Arbitrageurs are always looking for mispriced securities in the market. Sometime

Question

Arbitrageurs are always looking for mispriced securities in the market. Sometimes the easiest way to find pricing discrepancies is to look for pairs of securities that are mispriced relative to each other. (When you identify two securities that are mispriced relative to each other, you don’t have to worry about what the actual price of each of the securities should be.). Your roommate tells you that he found two put options on the same non-dividend paying stock that may be mispriced. In particular, the one with the higher exercise price is selling at a lower price. Design a trading strategy that takes advantage of the mispricing. Using the payoff and profit tablesand graphs from class, show that your strategy is always profitable no matter what happens to thestock price. Also show that the strategy has zero cost and zero risk.

Explanation / Answer

In the above given case the strategy to opted for would be to go in for Mispricing across Strike Prices. Under the above method spread should be the factor to be considered.for taking advantage of relative mispricing of options on the same underlying stock.  A spread is a combination of two or more options of the same type (call or put) on the same underlying asset. Bullish vertical put spread should be considered for the above case ie above two options with the same maturity but different exercise prices should be combined .

For mispricing  across Strike Prices-a put with a lower strike price should never be sold for more than a put with a higher strike price and the same maturity. If it is sold, one could buy the higher strike price put, sell the lower strike price put and make an arbitrage profit.

The strategy has zero cost and zero risk as There is an initial cash inflow with this strategy.

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