Option-Implied Probability Distributions and Currency Excess Returns

Malz, Allan M.

doi:10.2139/ssrn.943500

Cited by 57 publications

(60 citation statements)

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“…Parametric specifications include a mixture of lognormals [Ritchey (1990), Melick and Thomas (1997)], polynomials multiplied by a lognormal [Madan and Milne (1994)], a generalized beta [Anagnou, Bedendo, Hodges and Tompkins (2002)] and the densities of continuous-time price processes when volatility is stochastic [Bates (2000), Jondeau and Rockinger (2000)]. Other approaches include maximum entropy densities [Buchen and Kelly (1996)], non-parametric estimates [Ait-Sahalia and Lo (1998)], multi-parameter discrete distributions [Jackwerth and Rubinstein (1996)] and densities implied by smile functions, defined by either polynomials [Shimko (1993), Malz (1997)] or spline functions [Bliss and Panigirtzoglou (2002a)]. …”

Section: Introductionmentioning

confidence: 99%

Closed-form Transformations from Risk-neutral to Real-world Distributions

Liu¹,

et al. 2004

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Risk-neutral (RN) and real-world (RW) densities are derived from option prices and risk assumptions, and are compared with densities obtained from historical time series. Two parametric methods that adjust from RN to RW densities are investigated, firstly a CRRA risk aversion transformation and secondly a statistical calibration.Both risk transformations are estimated using likelihood techniques, for two flexible but tractable density families. Results for the FTSE-100 index show that densities derived from option prices have more explanatory power than historical time series.Furthermore, the pricing kernel between RN & RW densities may be more regular than previously reported and a more reasonable risk aversion function is estimated.

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Section: Introductionmentioning

confidence: 99%

Closed-form Transformations from Risk-neutral to Real-world Distributions

Liu¹,

et al. 2004

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“…Figures B1 -B4 in Appendix B demonstrate the relatively high liquidity of out-of-the-money options on Eurodollar futures. 10 Interpolating implied volatilities over deltas was first performed by Malz (1997).…”

Section: Interpolation Of Option Pricesmentioning

confidence: 99%

“…Breeden and Litzenberger (1978) directly relate the second partial derivative of call option price with respect to strike to the probability density function (pdf) assigned to the underlying. Since these results were established, option prices have been applied in various cases to derive estimates of market-assigned probabilities for different underlying securities or commodities (for example, see Malz (1997) in the case of foreign exchange rates, or Melick and Thomas (1997) and Datta, Londono, and Ross (2014) in the case of oil prices).…”

Section: Introductionmentioning

confidence: 99%

Option-Implied Libor Rate Expectations across Currencies

Gebbia

2016

internationalfinance

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In this paper, I study risk-neutral probability densities regarding future Libor rates denominated in British pounds, euros, and US dollars as implied by option prices. I apply Breeden and Litzenberger's (1978) result regarding the relationship between option prices and implied probabilities for the underlying to estimate full probability density functions for future Libor rates. I use these estimates in case studies, detailing the evolution of probabalistic expectations for future Libor rates over the course of several important market events. Next, I compute distributional moments from density functions estimated for fixed horizons and test for Granger causality across the three Libor rate distributions considering their mean, standard deviation, skewness, and kurtosis. I further break these relationships down by various fixed horizon lengths, as well as the slope and curvature in the term structure of moments over different horizons. The results show a rich interconnectedness among these three Libor rates that extends well beyond levels of future mean expectations. JEL Classifications: C14, E43, G13

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“…Our rationale is that derivative markets have been shown to exhibit some degree of forward-looking element into their pricing. 8 Foreign exchange is the largest and most liquid financial market by far. 9 It is also very effective in absorbing new information rapidly, suggesting that much of that information flow is reflected in the underlying time series of exchange rates volatilities.…”

Section: Introductionmentioning

confidence: 99%