Derivative markets mcdonald solutions pdf

The cheap call is the strike call; the expensive call is the strike call. Once again, we buy low and sell high. However, our payo is always non-negative. So we never lose money. Its important that the two calls are European options. If they are American, they can be exercised at dierent dates. Since we cant buy a partial option, well buy 3 units of the portfolio i.

Simultaneously,we sell three strike calls. The payo at expiration T : Transaction buy 3 portfolios buy one strike call buy two strike calls Portfolios total. If the stock pays dividend, then early exercise of an American call option may be optimal. Suppose the stock pays dividend at tD. Time T Pro and con for exercising the call early at tD.

If you exercise the call immediately before tD , youll receive dividend and earn interest during [tD ; T ]. Youll pay the strike price K at tD , losing interest you could have earned during [tD ; T ]. If the interest rate, however, is zero, you wont lose any interest. You throw away the remaining call option during [tD ; T ].

Had you waited, you would have the call option during [tD ; T ] If the accumulated value of the dividend exceeds the value of the remaining call option, then its optimal to exercise the stock at tD : As explained in my study guide, its never optimal to exercise an American put early if the interest rate is zero.

The only reason that early exercise might be optimal is that the underlying asset pays a dividend. If the underlying asset doesnt pay dividend, then its never optimal to exercise an American call early. Since Apple doesnt pay dividend, its never optimal to exercise early.

The only reason to exercise an American put early is to earn interest on the strike price. The strike price in this example is one share of AOL stock. Thus its never optimal to exercise the put. If the Apple stock price goes to zero and will always stay zero, then theres no benet for delaying exercising the put; theres no benet for exercising the deeperunderstandingfastercalc.

Exercising the put early and exercising the put at maturity have the same value. If, however, the Apple stock price goes to zero now but may go up in the future, then its never optimal to exercise the put early.

If you dont exercise early, you leave the door open that in the future the Apple stock price may exceed the AOL stock price, in which case you just let your put expire worthless. Theres no hurry to exercise the put early. If Apple is expected to pay dividend, then it might be optimal to exercise the American call early and exchange one AOL stock for one Apple stock.

However, as long as the AOL stock wont pay any dividend, its never optimal to exercise the American put early to exchange one Apple stock for one AOL stock. If the strike price grows over time, the longer-lived valuable as the shorter lived option.

The longer-lived call is cheaper than the shorter-lived call, leading to arbitrage opportunities. To arbitrage, we buy low Call 1 and sell high Call 2. ST2 becomes ST1 i. This is not an arbitrage. Sell a put, receiving P b 4. The payo is always zero. Sell a call, receiving C b 2. According to the put-call parity, the payo of the following position is always zero: 1. Buy the call 2. Sell the put 3. Short the stock 4. Lend the present value of the strike price plus dividend The existence of the bid-ask spread and the borrowing-lending rate dierence doesnt change the zero payo of the above position.

The above position always has a zero payo whether theres a bid-ask spread or a dierence between the borrowing rate and the lending rate. If there is no transaction cost such as a bid-ask spread, the initial gain of the above position is zero. However, if there is a bid-ask spread, then to avoid arbitrage, the initial gain of the above position should be zero or negative.

We are told to ignore the transaction cost. In addition, we are given that the current stock price is The dividend is on August 8, To nd the expiration date, you need to know this detail.

Expiration day for equity and index options is the Saturday immediately following the third Friday of the expiration month until February 15, On and after February 15, , the expiration date will be the third Friday of the expiration month. When is the last day to trade or exercise an equity option? The day expiring equity options last trade is the third Friday of the month. This is also generally the last day an investor may notify his brokerage rm of his intent to exercise an expiring equity call or put.

If this third Friday happens to be an exchange holiday, then the last day of trading for expiring equity options is the day before, or the third Thursday of the month. Check with your brokerage rm about its procedures and deadlines for instruction to exercise equity options.

The option is issued on May 6, Fortunately,we can use a calculator. ACT mode calculates the actual days between two dates. If you use the day mode, you are assuming that there are days between two dates.

When using the date worksheet, set DT1 i. Sell the call 2. Borrow the present value of the strike price plus dividend 3.

Buy the put 4. Buy one stock If there is transaction cost such as the bid-ask spread, then to avoid arbitrage, the initial gain of the above position is zero. However, if there is a bid-ask spread, the initial gain of the above position can be zero or negative. The net receipt should be non-positive, since the payo of the diversied portfolio of calls is always at least as good as the payo of two strike calls. Otherwise, arbitrage exists.

So the convexity condition is met. We sell a strike call and a strike call; simultaneously, we buy two strike calls. The net receipt should be non-negative, since the payo of the diversied portfolio of calls is always at least as good as the payo of two strike calls.

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