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Valuation with RiskNeutral Probabilities: Attempts to Quantify Q
"... 2 Riskadjusted discount rates.................................................................2 2.1 Interpretation of common practice....................................................2 2.2 Constant discount rate and constant risk premium.............................3 ..."
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2 Riskadjusted discount rates.................................................................2 2.1 Interpretation of common practice....................................................2 2.2 Constant discount rate and constant risk premium.............................3
1 Implied (risk neutral) probabilities, and betting odds
"... ABSTRACT We show that the well known equivalence between the "fundamental theorem of asset pricing" and the "dutch book argument " consists, in reality, of two parts: the first concerning the existence of a risk free investment, and the second the possibility of arbitrages. We s ..."
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;implied probabilities " are formally coherent, and the fundamental theorem of assets pricing (FTAP). This last states that in a market where one euro may be alternatively invested to give the random amount S or the certain amount r, no arbitrage is possible if and only if a (risk neutral: "
Financial Stability Report November 2002 RiskNeutral Probability Densities1
"... In a recent article, Andrade and Tabak (2001) demonstrated that implicit exchange volatility extracted from exchange options negotiated on the domestic market contains more information than models based on temporal series, such as in the ..."
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In a recent article, Andrade and Tabak (2001) demonstrated that implicit exchange volatility extracted from exchange options negotiated on the domestic market contains more information than models based on temporal series, such as in the
Recovering RiskNeutral Probability Density Functions from Options Prices using Cubic Splines
, 2004
"... We present a new approach to estimate the riskneutral probability density function (pdf) of the future prices of an underlying asset from the prices of options written on the asset. The estimation is carried out in the space of cubic spline functions, yielding appropriate smoothness. The resulting ..."
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We present a new approach to estimate the riskneutral probability density function (pdf) of the future prices of an underlying asset from the prices of options written on the asset. The estimation is carried out in the space of cubic spline functions, yielding appropriate smoothness. The resulting
Tomul LVI ŞtiinŃe Economice 2009 ROBUST RECOVERY OF THE RISK NEUTRAL PROBABILITY DENSITY FROM OPTION PRICES
"... We present in this paper a robust numerical procedure that allows extracting the risk neutral probability density data from a set of quoted European option prices. The procedure does not use any specific evolution model for the underlying; the probability density is the solution of a fitting problem ..."
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We present in this paper a robust numerical procedure that allows extracting the risk neutral probability density data from a set of quoted European option prices. The procedure does not use any specific evolution model for the underlying; the probability density is the solution of a fitting
1 Implied (risk neutral) probabilities, betting odds and prediction markets
"... ABSTRACT We show that the well known equivalence between the "fundamental theorem of asset pricing" and the "dutch book argument " consists, in reality, of two parts: the first concerning the existence of a risk free investment, and the second the possibility of arbitrages. We a ..."
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ABSTRACT We show that the well known equivalence between the "fundamental theorem of asset pricing" and the "dutch book argument " consists, in reality, of two parts: the first concerning the existence of a risk free investment, and the second the possibility of arbitrages. We
AMERICAN OPTION PRICING WITH IMPRECISE RISKNEUTRAL PROBABILITIES: FROM PLAIN INTERVALS TO FUZZY SETS
"... The aim of this paper is to price an American style option when there is uncertainty on the volatility of the underlying asset. An option contract can be either European or American style depending on whether the exercise is possible only at or also before the expiry date. A European option gives th ..."
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The aim of this paper is to price an American style option when there is uncertainty on the volatility of the underlying asset. An option contract can be either European or American style depending on whether the exercise is possible only at or also before the expiry date. A European option gives the
FEDERAL RESERVE BANK OF MINNEAPOLIS BANKING AND POLICY STUDIES Methodology for Estimating Risk Neutral Probability Density Functions
"... We estimate risk neutral probability density functions (RNPDs) for a variety of different asset classes using a variation of the technique developed by Shimko (1993). This procedure involves fitting a curve to the implied volatilities of a series of options and expressing the volatility as a functio ..."
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We estimate risk neutral probability density functions (RNPDs) for a variety of different asset classes using a variation of the technique developed by Shimko (1993). This procedure involves fitting a curve to the implied volatilities of a series of options and expressing the volatility as a
1 Pricing VIX Futures on Affine Stochastic Volatility Models with Simultaneous StateDependent Jumps both in the S&P 500 Price and Variance Processes: Evidence from Integrated Physical and RiskNeutral Probability Measures
, 2006
"... The paper presents alternate stochastic variance models of VIX time evolution, and develops closedform solutions to the fair price of VIX futures. The derivation for theoretical futures prices is based upon the conditional moments of VIX squared on affine stochastic volatility models with simultane ..."
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with simultaneous jumps both in the asset price and variance processes. An integrated analysis of spot and option prices, or equivalently integrated volatility and VIX time series, is proposed to estimate monthlyupdated model parameters and the market prices of risks. Existing literature, however, has not provided
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