GARCH option pricing with implied volatility

An empirical study is employed to investigate the performance of implied GARCH models in option pricing. The implied GARCH models are established by either the Esscher transform or the extended Girsanov principle. The empirical P-martingale simulation is adopted to compute the options efficiently. The empirical results show that: (i) the implied GARCH models obtain accurate standard option prices even the innovations are conveniently assumed to be normal distributed; (ii) the Esscher transform describes the data better than the extended Girsanov principle; (iii) significant model risk arises when using implied GARCH model with non-proper innovations in exotic option pricing.

Quantitative Finance, 2011

2006

Abstract: We investigate the information content in the S&P 500 index options market by using the" realized" volatility approach. We model realized volatility as an ARFIMA process to capture its long memory. We use encompassing regressions to analyze the forecast efficiency and information content of different volatility measures. We find that realized volatility has incremental value over implied volatility in forecasting future volatility. We evaluate the economic benefits of volatility timing by examining whether realized volatility ...

Exchange-traded currency options are a recent innovation in the Indian financial market and their pricing is as yet unexplored. The objective of this research paper is to empirically compare the pricing performance of two well-known option pricing models – the Black-Scholes-Merton Option Pricing Model (BSM) and Duan " s NGARCH option pricing model – for pricing exchange-traded currency options on the US dollar-Indian rupee during a recent turbulent period. The BSM is known to systematically misprice options on the same underlying asset but with different strike prices and maturities resulting in the phenomenon of the " volatility smile ". This bias of the BSM results from its assumption of a constant volatility over the option " s life. The NGARCH option pricing model developed by Duan is an attempt to incorporate time-varying volatility in pricing options. It is a deterministic volatility model which has no closed-form solution and therefore requires numerical techniques for evaluation. In this paper we have compared the pricing performance and examined the pricing bias of both models during a recent period of volatility in the Indian foreign exchange market. Contrary to our expectations the pricing performance of the more sophisticated NGARCH pricing model is inferior to that of the relatively simple BSM model. However orthogonality tests demonstrate that the NGARCH model is free of the strike price and maturity biases associated with the BSM. We conclude that the deterministic BSM does a better job of pricing options than the more advanced time-varying volatility model based on GARCH.

We price S&P 500 index options under the assumption that the conditional risk-neutral density function of the index follows a Semi-Nonparametric (SNP) process with GARCH variance. The model is estimated combining a set of option contracts written on the index and the daily index return time series in the period 1996 to 2011. The in-sample and out-sample performance of the model is compared with several benchmark models, beating most of them. We conclude that a pricing model dealing simultaneously with non-normalities and time-varying volatility helps to mitigate the observed S&P 500 index option biases.

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns and volatilities. Our model nests Duan's GARCH option models where conditional returns are constrained to being normal, as well as extends Merton's jump-diffusion model by allowing return volatility to exhibit GARCH-like behavior. Empirical analysis on the S&P 500 index returns reveals that the incorporation of jumps in returns and volatilities improves significantly the performance of the GARCH model in capturing the observed time series of the S&P 500 index returns. Moreover, the corresponding GARCH option pricing model with the jump component delivers a better performance on pricing the S&P 500 index options.

Journal of CENTRUM Cathedra: The Business and Economics Research Journal, 2012

Derivatives have become widely accepted as tools for hedging and risk-management, as well as speculation to some extent. A more recent trend has been gaining ground, namely, arbitrage in derivatives.

Academia Biology, 2024

Aquaculture, or the activity of raising aquatic organisms from early development stages to a commercial size mainly as food source for humans, is an ancient activity. It is known that fish aquaculture was done in Egypt as far as 2500 BC. In China, a book on fish culture has been recorded dating back to 500 BC. Culture of shellfish such as oyster has been done for 2000 years in Japan and China, whereas its culture in Europe was recorded by 100 BC in Italy and Greece [1]. At present, aquaculture is an important production industry of animal, algae and microorganisms living in fresh-, brackish-, and sea- water.