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Markov Chain Monte Carlo Method for Estimating Implied Volatility in Option Pricing

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  • Yao Elikem Ayekple
  • Charles Kofi Tetteh
  • Prince Kwaku Fefemwole

Abstract

Using market covered European call option prices, the Independence Metropolis-Hastings Sampler algorithm for estimating Implied volatility in option pricing was proposed. This algorithm has an acceptance criteria which facilitate accurate approximation of this volatility from an independent path in the Black Scholes Model, from a set of finite data observation from the stock market. Assuming the underlying asset indeed follow the geometric brownian motion, inverted version of the Black Scholes model was used to approximate this Implied Volatility which was not directly seen in the real market: for which the BS model assumes the volatility to be a constant. Moreover, it is demonstrated that, the Implied Volatility from the options market tends to overstate or understate the actual expectation of the market. In addition, a 3-month market Covered European call option data, from 30 different stock companies was acquired from Optionistic.Com, which was used to estimate the Implied volatility. This accurately approximate the actual expectation of the market with low standard errors ranging between 0.0035 to 0.0275.

Suggested Citation

  • Yao Elikem Ayekple & Charles Kofi Tetteh & Prince Kwaku Fefemwole, 2018. "Markov Chain Monte Carlo Method for Estimating Implied Volatility in Option Pricing," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(6), pages 108-116, December.
    • Handle: RePEc:ibn:jmrjnl:v:10:y:2018:i:6:p:108
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    References listed on IDEAS

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    More about this item

    Keywords

    implied volatility; Markov Chain Monte Carlo; Independence Metropolis-Hastings(IMH) method; option pricing;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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