The Empirical Performance of Option Based Densities of Foreign Exchange
read more
Citations
Forecasting Austrian Inflation
The Forecasting Performance of German Stock Option Densities
Evaluating density forecasts from models of stock market returns
Comments on O. Issing: “Europe’s hard fix: the Euro area”
Are Monetary Rules and Reforms Complements or Substitutes? : A Panel Analysis for the World versus OECD Countries
References
Remarks on a Multivariate Transformation
The stationary bootstrap
Prices of State-Contingent Claims Implicit in Option Prices
Evaluating Density Forecasts with Applications to Financial Risk Management
Recovering Probability Distributions from Option Prices
Frequently Asked Questions (16)
Q2. What future works have the authors mentioned in the paper "The empirical performance of option- based densities of foreign exchange" ?
Thus, the authors did not use all price data of options which expired within ten days of the trading day, options that are perhaps best designed to forecast the future exchange rate at one and seven days ahead. Amore powerful test might have much to say about which of the densities represent the market ’ s true assessment of possibilities. Malz, A. M. [ 1997 ]: ” Estimating the Probability Distribution of the Future Exchange Rate from Option Prices, ” The Journal of Derivatives, 4, pp. 18-36. These densities can be computed daily, and thus form a useful policy tool, as well as providing an important set of data with which to test deeper theories of foreign exchange determination.
Q3. Why is the sample distribution function dCvM calculated?
Because the sample distribution functiondCvM and all bootstrapped sample distribution functions CvMb are step functions, the integral expression in CvMb is calculated directly.
Q4. How long does prob suboptimally affect the bootstrap?
as long as prob → 0 and Nprob → ∞ fundamental consistency properties of the bootstrap are unaffected by choosing prob suboptimaly.
Q5. How do the authors handle the end effects of a block?
End effects (in case of a block going beyond the last observation) are handled by ordering the observations in a circle, so that the series ”restarts” after the last observation.
Q6. What is the method used to calculate the risk neutral density of the underlying futures contract?
The method adopted in this paper to calculate the risk neutral density in this case is to first estimate the underlying process of the underlying futures contract for foreign exchange, based on the traded price of the American puts and calls reported for the end of the trading day.
Q7. How did the value function of an option quickly converge to the theoretical value?
for a wide range of ω, calculation of the value of an option quickly converged to the theoretical true value where these were known.
Q8. Why is the CvM test of lower power than other more specific tests?
The tests of the densities that are explored in this paper are of lower power than other more specific tests in part because of their all encompassing character.
Q9. What is the definition of a risk neutral density?
It is well known that with complete markets, a sufficiently rich set of European options prices implies a state price density that one may interpret as a probability density over the price that underlies the derivative contract, if agents are risk neutral.
Q10. What is the way to test the departures for each prn?
One possible way to jointly test the departures for each prn would be to sum up their squares, as was suggested by Karl Pearson (1905) very early in the history of specification tests.
Q11. What is the simulated density of the diffusion function t(X,,?
The simulated density bΠt of the diffusion function σ̂t(X, τ, bβ) is on the right side at the top and bπt, the corresponding first empirical derivative of bΠt with respect to K, is situated at the bottom.
Q12. How is the inverse probability of the realized thirty day ahead spot correlated with the same number?
The inverse probability of the realized thirty day ahead spot at time, t, is correlated with the same corresponding number at time t− 1, because the spot shares twenty-nine days of history.
Q13. What is the probability of drawing a block of length L?
The procedure requires a sample of random blocks of random lengths out of the original time series, where the length L of each block is drawn from a geometric distribution, so that the probability of drawing a block of length L is (1−prob)L−1prob for L = 1, 2, ....
Q14. What are the tests that the authors use to evaluate implied densities?
Next the authors describe the tests that the authors use to evaluate their implied densities, especially those that take into account the time series nature of the overlapping windows of the forecasts.
Q15. What is the second group of conclusions?
The second group of conclusions concern the thirty to ninety day horizons where their tests clearly do not reject any of the specifications of the diffusion process as forecasting densities.
Q16. How do the authors circumvent the problem of ”too small” values of t?
In another version of this paper the authors circumvent the problem of ”too small” values of σ̂t(X, τ, bβ)2, and therefore of values of α below 1/6, by augmenting, if necessary, the state space increment ∆h , so that the critical value of α is only reached by smaller values of σ̂t(X, τ, bβ)2.