeconomic policy. THE BURGEONING MARKET FOR SOVEREIGN CREDIT DEFAULT SWAPS (CDS) contracts offers a nearly unique window for viewing investors ’ riskneutral probabilities of major credit events impinging on sovereign issuers, and their riskneutral losses of principal in the event of a restructuring or repudiation of external debts. In contrast to many “emerging market ” sovereign bonds, sovereign CDS
The moment formula for implied volatility at extreme strikes
 Mathematical Finance
, 2004
"... Consider options on a nonnegative underlying random variable with arbitrary distribution. In the absence of arbitrage, we show that at any maturity T, the largestrike tail of the BlackScholes implied volatility skew is bounded by the square root of 2x/T, where x is logmoneyness. The smallest co ..."
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Cited by 78 (5 self)
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Consider options on a nonnegative underlying random variable with arbitrary distribution. In the absence of arbitrage, we show that at any maturity T, the largestrike tail of the BlackScholes implied volatility skew is bounded by the square root of 2x/T, where x is logmoneyness. The smallest coefficient that can replace the 2 depends only on the number of finite moments in the underlying distribution. We prove the moment formula, which expresses explicitly this modelindependent relationship. We prove also the reciprocal moment formula for the smallstrike tail, and we exhibit the symmetry between the formulas. The moment formula, which evaluates readily in many cases of practical interest, has applications to skew extrapolation and model calibration.
Do Bonds Span the Fixed Income Markets? Theory and Evidence for ‘Unspanned’ Stochastic Volatility
 Journal of Finance
, 2002
"... Most term structure models assume bond markets are complete, i.e., that all fixed income derivatives can be perfectly replicated using solely bonds. However, we find that, in practice, swap rates have limited explanatory power for returns on atthemoney straddles – portfolios mainly exposed to vola ..."
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Cited by 71 (1 self)
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Most term structure models assume bond markets are complete, i.e., that all fixed income derivatives can be perfectly replicated using solely bonds. However, we find that, in practice, swap rates have limited explanatory power for returns on atthemoney straddles – portfolios mainly exposed to volatility risk. We term this empirical feature “unspanned stochastic volatility ” (USV). While USV can be captured within an HJM framework, we demonstrate that bivariate models cannot exhibit USV. We determine necessary and sufficient conditions for trivariate Markov affine systems to exhibit USV. For such USVmodels, bonds alone may not be sufficient to identify all parameters. Rather, derivatives are needed.
The relative valuation of caps and swaptions: Theory and empirical evidence
 Journal of Finance
"... Although traded as distinct products, caps and swaptions are linked by noarbitrage relations through the correlation structure of interest rates. Using a string market model, we solve for the correlation matrix implied by swaptions and examine the relative valuation of caps and swaptions. We find th ..."
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Cited by 68 (10 self)
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Although traded as distinct products, caps and swaptions are linked by noarbitrage relations through the correlation structure of interest rates. Using a string market model, we solve for the correlation matrix implied by swaptions and examine the relative valuation of caps and swaptions. We find that swaption prices are generated by four factors and that implied correlations are lower than historical correlations. Longdated swaptions appear mispriced and there were major pricing distortions during the 1998 hedgefund crisis. Cap prices periodically deviate significantly from the noarbitrage values implied by the swaptions market. THE GROWTH IN INTERESTRATE SWAPS during the past decade has led to the creation and rapid expansion of markets for two important types of swaprelated derivatives: interestrate caps and swaptions. These overthecounter derivatives are widely used by many firms to manage their interestrate risk exposure and collectively represent the largest class of fixedincome options in the financial markets. The International Swaps and Derivatives Association