Pricing realized variance options using integrated stochastic variance options in the Heston stochastic volatility model
Bibliographic record
Abstract
This paper presents a numerical method to price European options on realized variance. A European realized variance option is an option where payoff depends on the time of maturity, on the observed variance of the log-returns of the stock prices in a preassigned sequence of time values t_i , i = 0, 1, . . . , N . The realized variance is the variance observed in the sample of the log-returns considered, so that the value at maturity of the realized variance option depends on the discrete sample of the log-returns of the stock prices observed at the preassigned dates t_i , i = 0, 1, . . . , N . The method proposed to approximate the price of these options is based on the idea of approximating the discrete sum that gives the realized variance with an integral, using as model of the dynamics of the log-return of the stock price the Heston stochastic volatility model. In this way the price of a realized variance option is approximated with the price of an integrated stochastic variance option where payoff depends on the time of maturity and on the integrated stochastic variance. The integrated stochastic variance option is priced with the method of discounted expectations. We derive an integral representation formula for the price of this last kind of options. This integral formula reduces to a one dimensional Fourier integral in the case of the most commonly traded options that have a simple payoff function. The method has been validated on some test problems. The numerical experiments show that the approach suggested in this paper gives satisfactory approximations of the prices of the realized variance options (relative error 10^ [-2] , 10^[-3] ). This approach also allows substantial savings of computational time when compared with the Monte Carlo method used to evaluate with approximately the same accuracy. The website http://www.econ.univpm.it/recchioni/finance/w4 contains auxiliary material that can help in the understanding of this paper and makes available to the interested users the codes that implement the numerical method proposed here to price realized variance options. The use of these codes on a computing grid has been made user friendly developing a dedicated application using the software Symphony (that is, a Service Oriented Architecture (SOAM) software of Platform Computing Toronto, Canada). The website mentioned above makes this Symphony application available to the users.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".