How Does Implied Volatility Impact Options Pricing?

Dynamics of option prices

Anindya Goswami 1 Introduction The main motive of this project is modelling of stock prices in view of option pricing.

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We begin by answering questions such as, what are options, why do they exist and the problem of pricing them. Next, we answer how modelling future stock prices is fundamental to solving this problem.

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We look at continuous time models like Black-Sholes-Merton Model and discrete time models like Binomial Lattice Model for option pricing. While doing this we also try to understand the behaviour of volatility and capture it in our models.

Along the way, we learn computational techniques for simulating Brownian Motion, Markov Chains and statistical dynamics of option prices for justifying the results. These details are mentioned in the option contract.

Options Dynamics

The underlying asset can be a company stock, currency, commodity such as gold or an index. A simple example is a contract that binds two parties to a sale of crude oil, six months from now.

Another example is of a farmer buying a put option to ensure that he sells his produce three months from now. In fact, we have bought options ourselves!

A warranty gives buyer the right, but not the obligation, to exploit it under certain circumstances. Therefore, anyone who buys or is given a guarantee thus holds a kind of option.

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The same is true of an insurance contract. American Options allow exercising the agreement on or before the maturity date while in European Options, agreement can only be exercised on maturity.

Various contract expiry that are traded in the market currently are listed here.

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