Question

1. The interest rate is 2% per annum with continuous compounding and a bank wants to create a $1,000 principal protected note using a five-year zero-coupon bond plus a five-year call option.

What is the maximum price of the call option that will make this product viable for the bank (answer in $ and round to the nearest cent)?

2. Call options with strike prices of $70 and $87 cost $16 and $12, respectively. An investor creates a bear spread by selling (writing) the call with a strike of $70 and buying the call with a strike of $87.

What is the investor's profit at expiration if the terminal spot price turns out to be $72?

3. Call options with strike prices of $70 and $87 cost $16 and $12, respectively.

An investor creates a bear spread by selling (writing) the call with a strike of $70 and buying the call with a strike of $87.

For what range of prices of the underlying asset does the investor make a positive profit?

Answer 1

Solution:-

Rate = 2% , N=5, Future/Par value = 1000

PV = FV * exp(-rate * n)

PV = 1000 * exp(-.02 * 5)

=1000 * .904837 = 904.837

In order to make this note viable the call must be priced for --

1000-904.837 = $95.162

2)Price of the call option with strike 70 = 16

Price of the call option with strike 87 = 12

Now we form a bear spread by selling call with strike 70 and buying 87 stike call.

If at expiry the terminal price is 72. We will have a profit of $2 .

Net Credit by selling 70 strike call =16

Net debit by buying the 87 strike call =12

Intrinsic value of 70 strike call at expiry = 72-70 =2

Intrinsic value of 87 strike call at expiry = 0 (since a OTM call)

Net Profit at expiry = 16 -12 - 2 = $2

For a bear spread with options at strike of 70 and 87 respectively we will make a profit of $2 if the underlying have a price of $72 at expiry.

3) Carrying over from part 2 , we see that the net credit of the strategy is 4 .

So our profit making price range is , when the underlying expires less than (Lower strike + net credit) i.e.

Our profit range is when the underlying expires anywhere between $70 to $73.99