Question

The price of a call option with a strike of $100 is $10. The price of a put option with a strike of $100 is $5. Interest rates are 0 and the current price of the underlying is $100. Can you make an arbitrage profit? If so how? Describe the trade and your pay offs in detail?

Answer 1

As per put call parity = Current market price + Put option value = P.v. of EP and call option value      
      
100 +5 should be equal to 100/(1+0%)+10      
105 is not Equal to 110      
So there exists arbirtage opportunity.      
side having Put option and Current Market price is less. So Stock and put option will be long and Call option will be short       
      
Long put   -5  
Long stock   -100  
short call   10  
      
      
Net position   -95  
      
At Expiration, if stock price = $110      
Value of Put is   0  
Value of stock is   110  
Payoff to call option holder   -10  
      
Net position   100  
      
At Expiration, if stock price = $90      
Value of Put    10  
Value of stock is   90  
Payoff to call option holder   0  
      
Net position   100  
      
      
So in every situation gain = 100-95= $5      
Arbitrage profit of $5 can be earned