The Randomized Heston Model
| Autor: | Antoine Jacquier, Fangwei Shi |
|---|---|
| Přispěvatelé: | Engineering & Physical Science Research Council (EPSRC) |
| Rok vydání: | 2019 |
| Předmět: |
Mathematics
Interdisciplinary Applications Social Sciences SMILE ASYMPTOTICS Implied volatility 01 natural sciences STOCHASTIC VOLATILITY 010104 statistics & probability IMPLIED VOLATILITY JUMPS Computer Science::Computational Engineering Finance and Science Business & Economics TERM STRUCTURE 0102 Applied Mathematics 0502 economics and business Applied mathematics Point (geometry) 0101 mathematics Heston Mathematics LARGE DEVIATIONS Numerical Analysis Science & Technology asymptotic expansion 050208 finance Stochastic volatility 60F10 91G20 91B70 Applied Mathematics 05 social sciences Social Sciences Mathematical Methods Variance (accounting) Business Finance Heston model Physical Sciences Large deviations theory Asymptotic expansion q-fin.PR Mathematical Methods In Social Sciences BEHAVIOR Finance |
| Zdroj: | SIAM Journal on Financial Mathematics. 10:89-129 |
| ISSN: | 1945-497X |
| Popis: | We propose a randomised version of the Heston model-a widely used stochastic volatility model in mathematical finance-assuming that the starting point of the variance process is a random variable. In such a system, we study the small- and large-time behaviours of the implied volatility, and show that the proposed randomisation generates a short-maturity smile much steeper (`with explosion') than in the standard Heston model, thereby palliating the deficiency of classical stochastic volatility models in short time. We precisely quantify the speed of explosion of the smile for short maturities in terms of the right tail of the initial distribution, and in particular show that an explosion rate of~tγ (γ∈[0,1/2]) for the squared implied volatility-as observed on market data-can be obtained by a suitable choice of randomisation. The proofs are based on large deviations techniques and the theory of regular variations. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|