Question

A stock price is currently $40. Over each of the next two three-month periods it is expected to go up by 10% or down by 10% (meaning, precisely, if the stock price at the start of a period is $40, it will go to $40*1.1=$44 or to $40*0.9=$36 at the end of the period and if the stock price at the start of a period is $44, it will go to $44*1.1=$48.44 or to $44*0.9=$39.6 at the end of the period). The risk-free interest rate is 12% per annum with continuous compounding.

a. What is the value of a six-month European put option with a strike price of $42?

b. What is the value of a six-month American put option with a strike price of $42?

c. What is the value of a six-month American put option with a strike price of $45? What do you conclude about whether or not it is optimal to exercise this American option immediately (Hint: What would be the value of this American option if it were to be exercised immediately)

Answer 1

PART-A

Six-Month Euro Put option with a strike price of $42

The price of the option is $2.118

The Formula used are:

PART-B

Six-Month American Put option with a strike price of $42

The price of the option is $2.537

The Formula used are:

PART-C

Six-Month American Put option with a strike price of $45

The price of the option is $5.0

The Formula used are:

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