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# Question of the Week - Derivatives

Des Moines, IA, USAPosts: 211 Sr Associate
edited December 2015
Which of the following is most likely to cause an increase in option price?

## Question of the Week - Derivatives 28 votes

Higher exercise price for an American put
64%
Higher exercise price for a European call
14%
Shorter time to maturity for an American call
21%

• Des Moines, IA, USAPosts: 211 Sr Associate
Higher exercise price for an American put

A put option is the right to sell a security for \$X, where X is the exercise price. It logically follows that the right is likely to become more valuable if X increases.

A call option is the right to purchase a security for \$X, where X is the exercise price. It logically follows that the right can't become more valuable if X increases.

American options (both calls and puts) are generally worth more (and never worth less) as time to maturity lengthens, because the lengthening simply expands the right of the option owner to exercise.

• Denver - COPosts: 15 Associate
Higher exercise price for an American put
I personally think this questions i poorly asked. But nevertheless my logic follows.

First off we can throw out answer C after reading the question. If an option has a shorter time to maturity, it inherently has less "time" premium to it. (you can also think of this as the greek theta towards expiration. IE theta increases the less time there is to exp. Less chance to finishing in the money.)

Now all else equal, stock price, strike ETC. Let's give an example.

Stock = \$10 The straddle of the 10 strike is worth \$1 and the C and P are worth the same value (not taking into account Div or Int in this example).  If we change the exercise price, or essentially our strike price to 11 holding the price of the stock, vol time to ex the same. What is reflective of the value of the Put and the call now at a higher ex price? Well Let's just say our put is now worth 1.10 (\$1 ITM and .10 time premium). And our call is worth .10. Therefore holding all else equal the Inc in strike price the value of the put is increased while the call is decreased.

Side note 1. If we say our Put is worth 1.10 how do we know the call is worth .10? Put-call parity. IE Value of a call = P + Stockprice - strike price - (divs - int) . IE x = 1.10 + 10 - 10 - 0. = .10

P = call + strike - stock + (divs - int)

Side note 2 The value of Am vs euro options. Am > Euro given the right to early ex for Int and Divs.