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# P1.T3.727. Option spread strategies (Hull Chapter 12)

#### Nicole Seaman

##### Director of FRM Operations
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Learning objectives: Explain the motivation to initiate a covered call or a protective put strategy. Describe the use and calculate the payoffs of various spread strategies.

Questions:

727.1. Assume the current price of a stock is $30.00 and imagine that we can only trade the following four options at two strike prices: • At a strike price of$28.00, we can employ either a call or a put, where c(K=28.00) = $3.98 and p(K=28.00) =$1.46
• At a strike price of $32.00, we can employ either a call or a put, where c(K=32.00) =$2.05 and p(K=32.00) = $3.46 Each of these prices is approximately accurate for a six-month option when the volatility is 31.2% (but these details are not necessary to answering the question). If we want to implement a bull spread, how could we do that? a. We cannot create a bull spread with these options b. Long the call with strike of 32.00 plus Short the put with strike of 28.00 c. Long the call with strike of 28.00 plus Short the call with strike of 32.00; or Long the put with strike of 28.00 plus Short the put with strike of 32.00 d. Long the call with strike of 32.00 plus Short the call with strike of 28.00; or Short the put with strike of 28.00 plus Long the put with strike of 32.00 727.2. Her erstwhile favorite stock is currently trading at$52.00, but Olivia is now bearish on the stock's prospects. She wants to buys a European put option on the stock with a strike at $52.00 at a cost of$4.07. However, she worries the initial cash outlay on this trade is too high, so she wants to fund this view by ADDITIONALLY writing an option; in this way, her intention is to implement a bear spread. Further, while the long put by itself returns a break-even profit if the stock drops (at the time of option's expiration of course) to $47.93 because$52.00 - $4.07 =$47.93, she wants the bear spread strategy to achieve break-even if the stock drops (at the option's expiration) to $50.00. Assuming that each of the following option prices is correct (indeed these options are correctly priced under an assumption of 40.0% volatility, one year time to expiration and riskfree rate of 1.0%), which additional trade will complete Olivia's intention for a bear spread? a. Write a call with a strike price of$47.50 and a premium of $6.69 b. Write a put with a strike price of$47.50 and a premium of $2.07 c. Write a put with a strike price of$49.00 and a premium of $2.65 d. Write a put with a strike price of$57.50 and a premium of \$7.54

He wants to implement a trade strategy that BOTH generates an initial cash inflow (as opposed to an initial cost) AND will produce a profit if the stock drops significantly. Among the eight strategies listed above, which will achieve this goal?

a. Only the bear spread with calls
c. Both bear spread, the butterfly spread with puts, and the calendar spreed with puts
d. None of the trades both generate an initial inflow and produce a profit if the stock drops significantly

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