Discrete-Time Pricing Models

2012 ◽  
pp. 103-139
Author(s):  
Steven Roman
Keyword(s):  
Discrete Time ◽  
Pricing Models

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 Convergence of discrete time option pricing models under stochastic interest rates

2000 ◽  
Vol 4 (1) ◽  
pp. 81-93 ◽  
Author(s):  
J.-P. Lesne ◽  
J.-L. Prigent ◽  
O. Scaillet
Keyword(s):  
Option Pricing ◽  
Interest Rates ◽  
Discrete Time ◽  
Pricing Models ◽  
Stochastic Interest Rates ◽  
Stochastic Interest

scholarly journals Mathematical model of European option pricing in incomplete market without transaction costs (discrete time ). Part II.

2020 ◽  
Vol 20 (2) ◽  
pp. 5-22
Author(s):  
Zverev Oleg ◽  
◽  
Khametov Vladimir ◽  
Shelemekh Elena ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Option Pricing ◽  
Transaction Costs ◽  
Discrete Time ◽  
European Option ◽  
Pricing Models ◽  
One Dimensional ◽  
European Option Pricing ◽  
Special Cases ◽  
Time Part

This is the second part of the paper. Here general model of the first part is implemented to design pricing models for special cases of one-dimensional incomplete final market and compact (1; S)-market.

Building good deals with arbitrage-free discrete time pricing models

2012 ◽  
Vol 10 (2) ◽  
pp. 53-61
Author(s):  
Beatriz Balbás ◽  
Raquel Balbás
Keyword(s):  
Discrete Time ◽  
Pricing Models

The Effect of Partly Missing Covariates on Statistical Power in Randomized Controlled Trials With Discrete-Time Survival Endpoints

Methodology ◽  
2017 ◽  
Vol 13 (2) ◽  
pp. 41-60
Author(s):  
Shahab Jolani ◽  
Maryam Safarkhani
Keyword(s):  
Randomized Controlled Trials ◽  
Discrete Time ◽  
Treatment Effect ◽  
Survival Data ◽  
Controlled Trials ◽  
Missing Covariates ◽  
Indicator Method ◽  
Imputation Methods ◽  
Randomized Controlled ◽  
Baseline Covariates

Abstract. In randomized controlled trials (RCTs), a common strategy to increase power to detect a treatment effect is adjustment for baseline covariates. However, adjustment with partly missing covariates, where complete cases are only used, is inefficient. We consider different alternatives in trials with discrete-time survival data, where subjects are measured in discrete-time intervals while they may experience an event at any point in time. The results of a Monte Carlo simulation study, as well as a case study of randomized trials in smokers with attention deficit hyperactivity disorder (ADHD), indicated that single and multiple imputation methods outperform the other methods and increase precision in estimating the treatment effect. Missing indicator method, which uses a dummy variable in the statistical model to indicate whether the value for that variable is missing and sets the same value to all missing values, is comparable to imputation methods. Nevertheless, the power level to detect the treatment effect based on missing indicator method is marginally lower than the imputation methods, particularly when the missingness depends on the outcome. In conclusion, it appears that imputation of partly missing (baseline) covariates should be preferred in the analysis of discrete-time survival data.

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