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During his two-decade career in Asia and the US, Nathan has consulted in strategy, valuations, corporate finance and financial planning. Options, which come in the form of calls and puts, grant a right, but not an obligation to a buyer. Within the context of financial options, these are typically to purchase an underlying asset. Plain vanilla options can be worth something or nothing at expiry; they cannot be worth a negative value to a buyer since there are no net cash outflows after purchase.

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It also includes a basic Monte Carlo pricer, which is taken from this article. In this section we are going to apply the same technique, namely the discretisation of the partial derivatives, to create a simple approximation to the Greek sensitivities with which we can compare to the analytical solution. The essence of the method is that we will approximate the partial derivative representing the particular sensitivity of interest. To do this we make use of the analytical formulae for the Black-Scholes prices of the call and puts.

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We provide simple formulas for pricing both the European and American options. In response to these limitations, Duffie et alEraker et al and Eraker introduced discontinuous stochastic volatility models. However, this increases the number of the parameters to be estimated. Eberlein and Keller and Eberlein et al used inverse Gaussian distribution.

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Option pricing theory uses variables stock price, exercise price, volatility, interest rate, time to expiration to theoretically value an option. Essentially, it provides an estimation of an option's fair value which traders incorporate into their strategies to maximize profits. Some commonly used models to value options are Black-Scholesbinomial option pricingand Monte-Carlo simulation. Understanding Option Pricing Theory The primary goal of option pricing theory is to calculate the probability that an option will be exercised, or be in-the-money ITMat expiration.