Discrete-time stochastic volatility process in option pricing: a generalisation of the Amin-Ng and the Black-Scholes models

2016 ◽  
Vol 5 (2/3/4) ◽  
pp. 189
Author(s):  
Anna Pajor
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Discrete Time ◽  
Black Scholes ◽  
Stochastic Volatility Process

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.

An empirical exploration of the performance of alternative option pricing models

2019 ◽  
Vol 11 (1) ◽  
pp. 23-49
Author(s):  
Aparna Prasad Bhat
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Emerging Market ◽  
Pricing Models ◽  
Content Type ◽  
Black Scholes ◽  
Out Of Sample ◽  
Hedging Performance ◽  
Practical Implications ◽  
Skewness And Kurtosis

PurposeThe purpose of this paper is to ascertain the effectiveness of major deterministic and stochastic volatility-based option pricing models in pricing and hedging exchange-traded dollar–rupee options over a five-year period since the launch of these options in India.Design/methodology/approachThe paper examines the pricing and hedging performance of five different models, namely, the Black–Scholes–Merton model (BSM), skewness- and kurtosis-adjusted BSM, NGARCH model of Duan, Heston’s stochastic volatility model and anad hocBlack–Scholes (AHBS) model. Risk-neutral structural parameters are extracted by calibrating each model to the prices of traded dollar–rupee call options. These parameters are used to generate out-of-sample model option prices and to construct a delta-neutral hedge for a short option position. Out-of-sample pricing errors and hedging errors are compared to identify the best-performing model. Robustness is tested by comparing the performance of all models separately over turbulent and tranquil periods.FindingsThe study finds that relatively simpler models fare better than more mathematically complex models in pricing and hedging dollar–rupee options during the sample period. This superior performance is observed to persist even when comparisons are made separately over volatile periods and tranquil periods. However the more sophisticated models reveal a lower moneyness-maturity bias as compared to the BSM model.Practical implicationsThe study concludes that incorporation of skewness and kurtosis in the BSM model as well as the practitioners’ approach of using a moneyness-maturity-based volatility within the BSM model (AHBS model) results in better pricing and hedging effectiveness for dollar–rupee options. This conclusion has strong practical implications for market practitioners, hedgers and regulators in the light of increased volatility in the dollar–rupee pair.Originality/valueExisting literature on this topic has largely centered around either US equity index options or options on major liquid currencies. While many studies have solely focused on the pricing performance of option pricing models, this paper examines both the pricing and hedging performance of competing models in the context of Indian currency options. Robustness of findings is tested by comparing model performance across periods of stress and tranquility. To the best of the author’s knowledge, this paper is one of the first comprehensive studies to focus on an emerging market currency pair such as the dollar–rupee.

scholarly journals LONG MEMORY STOCHASTIC VOLATILITY IN OPTION PRICING

2005 ◽  
Vol 08 (03) ◽  
pp. 381-392 ◽  
Author(s):  
SERGEI FEDOTOV ◽  
ABBY TAN
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Long Memory ◽  
Option Price ◽  
Long Range Dependence ◽  
Asymptotic Equation ◽  
Random Deviation ◽  
Starting Point ◽  
Black Scholes ◽  
Different Time Scales

The aim of this paper is to present a stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black–Scholes equation involving volatility with long-range dependence. We define the stochastic option price as a sum of classical Black–Scholes price and random deviation describing the risk from the random volatility. By using the fact that the option price and random volatility change on different time scales, we derive the asymptotic equation for this deviation involving fractional Brownian motion. The solution to this equation allows us to find the pricing bands for options.

scholarly journals Option pricing under a discrete-time Markov switching stochastic volatility with co-jump model

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Michael C. Fu ◽  
Bingqing Li ◽  
Rongwen Wu ◽  
Tianqi Zhang
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Discrete Time ◽  
Asset Price ◽  
Markov Switching ◽  
European Options ◽  
Computationally Efficient ◽  
Volatility Clustering ◽  
European Option Pricing ◽  
Jump Model

