# Math Help - Call option and Put option

1. ## Call option and Put option

I have so much difficulties understanding call and put options concept properly.

Let C be the price of a call option to purchase a stock whose present price is S. Suppose that interest is compounded continuously at nominal rate r. Show that if

C>S, then buying one stock and selling one call gives an arbitrage opportunity. What relationship do you conclude must exist between S and C if there is to be no arbitrage opportunity?

Solution: Suppose C>S. Buying a stock and selling a call will give you C-S>0. ( I know call option is the right(but not the obligation to purchase stock at expiration time t for strike price K but what do they mean by selling a call? what do you really sell? how does it change if you sell 10 calls or buy a 5 puts etc?). Put C-S>0 in the bank at time t you will have $(C-S)e^{rt}$ in the bank and a stock.

Thanks for any help.

2. Originally Posted by charikaar
I have so much difficulties understanding call and put options concept properly.

Let C be the price of a call option to purchase a stock whose present price is S. Suppose that interest is compounded continuously at nominal rate r. Show that if

C>S, then buying one stock and selling one call gives an arbitrage opportunity. What relationship do you conclude must exist between S and C if there is to be no arbitrage opportunity?

Solution: Suppose C>S. Buying a stock and selling a call will give you C-S>0. ( I know call option is the right(but not the obligation to purchase stock at expiration time t for strike price K but what do they mean by selling a call? what do you really sell? how does it change if you sell 10 calls or buy a 5 puts etc?). Put C-S>0 in the bank at time t you will have $(C-S)e^{rt}$ in the bank and a stock.

Thanks for any help.

By selling a call in this case they mean selling in the sense of shorting the stock (it is better for the seller of the call if the price of the stock is below the strike price). You know what buying a call is, think about who is on the other side of the transaction/contract. So, if you sell a call with a strike price of $50 and the price of the stock goes up to$60, you would be obligated to sell the stock at $50. If you are the buyer of the call with the strike price of$50 and the stock goes up to $60, then you have the right to buy the stock for$50, thus making \$10 (not factoring in price of call).

Buying call - right to buy the stock - you hope stock price is higher than strike price
selling call- obligation to sell the stock if counter party wants it- you hope the stock price is lower than strike price

buying put- right to sell the stock- you hope stock price is lower than the strike price
selling put- obligation to buy the stock if couterparty wants it- you hope the stock price is higher than the strike price

when you think buying, think long the option
when you think selling, thing short the option
The rest of the question is a put call parity question as far as I can tell. To be honest, I dont understand what exactly you are asking.

Ivan