3) The data below summarizes data for call and put options on a stock trading at

Question

3) The data below summarizes data for call and put options on a stock trading at a current price of $425.06 The options all have 1 month to expiry and the risk-free rate is 1% as an annual rate. Calls Puts IV Delta Bid Ask Strike Bid Ask Delta IV 24.020.62619.9020.15 415 9.70 9.85-0.373 23.7 23.860.572 17.0017.20 42011.7511.90-0.427 23.5 23.750.518 14.40 14.5542515.00 15.25-0.48323.39 23.670.46312.0512.25 43016.7516.95-0.538 23.28 23.610.40910.00 10.20 43519.7019.90-0.593 23.21 23.530.357 4.00 4.20 44022.80 23.40-0.64523.29 Identify any options which are mispriced and in each case state clearly what the nature of the mispricing is, and demonstrate how an investor would set up arbitrage to take advantage of the mispricing.

Explanation / Answer

From the figures above, 440 call option is mispriced. Since 435 strike price call option is available for $10, and 440 call option is available only for $4, it is under priced. difference between the option premium is greater than the difference between the strike prices which means there is a arbitrage opportunity.

Since we know 440 call is underpriced, we buy 440 call and simultaneously sell 435 call.

Net cash inflow will be $10 (from selling 435 call) - $4 (from buying 440 call) = $6

Now where ever the stock price is at the end of the month, sure gain is of $1. If stock price closes less than 435, we profit $6 as both option will be worthless.

If the stock expires at 440, we will have to give $5 for 435 call option which we sold. Hence net profit is $1. If it expires at say 438, we only give $3 and net profit is $3

For stock expiring above 440, lets say (442) we will ive $7 but will receive $2 so net outflow (above stock expiring 440) will always be $5 and net profit will be $1.

So 440 call price is available cheap and hence mispriced.

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