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The purpose of this study is to analyse and compile the literature on various option pricing models (OPM) or methodologies. The report highlights the gaps in the existing literature review and builds recommendations for potential scholars interested in the subject area.

In this study, the researchers used a systematic literature review procedure to collect data from Scopus. Bibliometric and structured network analyses were used to examine the bibliometric properties of 864 research documents.

As per the findings of the study, publication in the field has been increasing at a rate of 6% on average. This study also includes a list of the most influential and productive researchers, frequently used keywords and primary publications in this subject area. In particular, Thematic map and Sankey’s diagram for conceptual structure and for intellectual structure co-citation analysis and bibliographic coupling were used.

Based on the conclusion presented in this paper, there are several potential implications for research, practice and society.

This study provides useful insights for future research in the area of OPM in financial derivatives. Researchers can focus on impactful authors, significant work and productive countries and identify potential collaborators. The study also highlights the commonly used OPMs and emerging themes like machine learning and deep neural network models, which can inform practitioners about new developments in the field and guide the development of new models to address existing limitations.

The accurate pricing of financial derivatives has significant implications for society, as it can impact the stability of financial markets and the wider economy. The findings of this study, which identify the most commonly used OPMs and emerging themes, can help improve the accuracy of pricing and risk management in the financial derivatives sector, which can ultimately benefit society as a whole.

It is possibly the initial effort to consolidate the literature on calibration on option price by evaluating and analysing alternative OPM applied by researchers to guide future research in the right direction.

In this paper, we examine which volatility estimation model best explains KOSPI200-realized volatility in the Korean stock market, which has both heteroscedasticity and jump risk. The sample covers from July 1, 2010 to July 31, 2014, which is a low-volatility period in Korean stock market by which time the effects of the global crisis had almost vanished. We use the intra-day return of KOSPI200, which has been measured by 5-minute intervals. This study finds GARCH-family models are efficient estimators compared to historical volatility and EWMA. Also, among the GARCH-family models, Jump-Diffusion GARCH has shown comparatively good results. Especially this study finds that VKOSPI200 is the most efficient model with the largest adj. R2 and the smallest evaluation statistics during the sample period. Meanwhile, it seems to be necessary to consider jump risk when we estimate volatility in Korean stock market.

This paper tries to empirically investigate whether the information contained in trading volume, volume volatility of Won/Dollar currency futures may be statistically useful in forecasting currency spot return. This paper uses both the jump-diffusion GARCH model and the bivariate GARCH type BEKK model to estimate the trading volume volatility of currency futures and the volatility of currency spot, sampled daily during 1/4/2000~12/30/2009 period. According to the findings of this study, previous information contained in both trading volume and the volume volatility of Won/Dollar currency futures might be useful in explaining the future return of the currency spot.

This paper tries to empirically investigate whether the jump risk of Korean stock market may be statistically useful in explaining the Korean CDS (5Y) premium rate. This paper uses the jump-diffusion model with heteroscedasticity to estimate the conditional volatility of KOSPI from 7/2/2007 to 7/30/2010.

The total volatility of Korean stock market is decomposed into a heteroscedasticity and a jump risk by using the jump-diffusion model. The finding is that the jump risk in stead of heteroscedasticity in Korean stock market can explain the Korean CDS premium rate.

I review the burgeoning literature on applications of Markov regime switching models in empirical finance. In particular, distinct attention is devoted to the ability of Markov Switching models to fit the data, filter unknown regimes and states on the basis of the data, to allow a powerful tool to test hypotheses formulated in light of financial theories, and to their forecasting performance with reference to both point and density predictions. The review covers papers concerning a multiplicity of sub-fields in financial economics, ranging from empirical analyses of stock returns, the term structure of default-free interest rates, the dynamics of exchange rates, as well as the joint process of stock and bond returns.

This study examines whether KOSPI200 intra-day return has jump risk and heteroscedasticity and we compare the estimation result of intra-day return and that of daily return. The sample covers from January 2, 2004 to July 31, 2014. We use 30-minute intervals for measuring KOSPI200 intra-day return. It seems this study finds the importance of the consideration of the intra-day data in Korean Stock Market. While some of the parameters of the daily returns for the jump are not significant, but those of intra-day returns are significant over the sample period. Also, the intra-day volatility has shown U-shaped or reverse J-shaped curve. In particular the pattern of intra-day volatility seems to come from the jump risk, which is interpreted as the information inflow in the market.

