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Abstract This paper uses option pricing to examine how the presence of hazardous materials affects real estate value.
References Brennan, Michael J. Google Scholar Capozza, Dennis R. Google Scholar Dewees, Donald N. Google Scholar Fischer, Stanley. Google Scholar Fisher, Jeffrey D. Google Scholar Friedman, Milton. Google Scholar Margrabe, William. Google Scholar Paddock, James L.
Google Scholar Quigg, Laura. Google Scholar Samuelson, Paul A. Google Scholar Shimko, David C. Google Scholar Download references.
Maurice Tse Authors George H. Lentz View author publications. However, this method could not cover the leptokurtic distribution after a certain level of exercise prices. Hamdi and Lemennicier compared six methods of RND extraction. They find that mixing log-normal method as well as Hermite polynomials and jumping model fits best historical densities.
The more the deadline is approaching, the more traders are confident in their expectations and show less risk aversion. Humphreys [ 34 ] suggested that uncertainty embodied in the densities tended to decline as we approached the expiration date and a very few exchanges usually took place on days immediately preceding this date.
Indeed, the distributions of probability densities show that traders are more confident in their expectations for the first date. According to Table 1 , the market is twice more confident on its expectation about underlying price expectation on the first maturity than the second farthest of 34 days. Also, note that the probability granted by the market to an extreme disturbance increases by more than times.
To analyze the dynamics of changes in attitudes, in particular risk perception, it is imperative to eliminate bias caused by daily maturity variation, which does not allow comparing the evolution of densities. Melik and Thomas [ 20 ] discussed the problem of daily change in the maturity options as well as that of replacing contracts which reached maturity.
One idea was to incorporate the dependence of maturity explicitly in the functional of the probability density. Butler and Davies [ 35 ] applied a correction of this kind to the implied probability densities in the interest rate contracts on three-month Euro-sterling.
The major drawback of this idea was that, using the Black-Scholes model, the density would be a log-normal, so it did not reflect the distribution asymmetry and the fear of extreme shock.
The second method is to freely estimate probability densities and to correct the results under the dependence of maturity. The authors were faced with the daily variation problem maturities in option contracts when exploring two areas, the first topic being the study of the predictive power of implied volatility of future changes in assets and the second being the dynamic analysis of daily changes in attitudes of agents through risk neutral densities.
Panigirtzoglou and Proudman [ 36 ] developed a method for obtaining a constant maturity series based on an interpolation of the implicit volatilities. This technique consisted of obtaining a smooth function of the smile via the technique of cubic spline. This method has been used by several subsequent works in analyzing the behavior of agents via the RND evolution. Indeed, this technique allowed Bliss and Panigirtzoglou [ 37 ] to estimate the implied risk aversion at different horizons.
Lynch and Panigirtzoglou [ 4 ] analyzed the evolution of the risk neutral densities extracted from constant maturity option prices. The major drawback of the method of Panigirtzoglou and Proudman [ 36 ] on which all this work was based was that, to get the price of options for a fixed maturity horizon, the authors were forced to go through a pricing model Black-Scholes model to extract the price from implied volatilities.
Indeed, this model and even every other pricing model were subject to much criticism. We developed a new option price of obtaining constant maturity approach fully nonparametric which has the advantage of not resorting to any pricing model. To compare the daily evolution of the risk neutral densities and collect time continuous indicators measuring the above variables, we developed an approach similar to that of Panigirtzoglou and Proudman [ 36 ]. These authors developed a method to obtain a series of constant maturity option prices based on an interpolation of the implicit volatilities with cubic spline.
The major drawback of the method of Panigirtzoglou Proudman [ 36 ] related to the fact that these authors were forced to go through a pricing model Black-Scholes model [ 22 ] to extract prices from implied volatilities. We have developed a new fully nonparametric approach to obtain constant maturity option price series which has the advantage of not resorting to any pricing model inspired from Ait-Sahalia and Lo [ 25 ] using kernel smoothing.
The method of Ait-Sahalia and Lo [ 25 ] supposed that this surface was smooth enough that the value at a given time could be calculated by taking the weighted average of all neighboring points.
The weight given to each neighboring point decreased as the point was located farther from the target point. To calculate the corresponding implied volatility, the authors used a kernel density function which included smoothing parameter that indicated a weighted average of the neighboring points to include.
