Question

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.

Answer 1

As there is an arbitrage opportunity, steps to encash the same

Steps

1. Sell the $1850 put option at a premium of $265.45 and buy the $1900 call option for $286.34 . Simultaneously short a stock by borrowing for $1913.76. Buy 1.9 Bonds (suppose it is allowed) for $970.87*1.9= $1844.653 and you are left with a cashflow of $1913.76+$265.45-$286.34-$1844.653 = $48.22

2.After one year,

If Price of Stock< 1850 , Put option will be exercised and call option will be worthless

So, purchase the stock for $1850 from the exercised put option and return the stock from the cash received from bonds which will mature to 1.9*1000 = $1900 , so there is an arbitrage profit of $50

If 1850<Price of Stock< 1900, both options will be worthless

So, purchase the stock from the market and return the stock at price P from the cash received from bonds which will mature to 1.9 *1000 = $1900 , so there is an arbitrage profit of 1900-P

The profit will be positive as 1850<P< 1900

If Price of Stock> 1900 , Put option will be worthless and call option will be exerised

So, purchase the stock for $1900 using the call option and return the same from the cash received from bonds which will mature to 1.90 *1000 = $1900 , so there is no profit nor loss

So under the above strategy, it leaves a cash of $48.22 today with us as well as gives non-negative cashflows in all possible future scenarios

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