Real-World and Risk-Neutral Probabilities in the Regulation on the Transparency of Structured Products

2013 ◽  
Author(s):  
Luca Giordano ◽  
Giovanni Siciliano
Keyword(s):  
Real World ◽  
Structured Products ◽  
Risk Neutral ◽  
Risk Neutral Probabilities

scholarly journals A STRUCTURAL RISK-NEUTRAL MODEL OF ELECTRICITY PRICES

2009 ◽  
Vol 12 (07) ◽  
pp. 925-947 ◽  
Author(s):  
RENÉ AÏD ◽  
LUCIANO CAMPI ◽  
ADRIEN NGUYEN HUU ◽  
NIZAR TOUZI
Keyword(s):  
Electricity Market ◽  
Structural Aspect ◽  
Electricity Prices ◽  
Forward Contracts ◽  
Spot Prices ◽  
Modeling Methodology ◽  
Risk Neutral ◽  
Risk Neutral Probabilities ◽  
Crude Approximation ◽  
Forward Prices

The objective of this paper is to present a model for electricity spot prices and the corresponding forward contracts, which relies on the underlying market of fuels, thus avoiding the electricity non-storability restriction. The structural aspect of our model comes from the fact that the electricity spot prices depend on the dynamics of the electricity demand at the maturity T, and on the random available capacity of each production means. Our model explains, in a stylized fact, how the prices of different fuels together with the demand combine to produce electricity prices. This modeling methodology allows one to transfer to electricity prices the risk-neutral probabilities of the market of fuels and under the hypothesis of independence between demand and outages on one hand, and prices of fuels on the other hand, it provides a regression-type relation between electricity forward prices and forward prices of fuels. Moreover, the model produces, by nature, the well-known peaks observed on electricity market data. In our model, spikes occur when the producer has to switch from one technology to the lowest cost available one. Numerical tests performed on a very crude approximation of the French electricity market using only two fuels (gas and oil) provide an illustration of the potential interest of this model.

scholarly journals A NOTE ON REAL-WORLD AND RISK-NEUTRAL DYNAMICS FOR HEATH–JARROW–MORTON FRAMEWORKS

2020 ◽  
Vol 23 (03) ◽  
pp. 2050020
Author(s):  
DAVID CRIENS
Keyword(s):  
Brownian Motion ◽  
Real World ◽  
Random Measure ◽  
Jump Condition ◽  
Poisson Random Measure ◽  
Change Of Measure ◽  
The Real ◽  
Infinite Dimensional ◽  
Risk Neutral ◽  
Equivalent Change Of Measure

We show that for time-inhomogeneous Markovian Heath–Jarrow–Morton models driven by an infinite-dimensional Brownian motion and a Poisson random measure an equivalent change of measure exists whenever the real-world and the risk-neutral dynamics can be defined uniquely and are related via a drift and a jump condition.

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

2004 ◽  
Author(s):  
Xiaoquan Liu ◽  
Mark B. Shackleton ◽  
Stephen J. Taylor ◽  
Xinzhong Xinzhong Xu
Keyword(s):  
Closed Form ◽  
Real World ◽  
Risk Neutral

Recovering Risk Neutral Densities from Option Prices: A New Approach

2008 ◽  
Vol 43 (4) ◽  
pp. 1037-1053 ◽  
Author(s):  
Leonidas S. Rompolis ◽  
Elias Tzavalis
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Empirical Evidence ◽  
Neutral Density ◽  
Option Prices ◽  
Exponential Form ◽  
New Approach ◽  
Risk Neutral ◽  
Risk Neutral Probabilities ◽  
Risk Neutral Density

AbstractIn this paper we present a new method of approximating the risk neutral density (RND) from option prices based on the C-type Gram-Charlier series expansion (GCSE) of a probability density function. The exponential form of this type of GCSE guarantees that it will always give positive values of the risk neutral probabilities, and it can allow for stronger deviations from normality, which are two drawbacks of the A-type GCSE used in practice. To evaluate the performance of the suggested expansion of the RND, the paper presents simulation and empirical evidence.

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