Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes

By Mark Broadie, Ö. Kaya. Operational Research, 2006

527 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5a0952df73e4150cf953d1bb6787888c720fab55

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Citations in the corpus

A comparison of biased simulation schemes for stochastic volatility models (2010, methodology): “It is our goal in this section to compare all five Euler fixes, as well as the schemes of Broadie and Kaya [2006] and the second order IJK-IMM scheme of Kahl and Jäckel [2005a].”
Exploring the sources of default clustering (2018, unknown): “Since Z follows a CIR process under P∗, a key result of Broadie and Kaya (2006) implies that for times 0 ≤ t1 < t2 ≤ τ and points z1, z2 ∈ R+, φ(z1, t1; z2, t2) = E∗ [ exp ( − ∫ t2 t1 λudu ) ∣∣∣Dτ , Zt1 = z1, Zt2 = z2] = Φ(z1, t1; z2, t2) exp ( − ∫ t2 t1 ( ea·(1,Xu) + Yu ) du ) , (9) where Φ(z1,…”
An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process (2012, methodology): “Thus, equation (1.1) can be simulated exactly at a finite number of time points using the Markov property (Glassermann 2004; Broadie & Kaya 2006).”
THE 4/2 STOCHASTIC VOLATILITY MODEL: A UNIFIED APPROACH FOR THE HESTON AND THE 3/2 MODEL (2017, methodology): “We will adapt the Broadie and Kaya (2006) algorithm to the 4/2 model in order to provide the exact simulation scheme for the model.”
Density Approximations for Multivariate Affine Jump-Diffusion Processes (2011, unknown): “To obtain exact draws from this model we refer the reader to the algorithm in Broadie and Kaya (2006). For Bayesian inference we specify the prior distribution as”
TIME‐CHANGED ORNSTEIN–UHLENBECK PROCESSES AND THEIR APPLICATIONS IN COMMODITY DERIVATIVE MODELS (2012, background): “The Laplace transform conditional on the state of the process at time t, LCIR(t, λ|z0, zt) := Ez0 [ e−λ ∫ t 0 Zudu | Zt = zt ] , is also known in closed form (Broadie and Kaya (2006)):”
COMPLEX LOGARITHMS IN HESTON‐LIKE MODELS (2010, methodology): “Another example of this is the calculation of density functions via inversion of the characteristic function, see the exact simulation algorithm of Broadie and Kaya [2006] for an application of this in the Heston model. To fix ideas, we will focus on the Heston stochastic volatility model throughout”
A LOW-BIAS SIMULATION SCHEME FOR THE SABR STOCHASTIC VOLATILITY MODEL (2012, methodology): “Broadie & Kaya [6]’s so-called exact simulation scheme (the BK scheme) is based on the insight in Willard [31] that the conditional distribution, given the terminal volatility ∗Corresponding author.”
Inference for Lévy‐Driven Stochastic Volatility Models via Adaptive Sequential Monte Carlo (2011, background): “2 Likelihood Construction In a paper of [8], it is demonstrated that it is possible to simulate exactly from a class of AJD processes.”
LIBOR market model with stochastic volatility (2006, methodology): “Sampling from a χ2 distribution: This method proposed by Broadie and Kaya [11] samples from the exact distribution of z(t) given z(u) for u < t.”
Fast strong approximation Monte Carlo schemes for stochastic volatility models (2006, methodology): “Broadie and Kaya (2004) used this transition density for the Monte Carlo simulation of European options.”
Prices and Asymptotics for Discrete Variance Swaps (2013, unknown): “The second set corresponds to Table 2 in Broadie and Kaya (2006).”
ARBITRAGE-FREE VALUATION OF BILATERAL COUNTERPARTY RISK FOR INTEREST-RATE PRODUCTS: IMPACT OF VOLATILITIES AND CORRELATIONS (2011, methodology): “For alternative approaches to the joint simulation of market relevant quantities with a Monte Carlo algorithm see [19] and [1].”