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.
Highlights
1.1 Introduction of ProblemThe revolution in exchanging and valuing financial securities started around the mid-1970s
Yu and Yang (2008) utilizes the Green Function technique in ideal control structure to expand on inverse problem (IP) in deciding the Implied Volatility when the normal option cost, that is, the estimation of the option cost comparing with an agreed price and all conceivable developments from the present date to a picked maturity time is known
This clearly shows that, the Independence Metropolis-Hastings Sampler algorithm accurately approximate better, the market expectation as compared to the Implied volatility. This is due to the fact, the algorithm updates the volatility of the stock price with time, thereby removing all the jumps that might occur in the real market
Summary
The revolution in exchanging and valuing financial securities started around the mid-1970s. Knowing that the volatility function takes into consideration a superior comprehension of the underlying stochastic process of option values. The volatility function is not straightforwardly perceptible from option values. On the off chance that volatility is a constant, (1) turns into the established Black-Scholes model. In the genuine market, volatility is evolving (Franks & Schwartz, 1991; Heynen, 1994). Volatility measure changes in the asset prices and in this research, volatility is standard deviation. The estimation of volatility has been an essential research theme of present day financial markets. To better gauge the volatility function of a genuine market, one takes volatility to be time dependent, that is, one considers σ(t) rather than the constant σ (Egger & Engl, 2005; Egger, Hein & Hoffman, 2006).
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