Explicit Heston Solutions and Stochastic Approximation for Path-dependent Option Pricing.

@article{Kouritzin2016ExplicitHS,
  title={Explicit Heston Solutions and Stochastic Approximation for Path-dependent Option Pricing.},
  author={Michael A. Kouritzin},
  journal={arXiv: Pricing of Securities},
  year={2016}
}
  • M. Kouritzin
  • Published 5 August 2016
  • Mathematics
  • arXiv: Pricing of Securities
New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: Stochastic approximation replaces regression in the LSM algorithm; Explicit weak solutions to stochastic differential equations are developed and applied to Heston model simulation; and Importance sampling expands these explicit solutions. The approach complements Heston (1993) and Broadie and Kaya (2006) by handling the case of path… 

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References

SHOWING 1-10 OF 56 REFERENCES

Efficient Simulation of the Heston Stochastic Volatility Model

Stochastic volatility models are increasingly important in practical derivatives pricing applications, yet relatively little work has been undertaken in the development of practical Monte Carlo

Efficient, Almost Exact Simulation of the Heston Stochastic Volatility Model

We deal with discretization schemes for the simulation of the Heston stochastic volatility model. These simulation methods yield a popular and flexible pricing alternative for pricing and managing a

Valuing American Options by Simulation: A Simple Least-Squares Approach

The key to this approach is the use of least squares to estimate the conditional expected payoff to the optionholder from continuation, which makes this approach readily applicable in path-dependent and multifactor situations where traditional finite difference techniqes cannot be used.

An analysis of a least squares regression method for American option pricing

Under fairly general conditions, this paper proves the almost sure convergence of the complete algorithm due to Longstaff and Schwartz and determines the rate of convergence of approximation two and proves that its normalized error is asymptotically Gaussian.

Fast strong approximation Monte Carlo schemes for stochastic volatility models

Numerical integration methods for stochastic volatility models in financial markets are discussed. We concentrate on two classes of stochastic volatility models where the volatility is either

The valuation of warrants: Implementing a new approach

Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes

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 and achieves an O(s-1/2) convergence rate, where s is the total computational budget.

A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options

I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and

SOLUTION OF THE EXTENDED CIR TERM STRUCTURE AND BOND OPTION VALUATION

The extended Cox-Ingersoll-Ross (ECIR) models of interest rates allow for time-dependent parameters in the CIR square-root model. This article presents closed-form pathwise unique solutions of these
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