Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives: Introduction to Stochastic Volatility Models

By Jean-Pierre Fouque 3, George Papanicolaou, Ronnie Sircar, Knut Sølna. 2011

248 citations recorded by the source corpus.

Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/d82b094123f9d21efa35c5592cdec0e7c0827aac

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Citations in the corpus

Productivity Losses from Financial Frictions: Can Self-Financing Undo Capital Misallocation? (2014, methodology): “The same notion of persistence of an ergodic stochastic process is also used in mathematical finance (Fouque et al., 2011), where θ is also called the “time scale” of the process, with a short time scale (low θ) corresponding to low persistence or fast mean reversion.”
A regime-switching Heston model for VIX and S&P 500 implied volatilities (2014, methodology): “In general, the operators M̂ and L̂n do not commute, so we cannot write a solution of the form in [21] (that is, P̂1 6= τM̂P̂0).”
EXPLICIT IMPLIED VOLATILITIES FOR MULTIFACTOR LOCAL‐STOCHASTIC VOLATILITY MODELS (2013, unknown): “Fouque et al. (2012) (see also Fouque et al. (2011)) derive an asymptotic expansion for general multiscale stochastic volatility models us-ing combined singular and regular perturbation theory.”
Option pricing under hybrid stochastic and local volatility (2013, methodology): “After estimating σ̄ (the effective historical volatility) from the risky asset price returns and confirming from the historical asset price returns that volatility is fast mean-reverting as in Fouque et al. (2011), fit (43) to the implied volatility surface I to obtain V ∗ i , i = 2, 3.”
Statistical inference for Vasicek-type model driven by Hermite processes (2017, background): “ed, any mean-reverting model in discrete or continuous time can be taken as a model for stochastic volatility. Classical texts can be consulted for this modeling idea; also see the research monograph [10]. Our paper proposes extensions in the type of tail weights for these processes. We acknowledge ”
PORTFOLIO OPTIMIZATION AND STOCHASTIC VOLATILITY ASYMPTOTICS (2017, methodology): “In particular, by Lemma 4.9 in Fouque et al. (2011), the diffusion process Zδt with infinitesimal generator δM2 +√ δM1 has moments of all order uniformly bounded in δ for t ≤ T, that is, for any k ∈ IN, we have supt≤T IE{|Zδt |k} ≤ Ck(T, z) where Ck(T, z) may depend on (k, T, z) but not on δ ≤ 1.”
Heston stochastic vol-of-vol model for joint calibration of VIX and S&P 500 options (2017, methodology): “Therefore, using the well-known arguments of Fouque et al. (2011), we might choose: • PS0 = PS0(t, s, v, z) and PS1,0 = PS1,0(t, s, v, z) independent of y; • PS0 satisfing 〈LS2 〉PS0 = 0;• PS1,0 solving 〈LS2 〉PS1,0 = −v〈LS1 PS2,0〉, where 〈·〉 is the average under the invariant measure of L0.”