On the micro-Corporate-Governance of a Strictly Informational Cascade, as illustrated with analysis of the performativity of the Black-Scholes-Merton Model

2021 ◽  
Author(s):  
Henry Wurts
Keyword(s):  
Corporate Governance ◽  
Merton Model ◽  
Black Scholes ◽  
Informational Cascade

Black–Scholes–Merton Model for Option Pricing

2019 ◽  
pp. 119-133
Author(s):  
Raymond H. Chan ◽  
Yves ZY. Guo ◽  
Spike T. Lee ◽  
Xun Li
Keyword(s):  
Option Pricing ◽  
Merton Model ◽  
Black Scholes

scholarly journals A Comparative Analysis of the Black-Scholes- Merton Model and the Heston Stochastic Volatility Model

2019 ◽  
Vol 39 ◽  
pp. 127-140
Author(s):  
Tahmid Tamrin Suki ◽  
ABM Shahadat Hossain
Keyword(s):  
Comparative Analysis ◽  
Stochastic Volatility ◽  
Stock Prices ◽  
Computer Algebra System ◽  
Stochastic Volatility Model ◽  
Affecting Factors ◽  
Pricing Models ◽  
Merton Model ◽  
Volatility Model ◽  
Black Scholes

This paper compares the performance of two different option pricing models, namely, the Black-Scholes-Merton (B-S-M) model and the Heston Stochastic Volatility (H-S-V) model. It is known that the most popular B-S-M Model makes the assumption that volatility of an asset is constant while the H-S-V model considers it to be random. We examine the behavior of both B-S-M and H-S-V formulae with the change of different affecting factors by graphical representations and hence assimilate them. We also compare the behavior of some of the Greeks computed by both of these models with changing stock prices and hence constitute 3D plots of these Greeks. All the numerical computations and graphical illustrations are generated by a powerful Computer Algebra System (CAS), MATLAB. GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 127-140

Modifying the Black-Scholes-Merton model to calculate the cost of employee stock options

2014 ◽  
Vol 40 (1) ◽  
pp. 2-32 ◽  
Author(s):  
John D. Finnerty
Keyword(s):  
Utility Maximization ◽  
Design Methodology ◽  
Lattice Models ◽  
Employee Stock Options ◽  
Content Type ◽  
Early Exercise ◽  
Merton Model ◽  
Black Scholes ◽  
Computationally Intensive ◽  
The Cost

Purpose – More than 80 percent of S&P 500 firms that issue ESOs use the Black-Scholes-Merton (BSM) model and substitute the estimated average term for the contractual expiration to calculate ESO expense. This simplification systematically overprices ESOs, which worsens as the stock's volatility increases. The purpose of this paper is to present a modification of the BSM model to explicitly incorporate the rates of forfeiture pre- and post-vesting and the rate of early exercise. Design/methodology/approach – The paper demonstrates the model's usefulness by employing historical exercise and forfeiture data for 127 separate ESO grants and 1.31 billion ESOs to calculate the exercise and forfeiture parameters and value ESOs for nine firms. Findings – The modified BSM model is just as accurate but easier to use than the more computationally intensive utility maximization and trinomial lattice models, and it avoids the ASC 718 BSM model's overpricing bias. Originality/value – If firms prefer the BSM model over more mathematically elegant alternatives, they should at least use a BSM model that is free of overpricing bias.

ASYMPTOTIC APPROXIMATIONS FOR PRICING DERIVATIVES UNDER MEAN-REVERTING PROCESSES

2016 ◽  
Vol 19 (05) ◽  
pp. 1650030 ◽  
Author(s):  
RICHARD JORDAN ◽  
CHARLES TIER
Keyword(s):  
Interest Rates ◽  
Implied Volatility ◽  
Asymptotic Approximations ◽  
Ray Method ◽  
Interest Rate Derivatives ◽  
Put Options ◽  
Merton Model ◽  
Volatility Model ◽  
Black Scholes ◽  
Efficient Alternative

The problem of fast pricing, hedging, and calibrating of derivatives is considered when the underlying does not follow the standard Black–Scholes–Merton model but rather a mean-reverting and deterministic volatility model. Mean-reverting models are often used for volatility, commodities, and interest-rate derivatives, while the deterministic volatility accounts for the nonconstant implied volatility. Trading desks often use numerical methods for real-time pricing, hedging, and calibration when implementing such models. A more efficient alternative is to use an analytic formula, even if only approximate. A systematic approach is presented, based on the WKB or ray method, to derive asymptotic approximations to the density function that can be used to derive simple formulas for pricing derivatives. Such approximations are usually only valid away from any boundaries, yet for some derivatives the values of the underlying near the boundaries are needed such as when interest rates are very low or for pricing put options. Hence, the ray approximation may not yield acceptable results. A new asymptotic approximation near boundaries is derived, which is shown to be of value for pricing certain derivatives. The results are illustrated by deriving new analytic approximations for European derivatives and their high accuracy is demonstrated numerically.

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