1.False.
When time to expiration gets extended the American put option will become more valuable.American put option becomes more valuable when the price of the underlying stock decreases.
2.True:
when the risk free interest rate decrease the American put option price will increase.When the interest rate decreases the price of the call option decreases where as the price of the put option increases.
3.False.
Higher the volatility of the underlying stock higher is the price of both put and call options.Here it is given that the volatility of underlying stock decreases thus the American put option price will decrease
4.False:
For a non dividend paying underlying stocks,American call options and European call options are the same because it's not optimal to exercise American call option before the maturity
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