Pricing Variance Swaps for Stochastic Volatilities with Delay and Jumps
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Bibliographic record
Abstract
We study the valuation of the variance swaps under stochastic volatility with delay and jumps. In our model, the volatility of the underlying stock price process not only incorporates jumps, which are found to be active empirically, but also exhibits past dependence: the behavior of a stock price right after a given time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:math> depends not only on the situation at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:math> but also on the whole past (history) of the process <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:math> up to time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:math> as well. The jump part in our model is finally represented by a general version of compound Poisson processes. We provide some analytical closed forms for the expectation of the realized variance for the stochastic volatility with delay and jumps. We also present a lower bound for delay as a measure of risk. As applications of our analytical solutions, a numerical example using S&P 60 Canada Index (1998–2002) is then provided to price variance swaps.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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