Option Pricing

In: Business and Management

Submitted By hussein99
Words 797
Pages 4
Overview and Major Findings:
This paper examines the problem of pricing a European call on an asset (Stock) that has a stochastic or variable volatility. Addressing this problem was done by investigating two cases: the first case is to determine the option price when the stochastic volatility is independent of stock price. The second case is to determine the option price when the stochastic volatility is correlated with the stock price.
This paper provides a solution in series form for the stochastic volatility option, in addition to a discussion about the numerical methods that are used to examine pricing biases, and an investigation about the occurrence of the biases in the case of stochastic volatility.
As for the results obtained, this paper presents interesting results for each of the two cases.
When the stochastic volatility is independent of stock price, the results show that the price calculated using Black-Scholes equation is overestimated for at-the-money options and underestimated for deep in-and out-of-the-money options. This overpricing takes place for stock prices within about ten percent of the exercise price. Moreover, it is shown that the degree of the pricing bias can be up to five percent of the Black-Scholes price.
For the second case when the stock price is positively correlated with the volatility, the results show that the Black-Scholes formula overprices in-the-money options and underprices out-of-the-money options. On the other hand, when the stock price is negatively correlated with the volatility, the Black-Scholes formula overprices out-of-the-money options and underprices in-the-money options.
Although these results are obtained for European call option, they can be directly used for European put options by applying the put-call parity equation. Furthermore, these results can be also applied for American call options on…...

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