20. In the absence of dividends, the holder of a European call always benefits from an increase in maturity since the insurance value and time value of the call both increase. However, for the holder of a European put in this case, insurance value increases but time value decreases, so the put value could increase or decrease. In general, for a given level of volatility, if interest rates are "high," the time-value effect will outweigh the insurance-value effect, so European put values will decrease as maturity increases; but if interest rates are "low," the insurance-value effect will dominate, so the put value will increase. This question illustrates these arguments.
Consider a binomial model with parameters S = 100, u = 1.10, and d = 0.90, and a European put with a strike of K = 100.
(a) First, consider a "high" interest rate environment where R = 1.02 (1 plus the interest rate). We can see that with these parameter values, a one-period put is worth 3.92, but a two-period European put is worth only 3.38. The increase in maturity hurts the put holder because the insurance-value effect is outweighed by the time-value effect.
(b) Now consider a "low" interest-rate environment where R = 1.00. Show that in this case, the one-period put is worth less than the two-period put.
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