Assignment 4: Option Arbitrage

Suppose you see the following prices in a market:

AMZN stock is currently trading for $1,913.76

A 1-year bond with a face value of $1,000 has a price of $970.87

A call option on AMZN stock with a maturity of 1 year and a strike of $1,900 has a premium of $286.34

A put option on AMZN stock with a maturity of 1 year and a strike of $1,850 has a premium of $265.45

There is an arbitrage opportunity in this market. Give me a list of trades that would generate both profit today and a guaranteed non-negative cash flow in the future.

Hints:

1. You cant directly use put-call parity here because the strikes arent the same. You should still calculate what the price of a $1,900 strike put and/or a $1,850 strike call.
2. Remember what the relationship should be between the strike of each kind of option and its price.
3. Any arbitrage opportunity follows the same pattern: Identify two portfolios, one of which should weakly dominate (i.e. its either the same or better in all instances). If the better/equal portfolio is cheaper, you can buy it and short the other portfolio.
4. Remember that shorting a portfolio means taking the opposite position of every asset in the portfolio. For example, if you want to short a portfolio that normally consists of a long call and a short put, you would do so by taking a short call and a long put.