Spreads created with calls have an initial upfront

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spreads created with calls have an initial upfront payment and lead to a payoff that is either positive or zero. Bull spreads created with puts result in a positive up-front cash inflow to the investor and the payoff is either negative or zero. An aggressive bear spread can be executed by buying a European put option with a certain strike price and selling a European option with a lower strike price. An aggressive bull spread can also be executed by buying a European call option with a high strike price and selling a European call option with a lower strike price. Bear spreads created with puts have an initial upfront payment and lead to a payoff that is either positive or zero. Bull spreads created with calls result in a positive up-front cash inflow to the investor and the payoff is either negative or zero. Why is an American put option more likely to be exercised the deeper in the money it goes holding all else constant? Why does a decrease in volatility make the early exercise of an American put more likely holding all else constant? The exercise of an American put is a trade of between the insurance value of the put and the opportunity cost of money invested. If the put option is sufficiently deep in the money, the difference between the strike price and the stock price can be invested and interest can be earned. When the put is sufficiently deep in the money, the return from investing the funds at the risk free rate can be greater than the additional gains from holding the put. When volatility decreases, the insurance element from holding the put becomes less valuable. This means that it is less likely that the put will go even deeper in the money. 9
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In the extreme, if volatility approaches zero, it is always optimal to exercise immediately if the option is in the money as the price will not change. 10
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  • Fall '16
  • Strike price

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