Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order
ACM Transactions on Mathematical Software (TOMS)
Estimating security price derivatives using simulation
Management Science
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Exact simulation of option greeks under stochastic volatility and jump diffusion models
WSC '04 Proceedings of the 36th conference on Winter simulation
Estimating tranche spreads by loss process simulation
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Simulating point processes by intensity projection
Proceedings of the 40th Conference on Winter Simulation
Beta approximations for bridge sampling
Proceedings of the 40th Conference on Winter Simulation
Connecting the top-down to the bottom-up: pricing CDO under a conditional survival (CS) model
Proceedings of the 40th Conference on Winter Simulation
Applied Numerical Mathematics
Computers & Mathematics with Applications
A smooth estimator for MC/QMC methods in finance
Mathematics and Computers in Simulation
Sensitivity Estimates from Characteristic Functions
Operations Research
FFT based option pricing under a mean reverting process with stochastic volatility and jumps
Journal of Computational and Applied Mathematics
Exact Simulation of Point Processes with Stochastic Intensities
Operations Research
Monte Carlo Algorithms for Default Timing Problems
Management Science
SIAM Journal on Financial Mathematics
Exact and Efficient Simulation of Correlated Defaults
SIAM Journal on Financial Mathematics
A Fourier-Based Valuation Method for Bermudan and Barrier Options under Heston's Model
SIAM Journal on Financial Mathematics
Sensitivity estimation of SABR model via derivative of random variables
Proceedings of the Winter Simulation Conference
Localization and Exact Simulation of Brownian Motion-Driven Stochastic Differential Equations
Mathematics of Operations Research
An Efficient Semi-Analytical Simulation for the Heston Model
Computational Economics
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The stochastic differential equations for affine jump diffusion models do not yield exact solutions that can be directly simulated. Discretization methods can be used for simulating security prices under these models. However, discretization introduces bias into the simulation results, and a large number of time steps may be needed to reduce the discretization bias to an acceptable level. This paper suggests a method for the exact simulation of the stock price and variance under Hestons stochastic volatility model and other affine jump diffusion processes. The sample stock price and variance from the exact distribution can then be used to generate an unbiased estimator of the price of a derivative security. We compare our method with the more conventional Euler discretization method and demonstrate the faster convergence rate of the error in our method. Specifically, our method achieves an O(s-1/2) convergence rate, where s is the total computational budget. The convergence rate for the Euler discretization method is O(s-1/3) or slower, depending on the model coefficients and option payoff function.