Question

Show that a bull spread can be created from a combination of positions in put options and a bond.

Answer 1

Creation of the Bull Put Spread:

A bull put spread consists of two put options.

First, an investor buys a put option and pays a premium. Next, the investor sells a second put option at a strike price higher than the one they purchased, receiving a premium. Both options have the same expiration date.

The premium recieved from selling the higher-strike put exceeds the price paid for the lower-strike put. At the onset of the trade, the investor receives the net difference of the premiums from the two put options. Investors who are bullish on an underlying stock could use a bull put spread to generate income with limited downside. However, there is a risk of loss with this strategy.

Bull Put Profit and Loss

The maximum profit for a bull put spread is equal to the difference between the amount received from the sold put and the amount paid for the purchased put. In other words, the net credit received initially is the maximum profit, which only happens if the stock's price closes above the higher strike price at expiry.

The goal of the bull put spread strategy is realized when the price of the underlying moves or stays above the higher strike price. The result is the sold option expires worthless. The reason it expires worthless is that no one would want to exercise it and sell their shares at the strike price if it's lower than the market price.

A drawback to the strategy is that it limits the profit earned if the stock rises well above the upper strike price of the sold put option. The investor would pocket the initial credit but miss out on any future gains.

If the stock is below the upper strike in the strategy, the investor will begin to lose money since the put option will likely be exercised. Someone in the market would want to sell their shares at this, more attractive, strike price.

However, the investor received a net credit for the strategy at the outset. This credit provides some cushion for the losses. Once the stock declines far enough to wipe out the credit received, the investor begins losing money on the trade.

If the stock price falls below the lower strike put option—the purchased put—both put options would have lost money, and maximum loss for the strategy is realized. The maximum loss is equal to the difference between the strike prices and the net credit received.