On this volatility surface, the corresponding value of implied volatility could be identified for each couple ratio, remaining time to maturity see Figure 2. Kermiche [ 39 ] extracted from the volatility surface corresponding smile curves for one-, three-, and six-month maturity.
Then, she uses the Black-Scholes model for the corresponding options prices. We used the method of Ait-Sahalia and Lo [ 25 ] to directly build a price surface to avoid any bias in pricing, and we adapted the smoothing parameters used by these authors. Indeed, their goals were to build a sufficiently smooth surface to be interpretable. The choice of parameters of the kernel function is forced to produce a sufficiently smooth surface while getting less biased values possible.
Our goal is just to get the least biased option prices. We try to optimize the choice of parameters in this direction regardless of the constraint of having smooth surfaces see Figure 2. The principle of the kernel regression is based on smoothing techniques. It seeks to estimate the link function at any point. This method is developed by Nadaraya and Watson [ 40 ].
The kernel estimator kernel estimate of the link function evaluated at the point noted is defined by. The link function evaluated at point is the weighted sum of the observations with , where the weights are dependent on. The function where defines the weight to be assigned to the couple of observations in the value of the link function evaluated at -axis of. Generally, the more the points are close to , the more the weight will be important: decreases with distance.
These weights depend on kernel function that represents the probability density functions. A kernel function satisfies the following properties: i.
Different kernel functions can be used uniform, triangular, quadratic, BiWeight, Epanechnikov, and Triweight. Generally, the choice of the kernel function slightly influences the estimation results. The only notable exception is related to the use of a uniform kernel function that can yield different results from other functions. The parameter represents the distance beyond which the observations have a light weight in the value of. This parameter represents the radius of the values of window around , the weight of which is significantly influential in computing.
This window magnitude is 2. In our sample, there are always options with an initial maturity of 1 and 2 months. Therefore, there is always a close observation of less than 15 days of the estimated value. In our study, since there is no advantage of having smooth surfaces but a less biased interpolation, we set the smoothing parameter as of the maximum distance that can separate the little reckoning of observation: In the obtained surface, we can get every day the price of option contracts defined by the pair maturity, mean Figure 3.
This technique has two advantages. Firstly it is performed directly on price and not on implied volatilities, which helps avoid any bias caused by the use of a model of pricing such as that of Black and Scholes [ 22 ]. Secondly, it optimizes the choice s of the kernel function parameter in order to obtain the least biased possible prices. To test the robustness of the method, we perform an interpolation of the price of options maturing on the last Friday of the second coming months, through the price of other options traded on the market.
Then, we compare the series obtained via the kernel technique and the observed series. The interpolation results seem to be acceptable. Indeed, the interpolated series and the observed are nearly coincident. We calculate for 30 random chosen days the mean error of the interpolated price compared to that observed for the puts and calls traded.
Table 2 shows the absolute values of the average differences between the observed prices and the interpolated calls and puts; indeed The interpolation error average is 3. The presented method is helpful to deeply analyze financial market dynamics and traders beliefs evolutions. We apply this method on Canadian market during period from 1 January to 31 December to extract 3 different indicators related to the evolution of asymmetry perception, extreme risk fear, and belief heterogeneity.
Asymmetry perception can be obtained comparing the lower anticipated value at the maturity to the highest index values and this is summarized in Figure 6. We collected from obtained densities the difference between these two corresponding probabilities: with being most anticipated value. The evolution of the series during the study period is summarized in Figure 7.
Statistics are presented in Table 3. This reference to the asymmetry of the price of options is relative to market expectations and reflected the margin of safety required by investors to hedge against the risk of adverse changes in asset prices financial. The causality test Table 4 shows that the fear of asymmetry is one of the influential variables in the overall risk perception in the markets.
Conversely, this fear of asymmetry increases with market volatility. Indeed, if the market is quite volatile and risky, agents require a higher margin to compensate for the risk resulting in an asymmetry in the prices of options contracts. We have assimilated the leptokurtic effect of the probability distribution that has values below or above Mathematically, The graphic analysis Figure 8 shows that during the first half of the agents develop a growing fear of underlying extreme variation.
When we explore Table 5 , we can conclude that the market gives 1. The Granger causality summarized in Table 6 shows that the fear of extreme shock is affected by changes in the market volatility index. However, this fear does not significantly influence the VIX. Options prices, like any financial asset, are the result of balancing by operative on the market.
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