The purpose of this study is to investigate the effects of uncertainty, namely, macroeconomic uncertainty (MU) and financial uncertainty (FU) on foreign exchange market stability, specifically on foreign exchange market pressure (EMP) and jump risk (RJV).

The latent threshold time-varying parameter VAR (LT-TVP-VAR) econometric approach is used in estimations to solve structural breaks.

The relationship of uncertainties and China's foreign exchange market stability is latent threshold nonlinear dynamic time-varying. In China's renminbi (RMB) appreciation stage, both MU and FU weaken the appreciation pressure of RMB. Moreover, MU and FU significantly increase the RJV, while MU significantly affects the RJV of the foreign exchange market. In the RMB depreciation stage, both MU and FU strengthen the EMP.

Findings based on data in China's foreign exchange market can be considered for other global markets in future research.

An increase in MU and FU has a negative effect on foreign exchange stability. Regulators can prevent the economic system uncertainty shocks on foreign exchange market stability through observation and judgment of MU and FU, which helps prevent and relieve financial risks. Investors can reduce foreign exchange risk as the exchange rate rebounds after hedging behavior during high uncertainty periods.

The effect of MU on the foreign exchange market stability is greater than that of FU, regardless of whether EMP or RJV occurs in the foreign exchange market.

In this paper we attempt to address, in a non‐technical way, the basic assumptions underlying option pricing theory and point out some of the inherent weaknesses they imply in the reliability of the resulting valuations. We present several concrete examples to illustrate the impact of the modeling assumptions and selecting input parameters for the models. We point out the importance for anybody involved in derivatives business to be aware of such issues and encourage them to obtain at least a superficial understanding of the quantitative aspects of option pricing.

Option pricing based on Black‐Scholes model is typically obtained under the assumption that the volatility of the return is a constant. The purpose of this paper is to develop a new method for pricing derivatives under the jump diffusion model with random volatility by viewing the call price as an expected value of a truncated lognormal distribution.

Using Taylor series expansion the call price under random volatility is expressed as a function of kurtosis of the observed volatility process and applied to various class of GARCH models.

A modified option pricing formula is developed for jump diffusion process model with random volatility.

The main contribution of the paper is the development of a kurtosis‐dependent option pricing formula for a jump diffusion model with random volatility.

The purpose of this paper is to investigate empirically the forecasting performance of jump-diffusion option pricing models of (Merton and Bates) with the benchmark Black–Scholes (BS) model relative to market, for pricing Nifty index options of India. The specific period chosen for this study canvasses the extreme up and down limits (jumps) of the Indian capital market. In addition, equity markets keep on facing high and low tides of financial flux amid new economic and financial considerations. With this backdrop, the paper focuses on finding an impeccable option-pricing model which can meet the requirements of option traders and practitioners during tumultuous periods in the future.

Envisioning the fact, the all option-pricing models normally does wrong valuation relative to market. For estimating the structural parameters that governs the underlying asset distribution purely from the underlying asset return data, we have used the nonlinear least-square method. As an approach, we analyzed model prices by dividing the option data into 15 moneyness-maturity groups – depending on the time to maturity and strike price. The prices are compared analytically by continuously updating the parameters of two models using cross-sectional option data on daily basis. Estimated parameters then used to figure out the forecasting performance of models with corresponding BS and market – for pricing day-ahead option prices and implied volatility.

The outcomes of the paper reveal that the jump-diffusion models are a better substitute of classical BS, thus improving the pricing bias significantly. But compared to jump-diffusion model of Merton’s, the model of Bates’ can be applied more uniquely to find out the pricing of three popularly traded categories: deep-out-of-the-money, out-of-the-money and at-the-money of Nifty index options.

The outcome of this research work reveals that the jumps are important components of pricing dynamics of Nifty index options. Incorporation of jump-diffusion process into option pricing of Nifty index options leads to a higher pricing effectiveness, reduces the pricing bias and gives values closer to the market. As the models have been tested in extreme conditions to determine the dominant effectuality, the outcome of this paper helps traders in keeping the investment protected under normal conditions.

The specific period chosen for this study is very unique; it canvasses the extreme up and down limits (jumps) of the Indian capital market and provides the most apt situation for testifying the pricing competitiveness of the models in question. To testify the robustness of models, they have been put into a practical implication of complete cycle of financial frame.