scholarly journals Discrete time option pricing with flexible volatility estimation

2000 ◽  
Vol 4 (2) ◽  
pp. 189-207 ◽  
Author(s):  
Wolfgang Härdle ◽  
Christian M. Hafner
Keyword(s):  
Option Pricing ◽  
Discrete Time ◽  
Volatility Estimation

Value-at-Risk and Expected Shortfall approaches for option premiums and the probability of default estimation based on ARMA models

2021 ◽  
Vol 57 (3) ◽  
pp. 126
Author(s):  
Nikolai Berzon
Keyword(s):  
Time Series ◽  
Option Pricing ◽  
Discrete Time ◽  
Value At Risk ◽  
Probability Of Default ◽  
Pricing Models ◽  
Arma Process ◽  
Underlying Asset ◽  
Black Scholes

The need to address the issue of risk management has given rise to a number of models for estimation the probability of default, as well as a special tool that allows to sell credit risk – a credit default swap (CDS). From the moment it appeared in 1994 until the crisis of 2008, that the CDS market was actively growing, and then sharply contracted. Currently, there is practically no CDS market in emerging economies (including Russia). This article is to improve the existing CDS valuation models by using discrete-time models that allow for more accurate assessment and forecasting of the selected asset dynamics, as well as new option pricing models that take into account the degree of risk acceptance by the option seller. This article is devoted to parametric discrete-time option pricing models that provide more accurate results than the traditional Black-Scholes continuous-time model. Improvement in the quality of assessment is achieved due to three factors: a more detailed consideration of the properties of the time series of the underlying asset (in particular, autocorrelation and heavy tails), the choice of the optimal number of parameters and the use of Value-at-Risk approach. As a result of the study, expressions were obtained for the premiums of European put and call options for a given level of risk under the assumption that the return on the underlying asset follows a stationary ARMA process with normal or Student's errors, as well as an expression for the credit spread under similar assumptions. The simplicity of the ARMA process underlying the model is a compromise between the complexity of model calibration and the quality of describing the dynamics of assets in the stock market. This approach allows to take into account both discreteness in asset pricing and take into account the current structure and the presence of interconnections for the time series of the asset under consideration (as opposed to the Black–Scholes model), which potentially allows better portfolio management in the stock market.

scholarly journals Option Pricing and Hedging for Discrete Time Regime-Switching Models

2017 ◽  
Vol 08 (08) ◽  
pp. 1005-1032 ◽  
Author(s):  
Bruno Rémillard ◽  
Alexandre Hocquard ◽  
Hugo Lamarre ◽  
Nicolas Papageorgiou
Keyword(s):  
Option Pricing ◽  
Discrete Time ◽  
Regime Switching ◽  
Regime Switching Models ◽  
Switching Models ◽  
Time Regime

An equilibrium debt option pricing model in discrete time

1989 ◽  
Vol 13 (3) ◽  
pp. 421-442 ◽  
Author(s):  
Kevin J. Maloney ◽  
Mark J. Byrne
Keyword(s):  
Option Pricing ◽  
Discrete Time ◽  
Pricing Model ◽  
Option Pricing Model

scholarly journals Robust Volatility Estimation and Analysis of the Leverage Effect

2021 ◽  
Author(s):  
◽  
John Randal
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Closed Form Solution ◽  
Estimation Procedure ◽  
Form Solution ◽  
Careful Study ◽  
Financial Problem ◽  
Volatility Estimation ◽  
Real Price ◽  
Price Relationships

<p>Using volatility estimation as the underlying commonality this thesis traverses the statistical problem of robust estimation of scale, through to the financial problem of valuing call options over stock. We use a large simulation study of robust scale estimators to benchmark a nonparametric volatility estimation procedure, which not only uses techniques which are particularly suited to observed financial returns, but also addresses the problem of bias in any robust volatility estimation procedure. Existing option pricing models are discussed with careful study of the assumed volatility and elasticity of volatility with respect to stock price relationships for each of these models. An option pricing formula is derived which extends existing methods, and provides a closed form solution which can be readily computed. Preliminary analysis of real price data suggests this model is able to explain observed leverage phenomena.</p>

scholarly journals Robust Volatility Estimation and Analysis of the Leverage Effect

2021 ◽  
Author(s):  
◽  
John Randal
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Closed Form Solution ◽  
Estimation Procedure ◽  
Form Solution ◽  
Careful Study ◽  
Financial Problem ◽  
Volatility Estimation ◽  
Real Price ◽  
Price Relationships

<p>Using volatility estimation as the underlying commonality this thesis traverses the statistical problem of robust estimation of scale, through to the financial problem of valuing call options over stock. We use a large simulation study of robust scale estimators to benchmark a nonparametric volatility estimation procedure, which not only uses techniques which are particularly suited to observed financial returns, but also addresses the problem of bias in any robust volatility estimation procedure. Existing option pricing models are discussed with careful study of the assumed volatility and elasticity of volatility with respect to stock price relationships for each of these models. An option pricing formula is derived which extends existing methods, and provides a closed form solution which can be readily computed. Preliminary analysis of real price data suggests this model is able to explain observed leverage phenomena.</p>

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