<p style='text-indent:20px;'>We consider option pricing using a discrete-time Markov switching stochastic volatility with co-jump model, which can capture asset price features such as leptokurtosis, skewness, volatility clustering, and varying mean-reversion speed of volatility. For pricing European options, we develop a computationally efficient method for obtaining the probability distribution of average integrated variance (AIV), which is key to option pricing under stochastic-volatility-type models. Building upon the efficiency of the European option pricing approach, we are able to price an American-style option, by converting its pricing into the pricing of a portfolio of European options. Our work also provides constructive guidance for analyzing derivatives based on variance, e.g., the variance swap. Numerical results indicate our methods can be implemented very efficiently and accurately.</p>

Empirical study based on the model of rough fractional stochastic volatility (RFSV)

2021 ◽  
Author(s):  
Songyan Zhang ◽  
Chaoyong Hu
Keyword(s):  
Monte Carlo Simulation ◽  
Option Pricing ◽  
Stochastic Volatility ◽  
Option Price ◽  
Pricing Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Research Findings ◽  
S Model ◽  
The Empirical Analysis

To estimate the parameters of the model of option pricing based on the model of rough fractional stochastic volatility (RFSV), we have carried out the empirical analysis during our study on the pricing of SSE 50ETF options in China. First, we have estimated the parameters of option pricing model by adopting the Monte Carlo simulation. Subsequently, we have empirically examined the pricing performance of the RFSV model by adopting the SSE 50ETF option price from January 2019 to December 2020. Our research findings indicate that by leveraging the RFSV model, we are able to attain a more accurate and stable level of option pricing than the conventional Black–Scholes (B-S) model on constant volatility. The errors of option pricing incurred by the B-S model proved to be larger and exhibited higher volatility, revealing the significant impact imposed by stochastic volatility on option pricing.

A Kaleidoscopic Study of Pricing Performance of Stochastic Volatility Option Pricing Models: Evidence from Recent Indian Economic Turbulence

2013 ◽  
Vol 38 (2) ◽  
pp. 61-80 ◽  
Author(s):  
Vipul Kumar Singh ◽  
Pushkar Pachori
Keyword(s):  
Stochastic Process ◽  
Option Pricing ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Heston Model ◽  
Percentage Error ◽  
Testing Time ◽  
Indian Economy ◽  
Black Scholes ◽  
Garch Process

A whole host of researchers have modeled volatility as a non-constant stochastic process, based on the principle that volatility follows a stochastic process whose parameters are not directly observable in the market. The objective of this research paper is to empirically investigate the forecasting performance of three most dominant models of this species namely, Hull-White (1988), Heston�s (1993), and Heston-Nandi GARCH (2000) option pricing model. These three models have been collaterally compared and contrasted against Black-Scholes and market for pricing S&P CNX Nifty 50 index option of India. The Hull-White model not only warrants a range of stochastic volatility specifications but also incorporates correlation of volatility of asset return and its price changes. The closed form Heston�s (1993) model explicitly and elaborately communicates non-lognormal distribution of the assets return, leverage effect, and mean-reverting property of volatility. The model of Heston-Nandi, also in closed form, successfully incorporates variance of asset returns as a range of GARCH process. It strongly permits correlation between returns of the spot asset and variance and also technically accepts multiple lags in the dynamics of the GARCH process. To decide, determine, and delineate the effectiveness of stochastic models against the Black-Scholes and market, the current paper adopts a structured approach of relative error price, viz., percentage mean error (PME) and mean absolute percentage error (MAPE). The most turbulent period of the Indian economy � January 1, 2008 to December 31, 2008 — was considered appropriate for testiing the suggested model. It was a testing time for the Indian economy as well as a critical period questioning the sustainability of all financial products/models and challenging their fundamental platform depicted as equity market. How to safeguard investors� faith and at least protect their investments if not multiply returns in the face of such financial hardships remained a burning question for all thinkers and experts on the subject. Data pertaining to the specific period of such drastic disturbance was analysed with the help of the proposed models. After rigorous churning of specific data taken across various models, the Heston model was found to outperform and surpass other models.

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