A DEGENERATE PARABOLIC VARIATIONAL INEQUALITY FOR THE AMERICAN OPTION PRICING PROBLEM

1998 ◽  
Vol 08 (03) ◽  
pp. 485-493
Author(s):  
LORETTA MASTROENI ◽  
MICHELE MATZEU
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Option Pricing ◽  
Weighted Sobolev Spaces ◽  
American Option Pricing ◽  
Ellipticity Condition ◽  
Put Option ◽  
Uniform Ellipticity ◽  
Degenerate Parabolic ◽  
American Put

A formulation in terms of degenerate parabolic variational inequalities for the price of an American put option is stated. The usual uniform ellipticity condition is weakened by the presence of a weight function. Then the appropriate framework is that of some suitable "weighted" Sobolev spaces. One applies a result previously stated by the authors in Ref. 8.

A SIMPLE AMERICAN OPTION PRICING METHOD USING THE FAST FOURIER TRANSFORM

2007 ◽  
Vol 10 (07) ◽  
pp. 1191-1202
Author(s):  
SUNEAL K. CHAUDHARY
Keyword(s):  
Fourier Transform ◽  
Brownian Motion ◽  
Option Pricing ◽  
Fast Fourier Transform ◽  
Numerical Technique ◽  
Transition Function ◽  
American Option Pricing ◽  
Underlying Asset ◽  
Variance Gamma Process ◽  
American Put

This paper describes a fast, flexible numerical technique to price American options and generate their value surface through time. The method runs faster and more accurately than the standard CRR binomial method in practical cases and calculates options on a considerably broader family of new, useful underlying asset processes. The technique relies on the Fast Fourier Transform (FFT) to convolve a transition function for the underlying asset process. The method allows the underlying asset process to be quite general; the previously known standard geometric Brownian motion and the Variance Gamma process [8], and a novel, purely empirical transition function are compared by computing their respective American put value surface and the exercise boundaries.

scholarly journals Examining the Efficiency of American Put Option Pricing by Monte Carlo Methods with Variance Reduction

2018 ◽  
Vol 10 (2) ◽  
pp. 10
Author(s):  
George Chang
Keyword(s):  
Monte Carlo ◽  
Option Pricing ◽  
Variance Reduction ◽  
American Options ◽  
Balance Sheet ◽  
Put Options ◽  
Control Variate ◽  
American Put Option ◽  
Put Option ◽  
American Put

We apply the Monte Carlo simulation algorithm developed by Broadie and Glasserman (1997) and the control variate technique first introduced to asset pricing via simulation by Boyle (1977) to examine the efficiency of American put option pricing via this combined method. The importance and effectiveness of variance reduction is clearly demonstrated in our simulation results. We also found that the control variates technique does not work as well for deep-in-the-money American put options. This is because deep-in-the-money American options are more likely to be exercised early, thus the value of the American options are less in line (or less correlated) with those of their European counterparts. the same FPESS can also be observed when investigators partition large datasets into smaller datasets to address a variety of auditing questions. In this study, we fill the empirical gap in the literature by investigating the sensitivity of the FPESS to partitioned datasets. We randomly selected 16 balance-sheet datasets from: China Stock Market Financial Statements Database™, that tested to be Benford Conforming noted as RBCD. We then explore how partitioning these datasets affects the FPESS by repeated randomly sampling: first 10% of the RBCD and then selecting 250 observations from the RBCD. This created two partitioned groups of 160 datasets each. The Statistical profile observed was: For the RBCD there were no indications of Non-Conformity; for the 10%-Sample there were no overall indications that Extended Procedures would be warranted; and for the 250-Sample there were a number of indications that the dataset was Non-Conforming. This demonstrated clearly that small datasets are indeed likely to create the FPESS. We offer a discussion of these results with implications for audits in the Big-Data context where the audit In-charge would find it necessary to partition the datasets of the client. 

RENORMALIZATION OF BLACK-SCHOLES EQUATION FOR STOCHASTICALLY FLUCTUATING INTEREST RATE

2001 ◽  
Vol 04 (04) ◽  
pp. 621-634
Author(s):  
ALEXANDER G. MUSLIMOV ◽  
NIKOLAI A. SILANT'EV
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Numerical Solution ◽  
Short Term ◽  
Stochastic Component ◽  
Put Option ◽  
Stochastic Fluctuations ◽  
Black Scholes ◽  
The Interest Rate ◽  
American Put

We investigate the effect of stochastic fluctuations of an interest rate on the value of a derivative. We derive the modified Black-Scholes equation that describes evolution of the value of a derivative averaged over an ensemble of stochastic fluctuations of the rate of interest and depends on the "renormalized" values of volatility and rate of interest. We present the explicit expressions for the renormalized volatility and interest rate that incorporate the corrections owing to the short-term stochastic variations of the interest rate. The stochastic component of the interest rate tends to enhance the effective volatility and reduce the effective interest rate that determine an evolution of the option pricing "smoothed out" over the stochastic variations. The results of numerical solution of the modified Black-Scholes equation with the renormalized coefficients are illustrated for an American put option on non-dividend-paying stock.

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