An Efficient Numerical Scheme for Simulation of Mean-reverting Square-root Diffusions
نویسندگان
چکیده
An efficient numerical scheme, which is based on the splitting-step idea [20], for simulation of mean-reverting square-root diffusions is presented in this paper. We prove positivity preservation for this scheme and an estimate of its local error in the second moment. A series of numerical experiments based on MATLAB programs is given to compare the suggested scheme with the schemes of the balanced implicit method (BIM) and the balanced Milstein method (BMM), which are reported in [15, 16, 19].
منابع مشابه
A Simple and Exact Simulation Approach to Heston Model
In this paper we will propose a simple approach to simulating Heston model efficiently and accurately. All existing simulation schemes so far directly work with the mean-reverting square root process of the variance in Heston model, instead we transform the variance to an equivalent volatility which follows a mean-reverting Ornstein-Uhlenbeck process. We will show it is more convenient to simul...
متن کاملComputing hitting time densities for CIR and OU diffusions: applications to mean- reverting models
This paper provides explicit analytical characterizations for first hitting time densities for Cox–Ingersoll–Ross (CIR) and Ornstein–Uhlenbeck (OU) diffusions in terms of relevant Sturm–Liouville eigenfunction expansions. Starting with Vasicek (1977) and Cox, Ingersoll and Ross (1985), the Gaussian Ornstein– Uhlenbeck and Feller’s (1951) square-root diffusions are among the most commonly used s...
متن کاملA Comparison of Biased Simulation Schemes for Stochastic Volatility Models
Using an Euler discretisation to simulate a mean-reverting CEV process gives rise to the problem that while the process itself is guaranteed to be nonnegative, the discretisation is not. Although an exact and efficient simulation algorithm exists for this process, at present this is not the case for the CEV-SV stochastic volatility model, with the Heston model as a special case, where the varia...
متن کاملEconomic Hysteresis Effects and Hitting Time Densities for CIR Diffusions
Using the so-called mean-reverting square-root process of Cox et al. (1985b) we generalize the work of Dias and Shackleton (2005) by introducing the mean reversion feature into the economic hysteresis analysis under stochastic interest rates and show that such issue highlights a tendency for a widening effect on the range of inaction, though both thresholds have risen when compared with the no ...
متن کاملNumerical Methods of Option Pricing for Two Specific Models of Electricity Prices
In this work, two models are proposed for electricity prices as energy commodity prices which in addition to mean-reverting properties have jumps and spikes, due to non-storability of electricity. The models are simulated using an Euler scheme, and then the Monte-Carlo method is used to estimate the expectation of the discounted cash-flow under historical probability, which is considered as the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009