in the designated hull chapter, we have the following explanation :
it can be optimal to execute an early
exercise on an American put. In general, we can say that for an American put, the early exercise
becomes more attractive as:
Stock price (S0) increases,
Risk-free (r) rate increases, and/or
Volatility decreases.
however in PQ related to this chapter, question 182.2 the answer is a bit different from the above when it comes to Stock prices.
182.2. C. I., II., and III. Unlike the American call on a non-dividend-paying stock, which is never optimal, the American put is often optimal to early exercise. Hull: “In general, the early exercise of a put option becomes more attractive as So decreases, as r increases, and as the volatility decreases.” As (r) increases, this increases the “interest element:” th interest earned on the strike price collected (a difference from the call option!). As volatility decreases, this decreases the “insurance element” making early exercise more attractive.
1) which one is right? As S0 increases or decreases?
2) if my reasoning is right, those 3 factors (assuming S0 increases is right) will decrease the value of the put options, is this why we should exercise the put ?
it can be optimal to execute an early
exercise on an American put. In general, we can say that for an American put, the early exercise
becomes more attractive as:
Stock price (S0) increases,
Risk-free (r) rate increases, and/or
Volatility decreases.
however in PQ related to this chapter, question 182.2 the answer is a bit different from the above when it comes to Stock prices.
182.2. C. I., II., and III. Unlike the American call on a non-dividend-paying stock, which is never optimal, the American put is often optimal to early exercise. Hull: “In general, the early exercise of a put option becomes more attractive as So decreases, as r increases, and as the volatility decreases.” As (r) increases, this increases the “interest element:” th interest earned on the strike price collected (a difference from the call option!). As volatility decreases, this decreases the “insurance element” making early exercise more attractive.
1) which one is right? As S0 increases or decreases?
2) if my reasoning is right, those 3 factors (assuming S0 increases is right) will decrease the value of the put options, is this why we should exercise the put ?
