# 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} }

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…

## 7 Citations

### Explicit Solution Simulation Method for the 3/2 Model

- MathematicsAdvances in Probability and Mathematical Statistics
- 2021

An explicit weak solution for the 3/2 stochastic volatility model is obtained and used to develop a simulation algorithm for option pricing purposes. The 3/2 model is a non-affine stochastic…

### Pricing of Arithmetic Asian Options under Stochastic Volatility Dynamics: Overcoming the Risks of High-Frequency Trading

- BusinessMathematics
- 2020

This research extended the model developed by Hull and White by integrating Taylor-series expansion into the model for deriving approximate analytical solutions for stochastic volatility forward-starting Asian options and demonstrated that the developed model has a pricing accuracy greater than 99%.

### A Closed-Form Pricing Formula for Log-Return Variance Swaps under Stochastic Volatility and Stochastic Interest Rate

- MathematicsMathematics
- 2021

At present, the study concerning pricing variance swaps under CIR the (Cox–Ingersoll–Ross)–Heston hybrid model has achieved many results; however, due to the instantaneous interest rate and…

### VIX-linked fees for GMWBs via explicit solution simulation methods

- EconomicsInsurance: Mathematics and Economics
- 2018

### Combined multiplicative–Heston model for stochastic volatility

- Economics, MathematicsPhysica A: Statistical Mechanics and its Applications
- 2021

### On explicit local solutions of Itô diffusions

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

### BRANCHING PARTICLE PRICERS WITH HESTON EXAMPLES

- Computer ScienceInternational Journal of Theoretical and Applied Finance
- 2020

It is recommended to use the so-called effective particle branching algorithm within importance-sampling Monte Carlo methods for path-dependent option pricing, based upon numeric comparison of option pricing problems in the Heston model.

## References

SHOWING 1-10 OF 56 REFERENCES

### Efficient Simulation of the Heston Stochastic Volatility Model

- Economics
- 2007

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

- Mathematics
- 2008

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

- Economics
- 2001

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

- MathematicsFinance Stochastics
- 2002

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

- Mathematics
- 2006

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…

### Valuation of the early-exercise price for options using simulations and nonparametric regression

- Mathematics
- 1996

### Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes

- Computer ScienceOper. Res.
- 2006

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

- Economics
- 1993

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

- Mathematics
- 1996

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…