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Task

Objective:
In this part of the assignment we sought to identify a mispriced option and develop an appropriate arbitrage strategy to lock in the profits.

Discussion:
Any mispricing that exists can essentially be decomposed into 2 basic components:

(1) Mispricing of the option relative to the asset at the time of purchase.
(2) Mispricing of the underlying asset.

If either of these two conditions is satisfied, an arbitrage may be possible. In the first instance, the mispricing profit may be either due a superior estimation of volatility or a superior option pricing formula to the one apparently used by the market. In the latter case, a superior analyst may identify an asset whose intrinsic value differs from that implied by the market price.

In this assignment, since arbitrage was to be achieved through a delta neutral hedge, mispricing of the underlying asset became irrelevant. Furthermore, the scope of our knowledge did not allow us to identify a superior option pricing model. Consequently, we attempted to identify mispriced options on the basis of their volatility, which is after all, the most significant input in ay option pricing model.

We took the stance that historical data, might provide a more accurate estimate of the underlying asset’s volatility than the value implied by the market price of the option. Although, implied volatility uses market information about future volatilities, these are no doubt based on past history as well as present assessment of the future based on recent history. In this sense, implied volatility might just be an alternative estimation of historical volatility. Therefore if we could derive a better estimate of this figure, mispriced options could be identified.







Method:
The method we employed is as follows. For a given stock, we obtained...