Consider a European call option with strike of $100 and maturity of one year. The current 1-year forward price is $120. The call option is quoted at $18. The dollar interest rate is fixed at 5%.1. Is there an arbitrage opportunity? If there is, how do you do the arbitrage trading to profit from it?2. If the call is quoted at $121, is there an arbitrage opportunity? If there is, how do you do the arbitrage trading to profit from it?Would please recommend some books about this kind of questions ? I would like to do more exercises about them .Any help is appreciated. thanks

Hull will help with understanding them and it does have a few similar questions to work through.

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@ gold digga: dont get why you assume the stock price to be at 100$1.call costs less then its minimum value - this implies an arbitrage opportunity!+call (18$)- forward (120$)=102$invest 102$ for 1yu will have more then 100$ (the strike price of the call option) in 1y and no risk!2.- call (121)+forward (120)forward = call with strike price 0u have at least 1$ and no risk!

QuoteOriginally posted by: JackBryanConsider a European call option with strike of $100 and maturity of one year. The current 1-year forward price is $120. The call option is quoted at $18. The dollar interest rate is fixed at 5%.1. Is there an arbitrage opportunity? If there is, how do you do the arbitrage trading to profit from it?2. If the call is quoted at $121, is there an arbitrage opportunity? If there is, how do you do the arbitrage trading to profit from it?Would please recommend some books about this kind of questions ? I would like to do more exercises about them .Any help is appreciated. thanksYou can use the Fundamental Theorem of Asset Pricing to answer this. The one period model is x in R^m - prices of m instruments at the beginning of the period, X : Omega -> R^m - prices of m instruments at the end of the period given omega in Omega occured. There is arbitrage if there is xi in R^m with xi . x < 0 and xi . X(omega) >= 0 for all omega in Omega. The period means dot (inner) product. This means you make a positive amount putting on the trade and never lose when you liquidate at the end of the period.The FTAP says there is no arbritrage if and only if x belongs to the smallest closed cone containing the range of X.Here the model is x = (1, 120, 18) [or x = (1, 120, 21)], Omega = [0, infinity), and X(omega) = (1.05, omega, max{omega - 100, }).You can find a short write up and similar examples at http://kalx.net/dsS2011/opm.pdf This also shows you how to find the arbitrage if it exists.