Question

An investor bought a 40-strike European put option on an index with 2 year to expiration. The premium for this option was 3.

The investor also wrote an 50-strike European put option on the same index with 2 year to expiration. The premium for this option was 7.

The continuously compounded risk-free interest rate is 8%.

Calculate the index price at expiration that will allow the investor to break even.

Answer 1

The investor bought a put option and write another

The net premium receive = 7-3 = 4

Now,

For if the price is less than 40 suppose its 35

Then both options will exercise and therefore he will buy at 50 and sell at 40

Net loss = 50 - 40 + 4 = 6

If it is more than 50

then both options will expire with getting exercised

Thus

Net profit = net premium received = 4

Now if the price is 45

The higher price option will be exercised

Net loss = 50 - 45 + 4 = 1

At 46

Net loss = 50 -46 +4 = 0

The break-even price is 46.

Hence, at expiration the index must have price = 46